Bayesian linearized amplitude-versus-frequency inversion for quality factor and its application

NASA Astrophysics Data System (ADS)

Yang, Xinchao; Teng, Long; Li, Jingnan; Cheng, Jiubing

2018-06-01

We propose a straightforward attenuation inversion method by utilizing the amplitude-versus-frequency (AVF) characteristics of seismic data. A new linearized approximation equation of the angle and frequency dependent reflectivity in viscoelastic media is derived. We then use the presented equation to implement the Bayesian linear AVF inversion. The inversion result includes not only P-wave and S-wave velocities, and densities, but also P-wave and S-wave quality factors. Synthetic tests show that the AVF inversion surpasses the AVA inversion for quality factor estimation. However, a higher signal noise ratio (SNR) of data is necessary for the AVF inversion. To show its feasibility, we apply both the new Bayesian AVF inversion and conventional AVA inversion to a tight gas reservoir data in Sichuan Basin in China. Considering the SNR of the field data, a combination of AVF inversion for attenuation parameters and AVA inversion for elastic parameters is recommended. The result reveals that attenuation estimations could serve as a useful complement in combination with the AVA inversion results for the detection of tight gas reservoirs.

Top-down estimates of methane and nitrogen oxide emissions from shale gas production regions using aircraft measurements and a mesoscale Bayesian inversion system together with a flux ratio inversion technique

NASA Astrophysics Data System (ADS)

Cui, Y.; Brioude, J. F.; Angevine, W. M.; McKeen, S. A.; Henze, D. K.; Bousserez, N.; Liu, Z.; McDonald, B.; Peischl, J.; Ryerson, T. B.; Frost, G. J.; Trainer, M.

2016-12-01

Production of unconventional natural gas grew rapidly during the past ten years in the US which led to an increase in emissions of methane (CH4) and, depending on the shale region, nitrogen oxides (NOx). In terms of radiative forcing, CH4 is the second most important greenhouse gas after CO2. NOx is a precursor of ozone (O3) in the troposphere and nitrate particles, both of which are regulated by the US Clean Air Act. Emission estimates of CH4 and NOx from the shale regions are still highly uncertain. We present top-down estimates of CH4 and NOx surface fluxes from the Haynesville and Fayetteville shale production regions using aircraft data collected during the Southeast Nexus of Climate Change and Air Quality (SENEX) field campaign (June-July, 2013) and the Shale Oil and Natural Gas Nexus (SONGNEX) field campaign (March-May, 2015) within a mesoscale inversion framework. The inversion method is based on a mesoscale Bayesian inversion system using multiple transport models. EPA's 2011 National CH4 and NOx Emission Inventories are used as prior information to optimize CH4 and NOx emissions. Furthermore, the posterior CH4 emission estimates are used to constrain NOx emission estimates using a flux ratio inversion technique. Sensitivity of the posterior estimates to the use of off-diagonal terms in the error covariance matrices, the transport models, and prior estimates is discussed. Compared to the ground-based in-situ observations, the optimized CH4 and NOx inventories improve ground level CH4 and O3 concentrations calculated by the Weather Research and Forecasting mesoscale model coupled with chemistry (WRF-Chem).

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

NASA Astrophysics Data System (ADS)

Cui, Tiangang; Marzouk, Youssef; Willcox, Karen

2016-06-01

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

Covariance specification and estimation to improve top-down Green House Gas emission estimates

NASA Astrophysics Data System (ADS)

Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Whetstone, J. R.

2015-12-01

The National Institute of Standards and Technology (NIST) operates the North-East Corridor (NEC) project and the Indianapolis Flux Experiment (INFLUX) in order to develop measurement methods to quantify sources of Greenhouse Gas (GHG) emissions as well as their uncertainties in urban domains using a top down inversion method. Top down inversion updates prior knowledge using observations in a Bayesian way. One primary consideration in a Bayesian inversion framework is the covariance structure of (1) the emission prior residuals and (2) the observation residuals (i.e. the difference between observations and model predicted observations). These covariance matrices are respectively referred to as the prior covariance matrix and the model-data mismatch covariance matrix. It is known that the choice of these covariances can have large effect on estimates. The main objective of this work is to determine the impact of different covariance models on inversion estimates and their associated uncertainties in urban domains. We use a pseudo-data Bayesian inversion framework using footprints (i.e. sensitivities of tower measurements of GHGs to surface emissions) and emission priors (based on Hestia project to quantify fossil-fuel emissions) to estimate posterior emissions using different covariance schemes. The posterior emission estimates and uncertainties are compared to the hypothetical truth. We find that, if we correctly specify spatial variability and spatio-temporal variability in prior and model-data mismatch covariances respectively, then we can compute more accurate posterior estimates. We discuss few covariance models to introduce space-time interacting mismatches along with estimation of the involved parameters. We then compare several candidate prior spatial covariance models from the Matern covariance class and estimate their parameters with specified mismatches. We find that best-fitted prior covariances are not always best in recovering the truth. To achieve accuracy, we perform a sensitivity study to further tune covariance parameters. Finally, we introduce a shrinkage based sample covariance estimation technique for both prior and mismatch covariances. This technique allows us to achieve similar accuracy nonparametrically in a more efficient and automated way.

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

NASA Astrophysics Data System (ADS)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

Bayesian coronal seismology

NASA Astrophysics Data System (ADS)

Arregui, Iñigo

2018-01-01

In contrast to the situation in a laboratory, the study of the solar atmosphere has to be pursued without direct access to the physical conditions of interest. Information is therefore incomplete and uncertain and inference methods need to be employed to diagnose the physical conditions and processes. One of such methods, solar atmospheric seismology, makes use of observed and theoretically predicted properties of waves to infer plasma and magnetic field properties. A recent development in solar atmospheric seismology consists in the use of inversion and model comparison methods based on Bayesian analysis. In this paper, the philosophy and methodology of Bayesian analysis are first explained. Then, we provide an account of what has been achieved so far from the application of these techniques to solar atmospheric seismology and a prospect of possible future extensions.

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Quantifying Uncertainty in Near Surface Electromagnetic Imaging Using Bayesian Methods

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Ray, A.; Key, K.

2017-12-01

Geoscientists commonly use electromagnetic methods to image the Earth's near surface. Field measurements of EM fields are made (often with the aid an artificial EM source) and then used to infer near surface electrical conductivity via a process known as inversion. In geophysics, the standard inversion tool kit is robust and can provide an estimate of the Earth's near surface conductivity that is both geologically reasonable and compatible with the measured field data. However, standard inverse methods struggle to provide a sense of the uncertainty in the estimate they provide. This is because the task of finding an Earth model that explains the data to within measurement error is non-unique - that is, there are many, many such models; but the standard methods provide only one "answer." An alternative method, known as Bayesian inversion, seeks to explore the full range of Earth model parameters that can adequately explain the measured data, rather than attempting to find a single, "ideal" model. Bayesian inverse methods can therefore provide a quantitative assessment of the uncertainty inherent in trying to infer near surface conductivity from noisy, measured field data. This study applies a Bayesian inverse method (called trans-dimensional Markov chain Monte Carlo) to transient airborne EM data previously collected over Taylor Valley - one of the McMurdo Dry Valleys in Antarctica. Our results confirm the reasonableness of previous estimates (made using standard methods) of near surface conductivity beneath Taylor Valley. In addition, we demonstrate quantitatively the uncertainty associated with those estimates. We demonstrate that Bayesian inverse methods can provide quantitative uncertainty to estimates of near surface conductivity.

A compressive sensing-based computational method for the inversion of wide-band ground penetrating radar data

NASA Astrophysics Data System (ADS)

Gelmini, A.; Gottardi, G.; Moriyama, T.

2017-10-01

This work presents an innovative computational approach for the inversion of wideband ground penetrating radar (GPR) data. The retrieval of the dielectric characteristics of sparse scatterers buried in a lossy soil is performed by combining a multi-task Bayesian compressive sensing (MT-BCS) solver and a frequency hopping (FH) strategy. The developed methodology is able to benefit from the regularization capabilities of the MT-BCS as well as to exploit the multi-chromatic informative content of GPR measurements. A set of numerical results is reported in order to assess the effectiveness of the proposed GPR inverse scattering technique, as well as to compare it to a simpler single-task implementation.

Approaches in highly parameterized inversion: bgaPEST, a Bayesian geostatistical approach implementation with PEST: documentation and instructions

USGS Publications Warehouse

Fienen, Michael N.; D'Oria, Marco; Doherty, John E.; Hunt, Randall J.

2013-01-01

The application bgaPEST is a highly parameterized inversion software package implementing the Bayesian Geostatistical Approach in a framework compatible with the parameter estimation suite PEST. Highly parameterized inversion refers to cases in which parameters are distributed in space or time and are correlated with one another. The Bayesian aspect of bgaPEST is related to Bayesian probability theory in which prior information about parameters is formally revised on the basis of the calibration dataset used for the inversion. Conceptually, this approach formalizes the conditionality of estimated parameters on the specific data and model available. The geostatistical component of the method refers to the way in which prior information about the parameters is used. A geostatistical autocorrelation function is used to enforce structure on the parameters to avoid overfitting and unrealistic results. Bayesian Geostatistical Approach is designed to provide the smoothest solution that is consistent with the data. Optionally, users can specify a level of fit or estimate a balance between fit and model complexity informed by the data. Groundwater and surface-water applications are used as examples in this text, but the possible uses of bgaPEST extend to any distributed parameter applications.

The Collaborative Seismic Earth Model: Generation 1

NASA Astrophysics Data System (ADS)

Fichtner, Andreas; van Herwaarden, Dirk-Philip; Afanasiev, Michael; SimutÄ--, SaulÄ--; Krischer, Lion; ćubuk-Sabuncu, Yeşim; Taymaz, Tuncay; Colli, Lorenzo; Saygin, Erdinc; Villaseñor, Antonio; Trampert, Jeannot; Cupillard, Paul; Bunge, Hans-Peter; Igel, Heiner

2018-05-01

We present a general concept for evolutionary, collaborative, multiscale inversion of geophysical data, specifically applied to the construction of a first-generation Collaborative Seismic Earth Model. This is intended to address the limited resources of individual researchers and the often limited use of previously accumulated knowledge. Model evolution rests on a Bayesian updating scheme, simplified into a deterministic method that honors today's computational restrictions. The scheme is able to harness distributed human and computing power. It furthermore handles conflicting updates, as well as variable parameterizations of different model refinements or different inversion techniques. The first-generation Collaborative Seismic Earth Model comprises 12 refinements from full seismic waveform inversion, ranging from regional crustal- to continental-scale models. A global full-waveform inversion ensures that regional refinements translate into whole-Earth structure.

3-D linear inversion of gravity data: method and application to Basse-Terre volcanic island, Guadeloupe, Lesser Antilles

NASA Astrophysics Data System (ADS)

Barnoud, Anne; Coutant, Olivier; Bouligand, Claire; Gunawan, Hendra; Deroussi, Sébastien

2016-04-01

We use a Bayesian formalism combined with a grid node discretization for the linear inversion of gravimetric data in terms of 3-D density distribution. The forward modelling and the inversion method are derived from seismological inversion techniques in order to facilitate joint inversion or interpretation of density and seismic velocity models. The Bayesian formulation introduces covariance matrices on model parameters to regularize the ill-posed problem and reduce the non-uniqueness of the solution. This formalism favours smooth solutions and allows us to specify a spatial correlation length and to perform inversions at multiple scales. We also extract resolution parameters from the resolution matrix to discuss how well our density models are resolved. This method is applied to the inversion of data from the volcanic island of Basse-Terre in Guadeloupe, Lesser Antilles. A series of synthetic tests are performed to investigate advantages and limitations of the methodology in this context. This study results in the first 3-D density models of the island of Basse-Terre for which we identify: (i) a southward decrease of densities parallel to the migration of volcanic activity within the island, (ii) three dense anomalies beneath Petite Plaine Valley, Beaugendre Valley and the Grande-Découverte-Carmichaël-Soufrière Complex that may reflect the trace of former major volcanic feeding systems, (iii) shallow low-density anomalies in the southern part of Basse-Terre, especially around La Soufrière active volcano, Piton de Bouillante edifice and along the western coast, reflecting the presence of hydrothermal systems and fractured and altered rocks.

Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.

Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models

NASA Astrophysics Data System (ADS)

Yang, Linxiao; Fang, Jun; Duan, Huiping; Li, Hongbin; Zeng, Bing

2018-06-01

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.

Atmospheric Tracer Inverse Modeling Using Markov Chain Monte Carlo (MCMC)

NASA Astrophysics Data System (ADS)

Kasibhatla, P.

2004-12-01

In recent years, there has been an increasing emphasis on the use of Bayesian statistical estimation techniques to characterize the temporal and spatial variability of atmospheric trace gas sources and sinks. The applications have been varied in terms of the particular species of interest, as well as in terms of the spatial and temporal resolution of the estimated fluxes. However, one common characteristic has been the use of relatively simple statistical models for describing the measurement and chemical transport model error statistics and prior source statistics. For example, multivariate normal probability distribution functions (pdfs) are commonly used to model these quantities and inverse source estimates are derived for fixed values of pdf paramaters. While the advantage of this approach is that closed form analytical solutions for the a posteriori pdfs of interest are available, it is worth exploring Bayesian analysis approaches which allow for a more general treatment of error and prior source statistics. Here, we present an application of the Markov Chain Monte Carlo (MCMC) methodology to an atmospheric tracer inversion problem to demonstrate how more gereral statistical models for errors can be incorporated into the analysis in a relatively straightforward manner. The MCMC approach to Bayesian analysis, which has found wide application in a variety of fields, is a statistical simulation approach that involves computing moments of interest of the a posteriori pdf by efficiently sampling this pdf. The specific inverse problem that we focus on is the annual mean CO2 source/sink estimation problem considered by the TransCom3 project. TransCom3 was a collaborative effort involving various modeling groups and followed a common modeling and analysis protocoal. As such, this problem provides a convenient case study to demonstrate the applicability of the MCMC methodology to atmospheric tracer source/sink estimation problems.

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

An interactive Bayesian geostatistical inverse protocol for hydraulic tomography

USGS Publications Warehouse

Fienen, Michael N.; Clemo, Tom; Kitanidis, Peter K.

2008-01-01

Hydraulic tomography is a powerful technique for characterizing heterogeneous hydrogeologic parameters. An explicit trade-off between characterization based on measurement misfit and subjective characterization using prior information is presented. We apply a Bayesian geostatistical inverse approach that is well suited to accommodate a flexible model with the level of complexity driven by the data and explicitly considering uncertainty. Prior information is incorporated through the selection of a parameter covariance model characterizing continuity and providing stability. Often, discontinuities in the parameter field, typically caused by geologic contacts between contrasting lithologic units, necessitate subdivision into zones across which there is no correlation among hydraulic parameters. We propose an interactive protocol in which zonation candidates are implied from the data and are evaluated using cross validation and expert knowledge. Uncertainty introduced by limited knowledge of dynamic regional conditions is mitigated by using drawdown rather than native head values. An adjoint state formulation of MODFLOW-2000 is used to calculate sensitivities which are used both for the solution to the inverse problem and to guide protocol decisions. The protocol is tested using synthetic two-dimensional steady state examples in which the wells are located at the edge of the region of interest.

Incorporating approximation error in surrogate based Bayesian inversion

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.; Li, W.; Wu, L.

2015-12-01

There are increasing interests in applying surrogates for inverse Bayesian modeling to reduce repetitive evaluations of original model. In this way, the computational cost is expected to be saved. However, the approximation error of surrogate model is usually overlooked. This is partly because that it is difficult to evaluate the approximation error for many surrogates. Previous studies have shown that, the direct combination of surrogates and Bayesian methods (e.g., Markov Chain Monte Carlo, MCMC) may lead to biased estimations when the surrogate cannot emulate the highly nonlinear original system. This problem can be alleviated by implementing MCMC in a two-stage manner. However, the computational cost is still high since a relatively large number of original model simulations are required. In this study, we illustrate the importance of incorporating approximation error in inverse Bayesian modeling. Gaussian process (GP) is chosen to construct the surrogate for its convenience in approximation error evaluation. Numerical cases of Bayesian experimental design and parameter estimation for contaminant source identification are used to illustrate this idea. It is shown that, once the surrogate approximation error is well incorporated into Bayesian framework, promising results can be obtained even when the surrogate is directly used, and no further original model simulations are required.

Inverse Bayesian inference as a key of consciousness featuring a macroscopic quantum logical structure.

PubMed

Gunji, Yukio-Pegio; Shinohara, Shuji; Haruna, Taichi; Basios, Vasileios

2017-02-01

To overcome the dualism between mind and matter and to implement consciousness in science, a physical entity has to be embedded with a measurement process. Although quantum mechanics have been regarded as a candidate for implementing consciousness, nature at its macroscopic level is inconsistent with quantum mechanics. We propose a measurement-oriented inference system comprising Bayesian and inverse Bayesian inferences. While Bayesian inference contracts probability space, the newly defined inverse one relaxes the space. These two inferences allow an agent to make a decision corresponding to an immediate change in their environment. They generate a particular pattern of joint probability for data and hypotheses, comprising multiple diagonal and noisy matrices. This is expressed as a nondistributive orthomodular lattice equivalent to quantum logic. We also show that an orthomodular lattice can reveal information generated by inverse syllogism as well as the solutions to the frame and symbol-grounding problems. Our model is the first to connect macroscopic cognitive processes with the mathematical structure of quantum mechanics with no additional assumptions. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Model selection and Bayesian inference for high-resolution seabed reflection inversion.

PubMed

Dettmer, Jan; Dosso, Stan E; Holland, Charles W

2009-02-01

This paper applies Bayesian inference, including model selection and posterior parameter inference, to inversion of seabed reflection data to resolve sediment structure at a spatial scale below the pulse length of the acoustic source. A practical approach to model selection is used, employing the Bayesian information criterion to decide on the number of sediment layers needed to sufficiently fit the data while satisfying parsimony to avoid overparametrization. Posterior parameter inference is carried out using an efficient Metropolis-Hastings algorithm for high-dimensional models, and results are presented as marginal-probability depth distributions for sound velocity, density, and attenuation. The approach is applied to plane-wave reflection-coefficient inversion of single-bounce data collected on the Malta Plateau, Mediterranean Sea, which indicate complex fine structure close to the water-sediment interface. This fine structure is resolved in the geoacoustic inversion results in terms of four layers within the upper meter of sediments. The inversion results are in good agreement with parameter estimates from a gravity core taken at the experiment site.

Bayesian parameter estimation in spectral quantitative photoacoustic tomography

NASA Astrophysics Data System (ADS)

Pulkkinen, Aki; Cox, Ben T.; Arridge, Simon R.; Kaipio, Jari P.; Tarvainen, Tanja

2016-03-01

Photoacoustic tomography (PAT) is an imaging technique combining strong contrast of optical imaging to high spatial resolution of ultrasound imaging. These strengths are achieved via photoacoustic effect, where a spatial absorption of light pulse is converted into a measurable propagating ultrasound wave. The method is seen as a potential tool for small animal imaging, pre-clinical investigations, study of blood vessels and vasculature, as well as for cancer imaging. The goal in PAT is to form an image of the absorbed optical energy density field via acoustic inverse problem approaches from the measured ultrasound data. Quantitative PAT (QPAT) proceeds from these images and forms quantitative estimates of the optical properties of the target. This optical inverse problem of QPAT is illposed. To alleviate the issue, spectral QPAT (SQPAT) utilizes PAT data formed at multiple optical wavelengths simultaneously with optical parameter models of tissue to form quantitative estimates of the parameters of interest. In this work, the inverse problem of SQPAT is investigated. Light propagation is modelled using the diffusion equation. Optical absorption is described with chromophore concentration weighted sum of known chromophore absorption spectra. Scattering is described by Mie scattering theory with an exponential power law. In the inverse problem, the spatially varying unknown parameters of interest are the chromophore concentrations, the Mie scattering parameters (power law factor and the exponent), and Gruneisen parameter. The inverse problem is approached with a Bayesian method. It is numerically demonstrated, that estimation of all parameters of interest is possible with the approach.

Distributed micro-releases of bioterror pathogens : threat characterizations and epidemiology from uncertain patient observables.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolf, Michael M.; Marzouk, Youssef M.; Adams, Brian M.

2008-10-01

Terrorist attacks using an aerosolized pathogen preparation have gained credibility as a national security concern since the anthrax attacks of 2001. The ability to characterize the parameters of such attacks, i.e., to estimate the number of people infected, the time of infection, the average dose received, and the rate of disease spread in contemporary American society (for contagious diseases), is important when planning a medical response. For non-contagious diseases, we address the characterization problem by formulating a Bayesian inverse problem predicated on a short time-series of diagnosed patients exhibiting symptoms. To keep the approach relevant for response planning, we limitmore » ourselves to 3.5 days of data. In computational tests performed for anthrax, we usually find these observation windows sufficient, especially if the outbreak model employed in the inverse problem is accurate. For contagious diseases, we formulated a Bayesian inversion technique to infer both pathogenic transmissibility and the social network from outbreak observations, ensuring that the two determinants of spreading are identified separately. We tested this technique on data collected from a 1967 smallpox epidemic in Abakaliki, Nigeria. We inferred, probabilistically, different transmissibilities in the structured Abakaliki population, the social network, and the chain of transmission. Finally, we developed an individual-based epidemic model to realistically simulate the spread of a rare (or eradicated) disease in a modern society. This model incorporates the mixing patterns observed in an (American) urban setting and accepts, as model input, pathogenic transmissibilities estimated from historical outbreaks that may have occurred in socio-economic environments with little resemblance to contemporary society. Techniques were also developed to simulate disease spread on static and sampled network reductions of the dynamic social networks originally in the individual-based model, yielding faster, though approximate, network-based epidemic models. These reduced-order models are useful in scenario analysis for medical response planning, as well as in computationally intensive inverse problems.« less

A three-step maximum a posteriori probability method for InSAR data inversion of coseismic rupture with application to the 14 April 2010 Mw 6.9 Yushu, China, earthquake

NASA Astrophysics Data System (ADS)

Sun, Jianbao; Shen, Zheng-Kang; Bürgmann, Roland; Wang, Min; Chen, Lichun; Xu, Xiwei

2013-08-01

develop a three-step maximum a posteriori probability method for coseismic rupture inversion, which aims at maximizing the a posterior probability density function (PDF) of elastic deformation solutions of earthquake rupture. The method originates from the fully Bayesian inversion and mixed linear-nonlinear Bayesian inversion methods and shares the same posterior PDF with them, while overcoming difficulties with convergence when large numbers of low-quality data are used and greatly improving the convergence rate using optimization procedures. A highly efficient global optimization algorithm, adaptive simulated annealing, is used to search for the maximum of a posterior PDF ("mode" in statistics) in the first step. The second step inversion approaches the "true" solution further using the Monte Carlo inversion technique with positivity constraints, with all parameters obtained from the first step as the initial solution. Then slip artifacts are eliminated from slip models in the third step using the same procedure of the second step, with fixed fault geometry parameters. We first design a fault model with 45° dip angle and oblique slip, and produce corresponding synthetic interferometric synthetic aperture radar (InSAR) data sets to validate the reliability and efficiency of the new method. We then apply this method to InSAR data inversion for the coseismic slip distribution of the 14 April 2010 Mw 6.9 Yushu, China earthquake. Our preferred slip model is composed of three segments with most of the slip occurring within 15 km depth and the maximum slip reaches 1.38 m at the surface. The seismic moment released is estimated to be 2.32e+19 Nm, consistent with the seismic estimate of 2.50e+19 Nm.

Bayesian Inference in Satellite Gravity Inversion

NASA Technical Reports Server (NTRS)

Kis, K. I.; Taylor, Patrick T.; Wittmann, G.; Kim, Hyung Rae; Torony, B.; Mayer-Guerr, T.

2005-01-01

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks

NASA Astrophysics Data System (ADS)

Jiang, Fei-Bo; Dai, Qian-Wei; Dong, Li

2016-06-01

Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter α k , which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hou, Z; Terry, N; Hubbard, S S

2013-02-12

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability distribution functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSim) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hou, Zhangshuan; Terry, Neil C.; Hubbard, Susan S.

2013-02-22

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability density functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSIM) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

Comparative interpretations of renormalization inversion technique for reconstructing unknown emissions from measured atmospheric concentrations

NASA Astrophysics Data System (ADS)

Singh, Sarvesh Kumar; Kumar, Pramod; Rani, Raj; Turbelin, Grégory

2017-04-01

The study highlights a theoretical comparison and various interpretations of a recent inversion technique, called renormalization, developed for the reconstruction of unknown tracer emissions from their measured concentrations. The comparative interpretations are presented in relation to the other inversion techniques based on principle of regularization, Bayesian, minimum norm, maximum entropy on mean, and model resolution optimization. It is shown that the renormalization technique can be interpreted in a similar manner to other techniques, with a practical choice of a priori information and error statistics, while eliminating the need of additional constraints. The study shows that the proposed weight matrix and weighted Gram matrix offer a suitable deterministic choice to the background error and measurement covariance matrices, respectively, in the absence of statistical knowledge about background and measurement errors. The technique is advantageous since it (i) utilizes weights representing a priori information apparent to the monitoring network, (ii) avoids dependence on background source estimates, (iii) improves on alternative choices for the error statistics, (iv) overcomes the colocalization problem in a natural manner, and (v) provides an optimally resolved source reconstruction. A comparative illustration of source retrieval is made by using the real measurements from a continuous point release conducted in Fusion Field Trials, Dugway Proving Ground, Utah.

Multimodal, high-dimensional, model-based, Bayesian inverse problems with applications in biomechanics

NASA Astrophysics Data System (ADS)

Franck, I. M.; Koutsourelakis, P. S.

2017-01-01

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of unknown (latent) variables is high. This is the setting in many problems in computational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse problems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, poses a formidable computational task. The goal of the present paper is two-fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors. On the other, we extend our work in [1] with regard to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the proposed model by employing Importance Sampling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

Bayesian Orbit Computation Tools for Objects on Geocentric Orbits

NASA Astrophysics Data System (ADS)

Virtanen, J.; Granvik, M.; Muinonen, K.; Oszkiewicz, D.

2013-08-01

We consider the space-debris orbital inversion problem via the concept of Bayesian inference. The methodology has been put forward for the orbital analysis of solar system small bodies in early 1990's [7] and results in a full solution of the statistical inverse problem given in terms of a posteriori probability density function (PDF) for the orbital parameters. We demonstrate the applicability of our statistical orbital analysis software to Earth orbiting objects, both using well-established Monte Carlo (MC) techniques (for a review, see e.g. [13] as well as recently developed Markov-chain MC (MCMC) techniques (e.g., [9]). In particular, we exploit the novel virtual observation MCMC method [8], which is based on the characterization of the phase-space volume of orbital solutions before the actual MCMC sampling. Our statistical methods and the resulting PDFs immediately enable probabilistic impact predictions to be carried out. Furthermore, this can be readily done also for very sparse data sets and data sets of poor quality - providing that some a priori information on the observational uncertainty is available. For asteroids, impact probabilities with the Earth from the discovery night onwards have been provided, e.g., by [11] and [10], the latter study includes the sampling of the observational-error standard deviation as a random variable.

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Peng, E-mail: peng@ices.utexas.edu; Schwab, Christoph, E-mail: christoph.schwab@sam.math.ethz.ch

2016-07-01

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by themore » so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.« less

Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system.

PubMed

Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C

2016-02-01

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

Bayesian estimation of seasonal course of canopy leaf area index from hyperspectral satellite data

NASA Astrophysics Data System (ADS)

Varvia, Petri; Rautiainen, Miina; Seppänen, Aku

2018-03-01

In this paper, Bayesian inversion of a physically-based forest reflectance model is investigated to estimate of boreal forest canopy leaf area index (LAI) from EO-1 Hyperion hyperspectral data. The data consist of multiple forest stands with different species compositions and structures, imaged in three phases of the growing season. The Bayesian estimates of canopy LAI are compared to reference estimates based on a spectral vegetation index. The forest reflectance model contains also other unknown variables in addition to LAI, for example leaf single scattering albedo and understory reflectance. In the Bayesian approach, these variables are estimated simultaneously with LAI. The feasibility and seasonal variation of these estimates is also examined. Credible intervals for the estimates are also calculated and evaluated. The results show that the Bayesian inversion approach is significantly better than using a comparable spectral vegetation index regression.

Improving chemical species tomography of turbulent flows using covariance estimation.

PubMed

Grauer, Samuel J; Hadwin, Paul J; Daun, Kyle J

2017-05-01

Chemical species tomography (CST) experiments can be divided into limited-data and full-rank cases. Both require solving ill-posed inverse problems, and thus the measurement data must be supplemented with prior information to carry out reconstructions. The Bayesian framework formalizes the role of additive information, expressed as the mean and covariance of a joint-normal prior probability density function. We present techniques for estimating the spatial covariance of a flow under limited-data and full-rank conditions. Our results show that incorporating a covariance estimate into CST reconstruction via a Bayesian prior increases the accuracy of instantaneous estimates. Improvements are especially dramatic in real-time limited-data CST, which is directly applicable to many industrially relevant experiments.

A stochastic approach for model reduction and memory function design in hydrogeophysical inversion

NASA Astrophysics Data System (ADS)

Hou, Z.; Kellogg, A.; Terry, N.

2009-12-01

Geophysical (e.g., seismic, electromagnetic, radar) techniques and statistical methods are essential for research related to subsurface characterization, including monitoring subsurface flow and transport processes, oil/gas reservoir identification, etc. For deep subsurface characterization such as reservoir petroleum exploration, seismic methods have been widely used. Recently, electromagnetic (EM) methods have drawn great attention in the area of reservoir characterization. However, considering the enormous computational demand corresponding to seismic and EM forward modeling, it is usually a big problem to have too many unknown parameters in the modeling domain. For shallow subsurface applications, the characterization can be very complicated considering the complexity and nonlinearity of flow and transport processes in the unsaturated zone. It is warranted to reduce the dimension of parameter space to a reasonable level. Another common concern is how to make the best use of time-lapse data with spatial-temporal correlations. This is even more critical when we try to monitor subsurface processes using geophysical data collected at different times. The normal practice is to get the inverse images individually. These images are not necessarily continuous or even reasonably related, because of the non-uniqueness of hydrogeophysical inversion. We propose to use a stochastic framework by integrating minimum-relative-entropy concept, quasi Monto Carlo sampling techniques, and statistical tests. The approach allows efficient and sufficient exploration of all possibilities of model parameters and evaluation of their significances to geophysical responses. The analyses enable us to reduce the parameter space significantly. The approach can be combined with Bayesian updating, allowing us to treat the updated ‘posterior’ pdf as a memory function, which stores all the information up to date about the distributions of soil/field attributes/properties, then consider the memory function as a new prior and generate samples from it for further updating when more geophysical data is available. We applied this approach for deep oil reservoir characterization and for shallow subsurface flow monitoring. The model reduction approach reliably helps reduce the joint seismic/EM/radar inversion computational time to reasonable levels. Continuous inversion images are obtained using time-lapse data with the “memory function” applied in the Bayesian inversion.

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian—MCMC method

NASA Astrophysics Data System (ADS)

Sheng, Zheng

2013-02-01

The estimation of lower atmospheric refractivity from radar sea clutter (RFC) is a complicated nonlinear optimization problem. This paper deals with the RFC problem in a Bayesian framework. It uses the unbiased Markov Chain Monte Carlo (MCMC) sampling technique, which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework. In contrast to the global optimization algorithm, the Bayesian—MCMC can obtain not only the approximate solutions, but also the probability distributions of the solutions, that is, uncertainty analyses of solutions. The Bayesian—MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar sea-clutter data. Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter. The inversion algorithm is assessed (i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data; (ii) the one-dimensional (1D) and two-dimensional (2D) posterior probability distribution of solutions.

Radial anisotropy of Northeast Asia inferred from Bayesian inversions of ambient noise data

NASA Astrophysics Data System (ADS)

Lee, S. J.; Kim, S.; Rhie, J.

2017-12-01

The eastern margin of the Eurasia plate exhibits complex tectonic settings due to interactions with the subducting Pacific and Philippine Sea plates and the colliding India plate. Distributed extensional basins and intraplate volcanoes, and their heterogeneous features in the region are not easily explained with a simple mechanism. Observations of radial anisotropy in the entire lithosphere and the part of the asthenosphere provide the most effective evidence for the deformation of the lithosphere and the associated variation of the lithosphere-asthenosphere boundary (LAB). To infer anisotropic structures of crustal and upper-mantle in this region, radial anisotropy is measured using ambient noise data. In a continuation of previous Rayleigh wave tomography study in Northeast Asia, we conduct Love wave tomography to determine radial anisotropy using the Bayesian inversion techniques. Continuous seismic noise recordings of 237 broad-band seismic stations are used and more than 55,000 group and phase velocities of fundamental mode are measured for periods of 5-60 s. Total 8 different types of dispersion maps of Love wave from this study (period 10-60 s), Rayleigh wave from previous tomographic study (Kim et al., 2016; period 8-70 s) and longer period data (period 70-200 s) from a global model (Ekstrom, 2011) are jointly inverted using a hierarchical and transdimensional Bayesian technique. For each grid-node, boundary depths, velocities and anisotropy parameters of layers are sampled simultaneously on the assumption of the layered half-space model. The constructed 3-D radial anisotropy model provides much more details about the crust and upper mantle anisotropic structures, and about the complex undulation of the LAB.

Inverse modeling of Asian (222)Rn flux using surface air (222)Rn concentration.

PubMed

Hirao, Shigekazu; Yamazawa, Hiromi; Moriizumi, Jun

2010-11-01

When used with an atmospheric transport model, the (222)Rn flux distribution estimated in our previous study using soil transport theory caused underestimation of atmospheric (222)Rn concentrations as compared with measurements in East Asia. In this study, we applied a Bayesian synthesis inverse method to produce revised estimates of the annual (222)Rn flux density in Asia by using atmospheric (222)Rn concentrations measured at seven sites in East Asia. The Bayesian synthesis inverse method requires a prior estimate of the flux distribution and its uncertainties. The atmospheric transport model MM5/HIRAT and our previous estimate of the (222)Rn flux distribution as the prior value were used to generate new flux estimates for the eastern half of the Eurasian continent dividing into 10 regions. The (222)Rn flux densities estimated using the Bayesian inversion technique were generally higher than the prior flux densities. The area-weighted average (222)Rn flux density for Asia was estimated to be 33.0 mBq m(-2) s(-1), which is substantially higher than the prior value (16.7 mBq m(-2) s(-1)). The estimated (222)Rn flux densities decrease with increasing latitude as follows: Southeast Asia (36.7 mBq m(-2) s(-1)); East Asia (28.6 mBq m(-2) s(-1)) including China, Korean Peninsula and Japan; and Siberia (14.1 mBq m(-2) s(-1)). Increase of the newly estimated fluxes in Southeast Asia, China, Japan, and the southern part of Eastern Siberia from the prior ones contributed most significantly to improved agreement of the model-calculated concentrations with the atmospheric measurements. The sensitivity analysis of prior flux errors and effects of locally exhaled (222)Rn showed that the estimated fluxes in Northern and Central China, Korea, Japan, and the southern part of Eastern Siberia were robust, but that in Central Asia had a large uncertainty.

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

NASA Astrophysics Data System (ADS)

Duan, Lian; Farmer, Chris L.; Moroz, Irene M.

2010-09-01

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection.

An Inverse Modeling Plugin for HydroDesktop using the Method of Anchored Distributions (MAD)

NASA Astrophysics Data System (ADS)

Ames, D. P.; Osorio, C.; Over, M. W.; Rubin, Y.

2011-12-01

The CUAHSI Hydrologic Information System (HIS) software stack is based on an open and extensible architecture that facilitates the addition of new functions and capabilities at both the server side (using HydroServer) and the client side (using HydroDesktop). The HydroDesktop client plugin architecture is used here to expose a new scripting based plugin that makes use of the R statistics software as a means for conducting inverse modeling using the Method of Anchored Distributions (MAD). MAD is a Bayesian inversion technique for conditioning computational model parameters on relevant field observations yielding probabilistic distributions of the model parameters, related to the spatial random variable of interest, by assimilating multi-type and multi-scale data. The implementation of a desktop software tool for using the MAD technique is expected to significantly lower the barrier to use of inverse modeling in education, research, and resource management. The HydroDesktop MAD plugin is being developed following a community-based, open-source approach that will help both its adoption and long term sustainability as a user tool. This presentation will briefly introduce MAD, HydroDesktop, and the MAD plugin and software development effort.

Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan

In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic amplitude versus angle (AVA) and controlled source electromagnetic (CSEM) data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo (MCMC) sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis (DREAM) and Adaptive Metropolis (AM) samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and CSEM data. The multi-chain MCMC is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration,more » the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic AVA and CSEM joint inversion provides better estimation of reservoir saturations than the seismic AVA-only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated – reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.« less

Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

NASA Astrophysics Data System (ADS)

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Bao, Jie; Swiler, Laura

2017-12-01

In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated - reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.

Bayesian inference for disease prevalence using negative binomial group testing

PubMed Central

Pritchard, Nicholas A.; Tebbs, Joshua M.

2011-01-01

Group testing, also known as pooled testing, and inverse sampling are both widely used methods of data collection when the goal is to estimate a small proportion. Taking a Bayesian approach, we consider the new problem of estimating disease prevalence from group testing when inverse (negative binomial) sampling is used. Using different distributions to incorporate prior knowledge of disease incidence and different loss functions, we derive closed form expressions for posterior distributions and resulting point and credible interval estimators. We then evaluate our new estimators, on Bayesian and classical grounds, and apply our methods to a West Nile Virus data set. PMID:21259308

Comparing interpolation techniques for annual temperature mapping across Xinjiang region

NASA Astrophysics Data System (ADS)

Ren-ping, Zhang; Jing, Guo; Tian-gang, Liang; Qi-sheng, Feng; Aimaiti, Yusupujiang

2016-11-01

Interpolating climatic variables such as temperature is challenging due to the highly variable nature of meteorological processes and the difficulty in establishing a representative network of stations. In this paper, based on the monthly temperature data which obtained from the 154 official meteorological stations in the Xinjiang region and surrounding areas, we compared five spatial interpolation techniques: Inverse distance weighting (IDW), Ordinary kriging, Cokriging, thin-plate smoothing splines (ANUSPLIN) and Empirical Bayesian kriging(EBK). Error metrics were used to validate interpolations against independent data. Results indicated that, the ANUSPLIN performed best than the other four interpolation methods.

Ultrafast current imaging by Bayesian inversion

DOE Data Explorer

Somnath, Suhas; Law, Kody J. H.; Morozovska, Anna; Maksymovych, Petro; Kim, Yunseok; Lu, Xiaoli; Alexe, Marin; Archibald, Richard K; Kalinin, Sergei V; Jesse, Stephen; Vasudevan, Rama K

2016-01-01

Spectroscopic measurements of current-voltage curves in scanning probe microscopy is the earliest and one of the most common methods for characterizing local energy-dependent electronic properties, providing insight into superconductive, semiconductor, and memristive behaviors. However, the quasistatic nature of these measurements renders them extremely slow. Here, we demonstrate a fundamentally new approach for dynamic spectroscopic current imaging via full information capture and Bayesian inference analysis. This "general-mode I-V"method allows three orders of magnitude faster rates than presently possible. The technique is demonstrated by acquiring I-V curves in ferroelectric nanocapacitors, yielding >100,000 I-V curves in <20 minutes. This allows detection of switching currents in the nanoscale capacitors, as well as determination of dielectric constant. These experiments show the potential for the use of full information capture and Bayesian inference towards extracting physics from rapid I-V measurements, and can be used for transport measurements in both atomic force and scanning tunneling microscopy. The data was analyzed using pycroscopy - an open-source python package available at https://github.com/pycroscopy/pycroscopy

Estimating the Earthquake Source Time Function by Markov Chain Monte Carlo Sampling

NASA Astrophysics Data System (ADS)

Dȩbski, Wojciech

2008-07-01

Many aspects of earthquake source dynamics like dynamic stress drop, rupture velocity and directivity, etc. are currently inferred from the source time functions obtained by a deconvolution of the propagation and recording effects from seismograms. The question of the accuracy of obtained results remains open. In this paper we address this issue by considering two aspects of the source time function deconvolution. First, we propose a new pseudo-spectral parameterization of the sought function which explicitly takes into account the physical constraints imposed on the sought functions. Such parameterization automatically excludes non-physical solutions and so improves the stability and uniqueness of the deconvolution. Secondly, we demonstrate that the Bayesian approach to the inverse problem at hand, combined with an efficient Markov Chain Monte Carlo sampling technique, is a method which allows efficient estimation of the source time function uncertainties. The key point of the approach is the description of the solution of the inverse problem by the a posteriori probability density function constructed according to the Bayesian (probabilistic) theory. Next, the Markov Chain Monte Carlo sampling technique is used to sample this function so the statistical estimator of a posteriori errors can be easily obtained with minimal additional computational effort with respect to modern inversion (optimization) algorithms. The methodological considerations are illustrated by a case study of the mining-induced seismic event of the magnitude M L ≈3.1 that occurred at Rudna (Poland) copper mine. The seismic P-wave records were inverted for the source time functions, using the proposed algorithm and the empirical Green function technique to approximate Green functions. The obtained solutions seem to suggest some complexity of the rupture process with double pulses of energy release. However, the error analysis shows that the hypothesis of source complexity is not justified at the 95% confidence level. On the basis of the analyzed event we also show that the separation of the source inversion into two steps introduces limitations on the completeness of the a posteriori error analysis.

Efficient Bayesian parameter estimation with implicit sampling and surrogate modeling for a vadose zone hydrological problem

NASA Astrophysics Data System (ADS)

Liu, Y.; Pau, G. S. H.; Finsterle, S.

2015-12-01

Parameter inversion involves inferring the model parameter values based on sparse observations of some observables. To infer the posterior probability distributions of the parameters, Markov chain Monte Carlo (MCMC) methods are typically used. However, the large number of forward simulations needed and limited computational resources limit the complexity of the hydrological model we can use in these methods. In view of this, we studied the implicit sampling (IS) method, an efficient importance sampling technique that generates samples in the high-probability region of the posterior distribution and thus reduces the number of forward simulations that we need to run. For a pilot-point inversion of a heterogeneous permeability field based on a synthetic ponded infiltration experiment simu­lated with TOUGH2 (a subsurface modeling code), we showed that IS with linear map provides an accurate Bayesian description of the parameterized permeability field at the pilot points with just approximately 500 forward simulations. We further studied the use of surrogate models to improve the computational efficiency of parameter inversion. We implemented two reduced-order models (ROMs) for the TOUGH2 forward model. One is based on polynomial chaos expansion (PCE), of which the coefficients are obtained using the sparse Bayesian learning technique to mitigate the "curse of dimensionality" of the PCE terms. The other model is Gaussian process regression (GPR) for which different covariance, likelihood and inference models are considered. Preliminary results indicate that ROMs constructed based on the prior parameter space perform poorly. It is thus impractical to replace this hydrological model by a ROM directly in a MCMC method. However, the IS method can work with a ROM constructed for parameters in the close vicinity of the maximum a posteriori probability (MAP) estimate. We will discuss the accuracy and computational efficiency of using ROMs in the implicit sampling procedure for the hydrological problem considered. This work was supported, in part, by the U.S. Dept. of Energy under Contract No. DE-AC02-05CH11231

Sensitivity of a Bayesian atmospheric-transport inversion model to spatio-temporal sensor resolution applied to the 2006 North Korean nuclear test

NASA Astrophysics Data System (ADS)

Lundquist, K. A.; Jensen, D. D.; Lucas, D. D.

2017-12-01

Atmospheric source reconstruction allows for the probabilistic estimate of source characteristics of an atmospheric release using observations of the release. Performance of the inversion depends partially on the temporal frequency and spatial scale of the observations. The objective of this study is to quantify the sensitivity of the source reconstruction method to sparse spatial and temporal observations. To this end, simulations of atmospheric transport of noble gasses are created for the 2006 nuclear test at the Punggye-ri nuclear test site. Synthetic observations are collected from the simulation, and are taken as "ground truth". Data denial techniques are used to progressively coarsen the temporal and spatial resolution of the synthetic observations, while the source reconstruction model seeks to recover the true input parameters from the synthetic observations. Reconstructed parameters considered here are source location, source timing and source quantity. Reconstruction is achieved by running an ensemble of thousands of dispersion model runs that sample from a uniform distribution of the input parameters. Machine learning is used to train a computationally-efficient surrogate model from the ensemble simulations. Monte Carlo sampling and Bayesian inversion are then used in conjunction with the surrogate model to quantify the posterior probability density functions of source input parameters. This research seeks to inform decision makers of the tradeoffs between more expensive, high frequency observations and less expensive, low frequency observations.

The Approximate Bayesian Computation methods in the localization of the atmospheric contamination source

NASA Astrophysics Data System (ADS)

Kopka, P.; Wawrzynczak, A.; Borysiewicz, M.

2015-09-01

In many areas of application, a central problem is a solution to the inverse problem, especially estimation of the unknown model parameters to model the underlying dynamics of a physical system precisely. In this situation, the Bayesian inference is a powerful tool to combine observed data with prior knowledge to gain the probability distribution of searched parameters. We have applied the modern methodology named Sequential Approximate Bayesian Computation (S-ABC) to the problem of tracing the atmospheric contaminant source. The ABC is technique commonly used in the Bayesian analysis of complex models and dynamic system. Sequential methods can significantly increase the efficiency of the ABC. In the presented algorithm, the input data are the on-line arriving concentrations of released substance registered by distributed sensor network from OVER-LAND ATMOSPHERIC DISPERSION (OLAD) experiment. The algorithm output are the probability distributions of a contamination source parameters i.e. its particular location, release rate, speed and direction of the movement, start time and duration. The stochastic approach presented in this paper is completely general and can be used in other fields where the parameters of the model bet fitted to the observable data should be found.

Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Girolami, M.

2014-11-01

We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint technique. Various numerical results up to 1025 parameters are presented to demonstrate the ability of the RMHMC method in exploring the geometric structure of the problem to propose (almost) uncorrelated/independent samples that are far away from each other, and yet the acceptance rate is almost unity. The results also suggest that for the PDE models considered the proposed fixed metric RMHMC can attain almost as high a quality performance as the original RMHMC, i.e. generating (almost) uncorrelated/independent samples, while being two orders of magnitude less computationally expensive.

Using a pseudo-dynamic source inversion approach to improve earthquake source imaging

NASA Astrophysics Data System (ADS)

Zhang, Y.; Song, S. G.; Dalguer, L. A.; Clinton, J. F.

2014-12-01

Imaging a high-resolution spatio-temporal slip distribution of an earthquake rupture is a core research goal in seismology. In general we expect to obtain a higher quality source image by improving the observational input data (e.g. using more higher quality near-source stations). However, recent studies show that increasing the surface station density alone does not significantly improve source inversion results (Custodio et al. 2005; Zhang et al. 2014). We introduce correlation structures between the kinematic source parameters: slip, rupture velocity, and peak slip velocity (Song et al. 2009; Song and Dalguer 2013) in the non-linear source inversion. The correlation structures are physical constraints derived from rupture dynamics that effectively regularize the model space and may improve source imaging. We name this approach pseudo-dynamic source inversion. We investigate the effectiveness of this pseudo-dynamic source inversion method by inverting low frequency velocity waveforms from a synthetic dynamic rupture model of a buried vertical strike-slip event (Mw 6.5) in a homogeneous half space. In the inversion, we use a genetic algorithm in a Bayesian framework (Moneli et al. 2008), and a dynamically consistent regularized Yoffe function (Tinti, et al. 2005) was used for a single-window slip velocity function. We search for local rupture velocity directly in the inversion, and calculate the rupture time using a ray-tracing technique. We implement both auto- and cross-correlation of slip, rupture velocity, and peak slip velocity in the prior distribution. Our results suggest that kinematic source model estimates capture the major features of the target dynamic model. The estimated rupture velocity closely matches the target distribution from the dynamic rupture model, and the derived rupture time is smoother than the one we searched directly. By implementing both auto- and cross-correlation of kinematic source parameters, in comparison to traditional smoothing constraints, we are in effect regularizing the model space in a more physics-based manner without loosing resolution of the source image. Further investigation is needed to tune the related parameters of pseudo-dynamic source inversion and relative weighting between the prior and the likelihood function in the Bayesian inversion.

A three-step Maximum-A-Posterior probability method for InSAR data inversion of coseismic rupture with application to four recent large earthquakes in Asia

NASA Astrophysics Data System (ADS)

Sun, J.; Shen, Z.; Burgmann, R.; Liang, F.

2012-12-01

We develop a three-step Maximum-A-Posterior probability (MAP) method for coseismic rupture inversion, which aims at maximizing the a posterior probability density function (PDF) of elastic solutions of earthquake rupture. The method originates from the Fully Bayesian Inversion (FBI) and the Mixed linear-nonlinear Bayesian inversion (MBI) methods , shares the same a posterior PDF with them and keeps most of their merits, while overcoming its convergence difficulty when large numbers of low quality data are used and improving the convergence rate greatly using optimization procedures. A highly efficient global optimization algorithm, Adaptive Simulated Annealing (ASA), is used to search for the maximum posterior probability in the first step. The non-slip parameters are determined by the global optimization method, and the slip parameters are inverted for using the least squares method without positivity constraint initially, and then damped to physically reasonable range. This step MAP inversion brings the inversion close to 'true' solution quickly and jumps over local maximum regions in high-dimensional parameter space. The second step inversion approaches the 'true' solution further with positivity constraints subsequently applied on slip parameters using the Monte Carlo Inversion (MCI) technique, with all parameters obtained from step one as the initial solution. Then the slip artifacts are eliminated from slip models in the third step MAP inversion with fault geometry parameters fixed. We first used a designed model with 45 degree dipping angle and oblique slip, and corresponding synthetic InSAR data sets to validate the efficiency and accuracy of method. We then applied the method on four recent large earthquakes in Asia, namely the 2010 Yushu, China earthquake, the 2011 Burma earthquake, the 2011 New Zealand earthquake and the 2008 Qinghai, China earthquake, and compared our results with those results from other groups. Our results show the effectiveness of the method in earthquake studies and a number of advantages of it over other methods. The details will be reported on the meeting.

Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

DOE PAGES

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; ...

2017-10-17

In this paper we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach ismore » used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.« less

Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan

In this paper we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach ismore » used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.« less

Applications of Bayesian spectrum representation in acoustics

NASA Astrophysics Data System (ADS)

Botts, Jonathan M.

This dissertation utilizes a Bayesian inference framework to enhance the solution of inverse problems where the forward model maps to acoustic spectra. A Bayesian solution to filter design inverts a acoustic spectra to pole-zero locations of a discrete-time filter model. Spatial sound field analysis with a spherical microphone array is a data analysis problem that requires inversion of spatio-temporal spectra to directions of arrival. As with many inverse problems, a probabilistic analysis results in richer solutions than can be achieved with ad-hoc methods. In the filter design problem, the Bayesian inversion results in globally optimal coefficient estimates as well as an estimate the most concise filter capable of representing the given spectrum, within a single framework. This approach is demonstrated on synthetic spectra, head-related transfer function spectra, and measured acoustic reflection spectra. The Bayesian model-based analysis of spatial room impulse responses is presented as an analogous problem with equally rich solution. The model selection mechanism provides an estimate of the number of arrivals, which is necessary to properly infer the directions of simultaneous arrivals. Although, spectrum inversion problems are fairly ubiquitous, the scope of this dissertation has been limited to these two and derivative problems. The Bayesian approach to filter design is demonstrated on an artificial spectrum to illustrate the model comparison mechanism and then on measured head-related transfer functions to show the potential range of application. Coupled with sampling methods, the Bayesian approach is shown to outperform least-squares filter design methods commonly used in commercial software, confirming the need for a global search of the parameter space. The resulting designs are shown to be comparable to those that result from global optimization methods, but the Bayesian approach has the added advantage of a filter length estimate within the same unified framework. The application to reflection data is useful for representing frequency-dependent impedance boundaries in finite difference acoustic simulations. Furthermore, since the filter transfer function is a parametric model, it can be modified to incorporate arbitrary frequency weighting and account for the band-limited nature of measured reflection spectra. Finally, the model is modified to compensate for dispersive error in the finite difference simulation, from the filter design process. Stemming from the filter boundary problem, the implementation of pressure sources in finite difference simulation is addressed in order to assure that schemes properly converge. A class of parameterized source functions is proposed and shown to offer straightforward control of residual error in the simulation. Guided by the notion that the solution to be approximated affects the approximation error, sources are designed which reduce residual dispersive error to the size of round-off errors. The early part of a room impulse response can be characterized by a series of isolated plane waves. Measured with an array of microphones, plane waves map to a directional response of the array or spatial intensity map. Probabilistic inversion of this response results in estimates of the number and directions of image source arrivals. The model-based inversion is shown to avoid ambiguities associated with peak-finding or inspection of the spatial intensity map. For this problem, determining the number of arrivals in a given frame is critical for properly inferring the state of the sound field. This analysis is effectively compression of the spatial room response, which is useful for analysis or encoding of the spatial sound field. Parametric, model-based formulations of these problems enhance the solution in all cases, and a Bayesian interpretation provides a principled approach to model comparison and parameter estimation. v

Uncertainty Analysis and Parameter Estimation For Nearshore Hydrodynamic Models

NASA Astrophysics Data System (ADS)

Ardani, S.; Kaihatu, J. M.

2012-12-01

Numerical models represent deterministic approaches used for the relevant physical processes in the nearshore. Complexity of the physics of the model and uncertainty involved in the model inputs compel us to apply a stochastic approach to analyze the robustness of the model. The Bayesian inverse problem is one powerful way to estimate the important input model parameters (determined by apriori sensitivity analysis) and can be used for uncertainty analysis of the outputs. Bayesian techniques can be used to find the range of most probable parameters based on the probability of the observed data and the residual errors. In this study, the effect of input data involving lateral (Neumann) boundary conditions, bathymetry and off-shore wave conditions on nearshore numerical models are considered. Monte Carlo simulation is applied to a deterministic numerical model (the Delft3D modeling suite for coupled waves and flow) for the resulting uncertainty analysis of the outputs (wave height, flow velocity, mean sea level and etc.). Uncertainty analysis of outputs is performed by random sampling from the input probability distribution functions and running the model as required until convergence to the consistent results is achieved. The case study used in this analysis is the Duck94 experiment, which was conducted at the U.S. Army Field Research Facility at Duck, North Carolina, USA in the fall of 1994. The joint probability of model parameters relevant for the Duck94 experiments will be found using the Bayesian approach. We will further show that, by using Bayesian techniques to estimate the optimized model parameters as inputs and applying them for uncertainty analysis, we can obtain more consistent results than using the prior information for input data which means that the variation of the uncertain parameter will be decreased and the probability of the observed data will improve as well. Keywords: Monte Carlo Simulation, Delft3D, uncertainty analysis, Bayesian techniques, MCMC

A surrogate-based sensitivity quantification and Bayesian inversion of a regional groundwater flow model

NASA Astrophysics Data System (ADS)

Chen, Mingjie; Izady, Azizallah; Abdalla, Osman A.; Amerjeed, Mansoor

2018-02-01

Bayesian inference using Markov Chain Monte Carlo (MCMC) provides an explicit framework for stochastic calibration of hydrogeologic models accounting for uncertainties; however, the MCMC sampling entails a large number of model calls, and could easily become computationally unwieldy if the high-fidelity hydrogeologic model simulation is time consuming. This study proposes a surrogate-based Bayesian framework to address this notorious issue, and illustrates the methodology by inverse modeling a regional MODFLOW model. The high-fidelity groundwater model is approximated by a fast statistical model using Bagging Multivariate Adaptive Regression Spline (BMARS) algorithm, and hence the MCMC sampling can be efficiently performed. In this study, the MODFLOW model is developed to simulate the groundwater flow in an arid region of Oman consisting of mountain-coast aquifers, and used to run representative simulations to generate training dataset for BMARS model construction. A BMARS-based Sobol' method is also employed to efficiently calculate input parameter sensitivities, which are used to evaluate and rank their importance for the groundwater flow model system. According to sensitivity analysis, insensitive parameters are screened out of Bayesian inversion of the MODFLOW model, further saving computing efforts. The posterior probability distribution of input parameters is efficiently inferred from the prescribed prior distribution using observed head data, demonstrating that the presented BMARS-based Bayesian framework is an efficient tool to reduce parameter uncertainties of a groundwater system.

Resolution analysis of marine seismic full waveform data by Bayesian inversion

NASA Astrophysics Data System (ADS)

Ray, A.; Sekar, A.; Hoversten, G. M.; Albertin, U.

2015-12-01

The Bayesian posterior density function (PDF) of earth models that fit full waveform seismic data convey information on the uncertainty with which the elastic model parameters are resolved. In this work, we apply the trans-dimensional reversible jump Markov Chain Monte Carlo method (RJ-MCMC) for the 1D inversion of noisy synthetic full-waveform seismic data in the frequency-wavenumber domain. While seismic full waveform inversion (FWI) is a powerful method for characterizing subsurface elastic parameters, the uncertainty in the inverted models has remained poorly known, if at all and is highly initial model dependent. The Bayesian method we use is trans-dimensional in that the number of model layers is not fixed, and flexible such that the layer boundaries are free to move around. The resulting parameterization does not require regularization to stabilize the inversion. Depth resolution is traded off with the number of layers, providing an estimate of uncertainty in elastic parameters (compressional and shear velocities Vp and Vs as well as density) with depth. We find that in the absence of additional constraints, Bayesian inversion can result in a wide range of posterior PDFs on Vp, Vs and density. These PDFs range from being clustered around the true model, to those that contain little resolution of any particular features other than those in the near surface, depending on the particular data and target geometry. We present results for a suite of different frequencies and offset ranges, examining the differences in the posterior model densities thus derived. Though these results are for a 1D earth, they are applicable to areas with simple, layered geology and provide valuable insight into the resolving capabilities of FWI, as well as highlight the challenges in solving a highly non-linear problem. The RJ-MCMC method also presents a tantalizing possibility for extension to 2D and 3D Bayesian inversion of full waveform seismic data in the future, as it objectively tackles the problem of model selection (i.e., the number of layers or cells for parameterization), which could ease the computational burden of evaluating forward models with many parameters.

Ambient Noise Tomography of central Java, with Transdimensional Bayesian Inversion

NASA Astrophysics Data System (ADS)

Zulhan, Zulfakriza; Saygin, Erdinc; Cummins, Phil; Widiyantoro, Sri; Nugraha, Andri Dian; Luehr, Birger-G.; Bodin, Thomas

2014-05-01

Delineating the crustal structure of central Java is crucial for understanding its complex tectonic setting. However, seismic imaging of the strong heterogeneity typical of such a tectonically active region can be challenging, particularly in the upper crust where velocity contrasts are strongest and steep body wave ray-paths provide poor resolution. We have applied ambient noise cross correlation of pair stations in central Java, Indonesia by using the MERapi Amphibious EXperiment (MERAMEX) dataset. The data were collected between May to October 2004. We used 120 of 134 temporary seismic stations for about 150 days of observation, which covered central Java. More than 5000 Rayleigh wave Green's function were extracted by cross-correlating the noise simultaneously recorded at available station pairs. We applied a fully nonlinear 2D Bayesian inversion technique to the retrieved travel times. Features in the derived tomographic images correlate well with previous studies, and some shallow structures that were not evident in previous studies are clearly imaged with Ambient Noise Tomography. The Kendeng Basin and several active volcanoes appear with very low group velocities, and anomalies with relatively high velocities can be interpreted in terms of crustal sutures and/or surface geological features.

Free will in Bayesian and inverse Bayesian inference-driven endo-consciousness.

PubMed

Gunji, Yukio-Pegio; Minoura, Mai; Kojima, Kei; Horry, Yoichi

2017-12-01

How can we link challenging issues related to consciousness and/or qualia with natural science? The introduction of endo-perspective, instead of exo-perspective, as proposed by Matsuno, Rössler, and Gunji, is considered one of the most promising candidate approaches. Here, we distinguish the endo-from the exo-perspective in terms of whether the external is or is not directly operated. In the endo-perspective, the external can be neither perceived nor recognized directly; rather, one can only indirectly summon something outside of the perspective, which can be illustrated by a causation-reversal pair. On one hand, causation logically proceeds from the cause to the effect. On the other hand, a reversal from the effect to the cause is non-logical and is equipped with a metaphorical structure. We argue that the differences in exo- and endo-perspectives result not from the difference between Western and Eastern cultures, but from differences between modernism and animism. Here, a causation-reversal pair described using a pair of upward (from premise to consequence) and downward (from consequence to premise) causation and a pair of Bayesian and inverse Bayesian inference (BIB inference). Accordingly, the notion of endo-consciousness is proposed as an agent equipped with BIB inference. We also argue that BIB inference can yield both highly efficient computations through Bayesian interference and robust computations through inverse Bayesian inference. By adapting a logical model of the free will theorem to the BIB inference, we show that endo-consciousness can explain free will as a regression of the controllability of voluntary action. Copyright © 2017. Published by Elsevier Ltd.

The Variability and Interpretation of Earthquake Source Mechanisms in The Geysers Geothermal Field From a Bayesian Standpoint Based on the Choice of a Noise Model

NASA Astrophysics Data System (ADS)

Mustać, Marija; Tkalčić, Hrvoje; Burky, Alexander L.

2018-01-01

Moment tensor (MT) inversion studies of events in The Geysers geothermal field mostly focused on microseismicity and found a large number of earthquakes with significant non-double-couple (non-DC) seismic radiation. Here we concentrate on the largest events in the area in recent years using a hierarchical Bayesian MT inversion. Initially, we show that the non-DC components of the MT can be reliably retrieved using regional waveform data from a small number of stations. Subsequently, we present results for a number of events and show that accounting for noise correlations can lead to retrieval of a lower isotropic (ISO) component and significantly different focal mechanisms. We compute the Bayesian evidence to compare solutions obtained with different assumptions of the noise covariance matrix. Although a diagonal covariance matrix produces a better waveform fit, inversions that account for noise correlations via an empirically estimated noise covariance matrix account for interdependences of data errors and are preferred from a Bayesian point of view. This implies that improper treatment of data noise in waveform inversions can result in fitting the noise and misinterpreting the non-DC components. Finally, one of the analyzed events is characterized as predominantly DC, while the others still have significant non-DC components, probably as a result of crack opening, which is a reasonable hypothesis for The Geysers geothermal field geological setting.

Wavelet extractor: A Bayesian well-tie and wavelet extraction program

NASA Astrophysics Data System (ADS)

Gunning, James; Glinsky, Michael E.

2006-06-01

We introduce a new open-source toolkit for the well-tie or wavelet extraction problem of estimating seismic wavelets from seismic data, time-to-depth information, and well-log suites. The wavelet extraction model is formulated as a Bayesian inverse problem, and the software will simultaneously estimate wavelet coefficients, other parameters associated with uncertainty in the time-to-depth mapping, positioning errors in the seismic imaging, and useful amplitude-variation-with-offset (AVO) related parameters in multi-stack extractions. It is capable of multi-well, multi-stack extractions, and uses continuous seismic data-cube interpolation to cope with the problem of arbitrary well paths. Velocity constraints in the form of checkshot data, interpreted markers, and sonic logs are integrated in a natural way. The Bayesian formulation allows computation of full posterior uncertainties of the model parameters, and the important problem of the uncertain wavelet span is addressed uses a multi-model posterior developed from Bayesian model selection theory. The wavelet extraction tool is distributed as part of the Delivery seismic inversion toolkit. A simple log and seismic viewing tool is included in the distribution. The code is written in Java, and thus platform independent, but the Seismic Unix (SU) data model makes the inversion particularly suited to Unix/Linux environments. It is a natural companion piece of software to Delivery, having the capacity to produce maximum likelihood wavelet and noise estimates, but will also be of significant utility to practitioners wanting to produce wavelet estimates for other inversion codes or purposes. The generation of full parameter uncertainties is a crucial function for workers wishing to investigate questions of wavelet stability before proceeding to more advanced inversion studies.

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging.

PubMed

Kolehmainen, Ville; Vanne, Antti; Siltanen, Samuli; Järvenpää, Seppo; Kaipio, Jari P; Lassas, Matti; Kalke, Martti

2006-02-01

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted l1 and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.

Real-time inversions for finite fault slip models and rupture geometry based on high-rate GPS data

USGS Publications Warehouse

Minson, Sarah E.; Murray, Jessica R.; Langbein, John O.; Gomberg, Joan S.

2015-01-01

We present an inversion strategy capable of using real-time high-rate GPS data to simultaneously solve for a distributed slip model and fault geometry in real time as a rupture unfolds. We employ Bayesian inference to find the optimal fault geometry and the distribution of possible slip models for that geometry using a simple analytical solution. By adopting an analytical Bayesian approach, we can solve this complex inversion problem (including calculating the uncertainties on our results) in real time. Furthermore, since the joint inversion for distributed slip and fault geometry can be computed in real time, the time required to obtain a source model of the earthquake does not depend on the computational cost. Instead, the time required is controlled by the duration of the rupture and the time required for information to propagate from the source to the receivers. We apply our modeling approach, called Bayesian Evidence-based Fault Orientation and Real-time Earthquake Slip, to the 2011 Tohoku-oki earthquake, 2003 Tokachi-oki earthquake, and a simulated Hayward fault earthquake. In all three cases, the inversion recovers the magnitude, spatial distribution of slip, and fault geometry in real time. Since our inversion relies on static offsets estimated from real-time high-rate GPS data, we also present performance tests of various approaches to estimating quasi-static offsets in real time. We find that the raw high-rate time series are the best data to use for determining the moment magnitude of the event, but slightly smoothing the raw time series helps stabilize the inversion for fault geometry.

An Adaptive Model of Student Performance Using Inverse Bayes

ERIC Educational Resources Information Center

Lang, Charles

2014-01-01

This article proposes a coherent framework for the use of Inverse Bayesian estimation to summarize and make predictions about student behaviour in adaptive educational settings. The Inverse Bayes Filter utilizes Bayes theorem to estimate the relative impact of contextual factors and internal student factors on student performance using time series…

EDITORIAL: Inverse Problems in Engineering

NASA Astrophysics Data System (ADS)

West, Robert M.; Lesnic, Daniel

2007-01-01

Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.

Carbon Tetrachloride Emissions from the US during 2008 - 2012 Derived from Atmospheric Data Using Bayesian and Geostatistical Inversions

NASA Astrophysics Data System (ADS)

Hu, L.; Montzka, S. A.; Miller, B.; Andrews, A. E.; Miller, J. B.; Lehman, S.; Sweeney, C.; Miller, S. M.; Thoning, K. W.; Siso, C.; Atlas, E. L.; Blake, D. R.; De Gouw, J. A.; Gilman, J.; Dutton, G. S.; Elkins, J. W.; Hall, B. D.; Chen, H.; Fischer, M. L.; Mountain, M. E.; Nehrkorn, T.; Biraud, S.; Tans, P. P.

2015-12-01

Global atmospheric observations suggest substantial ongoing emissions of carbon tetrachloride (CCl4) despite a 100% phase-out of production for dispersive uses since 1996 in developed countries and 2010 in other countries. Little progress has been made in understanding the causes of these ongoing emissions or identifying their contributing sources. In this study, we employed multiple inverse modeling techniques (i.e. Bayesian and geostatistical inversions) to assimilate CCl4 mole fractions observed from the National Oceanic and Atmospheric Administration (NOAA) flask-air sampling network over the US, and quantify its national and regional emissions during 2008 - 2012. Average national total emissions of CCl4 between 2008 and 2012 determined from these observations and an ensemble of inversions range between 2.1 and 6.1 Gg yr-1. This emission is substantially larger than the mean of 0.06 Gg/yr reported to the US EPA Toxics Release Inventory over these years, suggesting that under-reported emissions or non-reporting sources make up the bulk of CCl4 emissions from the US. But while the inventory does not account for the magnitude of observationally-derived CCl4 emissions, the regional distribution of derived and inventory emissions is similar. Furthermore, when considered relative to the distribution of uncapped landfills or population, the variability in measured mole fractions was most consistent with the distribution of industrial sources (i.e., those from the Toxics Release Inventory). Our results suggest that emissions from the US only account for a small fraction of the global on-going emissions of CCl4 (30 - 80 Gg yr-1 over this period). Finally, to ascertain the importance of the US emissions relative to the unaccounted global emission rate we considered multiple approaches to extrapolate our results to other countries and the globe.

Sensitivity of Global Methane Bayesian Inversion to Surface Observation Data Sets and Chemical-Transport Model Resolution

NASA Astrophysics Data System (ADS)

Lew, E. J.; Butenhoff, C. L.; Karmakar, S.; Rice, A. L.; Khalil, A. K.

2017-12-01

Methane is the second most important greenhouse gas after carbon dioxide. In efforts to control emissions, a careful examination of the methane budget and source strengths is required. To determine methane surface fluxes, Bayesian methods are often used to provide top-down constraints. Inverse modeling derives unknown fluxes using observed methane concentrations, a chemical transport model (CTM) and prior information. The Bayesian inversion reduces prior flux uncertainties by exploiting information content in the data. While the Bayesian formalism produces internal error estimates of source fluxes, systematic or external errors that arise from user choices in the inversion scheme are often much larger. Here we examine model sensitivity and uncertainty of our inversion under different observation data sets and CTM grid resolution. We compare posterior surface fluxes using the data product GLOBALVIEW-CH4 against the event-level molar mixing ratio data available from NOAA. GLOBALVIEW-CH4 is a collection of CH4 concentration estimates from 221 sites, collected by 12 laboratories, that have been interpolated and extracted to provide weekly records from 1984-2008. Differently, the event-level NOAA data records methane mixing ratios field measurements from 102 sites, containing sampling frequency irregularities and gaps in time. Furthermore, the sampling platform types used by the data sets may influence the posterior flux estimates, namely fixed surface, tower, ship and aircraft sites. To explore the sensitivity of the posterior surface fluxes to the observation network geometry, inversions composed of all sites, only aircraft, only ship, only tower and only fixed surface sites, are performed and compared. Also, we investigate the sensitivity of the error reduction associated with the resolution of the GEOS-Chem simulation (4°×5° vs 2°×2.5°) used to calculate the response matrix. Using a higher resolution grid decreased the model-data error at most sites, thereby increasing the information at that site. These different inversions—event-level and interpolated data, higher and lower resolutions—are compared using an ensemble of descriptive and comparative statistics. Analyzing the sensitivity of the inverse model leads to more accurate estimates of the methane source category uncertainty.

Estimates of CO2 fluxes over the city of Cape Town, South Africa, through Bayesian inverse modelling

NASA Astrophysics Data System (ADS)

Nickless, Alecia; Rayner, Peter J.; Engelbrecht, Francois; Brunke, Ernst-Günther; Erni, Birgit; Scholes, Robert J.

2018-04-01

We present a city-scale inversion over Cape Town, South Africa. Measurement sites for atmospheric CO2 concentrations were installed at Robben Island and Hangklip lighthouses, located downwind and upwind of the metropolis. Prior estimates of the fossil fuel fluxes were obtained from a bespoke inventory analysis where emissions were spatially and temporally disaggregated and uncertainty estimates determined by means of error propagation techniques. Net ecosystem exchange (NEE) fluxes from biogenic processes were obtained from the land atmosphere exchange model CABLE (Community Atmosphere Biosphere Land Exchange). Uncertainty estimates were based on the estimates of net primary productivity. CABLE was dynamically coupled to the regional climate model CCAM (Conformal Cubic Atmospheric Model), which provided the climate inputs required to drive the Lagrangian particle dispersion model. The Bayesian inversion framework included a control vector where fossil fuel and NEE fluxes were solved for separately.Due to the large prior uncertainty prescribed to the NEE fluxes, the current inversion framework was unable to adequately distinguish between the fossil fuel and NEE fluxes, but the inversion was able to obtain improved estimates of the total fluxes within pixels and across the domain. The median of the uncertainty reductions of the total weekly flux estimates for the inversion domain of Cape Town was 28 %, but reach as high as 50 %. At the pixel level, uncertainty reductions of the total weekly flux reached up to 98 %, but these large uncertainty reductions were for NEE-dominated pixels. Improved corrections to the fossil fuel fluxes would be possible if the uncertainty around the prior NEE fluxes could be reduced. In order for this inversion framework to be operationalised for monitoring, reporting, and verification (MRV) of emissions from Cape Town, the NEE component of the CO2 budget needs to be better understood. Additional measurements of Δ14C and δ13C isotope measurements would be a beneficial component of an atmospheric monitoring programme aimed at MRV of CO2 for any city which has significant biogenic influence, allowing improved separation of contributions from NEE and fossil fuel fluxes to the observed CO2 concentration.

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less

Probabilistic inversion of expert assessments to inform projections about Antarctic ice sheet responses.

PubMed

Fuller, Robert William; Wong, Tony E; Keller, Klaus

2017-01-01

The response of the Antarctic ice sheet (AIS) to changing global temperatures is a key component of sea-level projections. Current projections of the AIS contribution to sea-level changes are deeply uncertain. This deep uncertainty stems, in part, from (i) the inability of current models to fully resolve key processes and scales, (ii) the relatively sparse available data, and (iii) divergent expert assessments. One promising approach to characterizing the deep uncertainty stemming from divergent expert assessments is to combine expert assessments, observations, and simple models by coupling probabilistic inversion and Bayesian inversion. Here, we present a proof-of-concept study that uses probabilistic inversion to fuse a simple AIS model and diverse expert assessments. We demonstrate the ability of probabilistic inversion to infer joint prior probability distributions of model parameters that are consistent with expert assessments. We then confront these inferred expert priors with instrumental and paleoclimatic observational data in a Bayesian inversion. These additional constraints yield tighter hindcasts and projections. We use this approach to quantify how the deep uncertainty surrounding expert assessments affects the joint probability distributions of model parameters and future projections.

Quantum Mechanics, Pattern Recognition, and the Mammalian Brain

NASA Astrophysics Data System (ADS)

Chapline, George

2008-10-01

Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantum mechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantum mechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the "wake-sleep" algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi-channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.

Bayesian Meta-Analysis of Coefficient Alpha

ERIC Educational Resources Information Center

Brannick, Michael T.; Zhang, Nanhua

2013-01-01

The current paper describes and illustrates a Bayesian approach to the meta-analysis of coefficient alpha. Alpha is the most commonly used estimate of the reliability or consistency (freedom from measurement error) for educational and psychological measures. The conventional approach to meta-analysis uses inverse variance weights to combine…

Objectified quantification of uncertainties in Bayesian atmospheric inversions

NASA Astrophysics Data System (ADS)

Berchet, A.; Pison, I.; Chevallier, F.; Bousquet, P.; Bonne, J.-L.; Paris, J.-D.

2015-05-01

Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. When data pieces are sparse, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results to enhance the classical Bayesian inversion framework through a marginalization on a large set of plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurrence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is not explicitly describable. As a consequence, we carry out a Monte Carlo sampling based on an approximation of the probability of occurrence of the error distributions. This approximation is deduced from the well-tested method of the maximum likelihood estimation. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly accounts for the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of an emission aggregation pattern and of a sampling protocol in order to reduce the computation cost. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the mesoscale with virtual observations on a realistic network in Eurasia. Observing system simulation experiments are carried out with different transport patterns, flux distributions and total prior amounts of emitted methane. The method proves to consistently reproduce the known "truth" in most cases, with satisfactory tolerance intervals. Additionally, the method explicitly provides influence scores and posterior correlation matrices. An in-depth interpretation of the inversion results is then possible. The more objective quantification of the influence of the observations on the fluxes proposed here allows us to evaluate the impact of the observation network on the characterization of the surface fluxes. The explicit correlations between emission aggregates reveal the mis-separated regions, hence the typical temporal and spatial scales the inversion can analyse. These scales are consistent with the chosen aggregation patterns.

Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio

2018-04-01

We consider the inverse problem of recovering an unknown functional parameter u in a separable Banach space, from a noisy observation vector y of its image through a known possibly non-linear map {{\\mathcal G}} . We adopt a Bayesian approach to the problem and consider Besov space priors (see Lassas et al (2009 Inverse Problems Imaging 3 87-122)), which are well-known for their edge-preserving and sparsity-promoting properties and have recently attracted wide attention especially in the medical imaging community. Our key result is to show that in this non-parametric setup the maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. This is done independently for the so-called weak and strong MAP estimates, which as we show coincide in our context. In addition, we prove a form of weak consistency for the MAP estimators in the infinitely informative data limit. Our results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on non-parametric MAP estimates. Second, the result analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.

a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Myers, A.; Wang, K.; Thiery, A.

2017-12-01

We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.

A Bayesian inverse modeling approach to estimate soil hydraulic properties of a toposequence in southeastern Amazonia.

NASA Astrophysics Data System (ADS)

Stucchi Boschi, Raquel; Qin, Mingming; Gimenez, Daniel; Cooper, Miguel

2016-04-01

Modeling is an important tool for better understanding and assessing land use impacts on landscape processes. A key point for environmental modeling is the knowledge of soil hydraulic properties. However, direct determination of soil hydraulic properties is difficult and costly, particularly in vast and remote regions such as one constituting the Amazon Biome. One way to overcome this problem is to extrapolate accurately estimated data to pedologically similar sites. The van Genuchten (VG) parametric equation is the most commonly used for modeling SWRC. The use of a Bayesian approach in combination with the Markov chain Monte Carlo to estimate the VG parameters has several advantages compared to the widely used global optimization techniques. The Bayesian approach provides posterior distributions of parameters that are independent from the initial values and allow for uncertainty analyses. The main objectives of this study were: i) to estimate hydraulic parameters from data of pasture and forest sites by the Bayesian inverse modeling approach; and ii) to investigate the extrapolation of the estimated VG parameters to a nearby toposequence with pedologically similar soils to those used for its estimate. The parameters were estimated from volumetric water content and tension observations obtained after rainfall events during a 207-day period from pasture and forest sites located in the southeastern Amazon region. These data were used to run HYDRUS-1D under a Differential Evolution Adaptive Metropolis (DREAM) scheme 10,000 times, and only the last 2,500 times were used to calculate the posterior distributions of each hydraulic parameter along with 95% confidence intervals (CI) of volumetric water content and tension time series. Then, the posterior distributions were used to generate hydraulic parameters for two nearby toposequences composed by six soil profiles, three are under forest and three are under pasture. The parameters of the nearby site were accepted when the predicted tension time series were within the 95% CI which is derived from the calibration site using DREAM scheme.

Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Fei; Department of Mathematics, University of California, Berkeley; Morzfeld, Matthias, E-mail: mmo@math.lbl.gov

2015-02-01

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.

Impact of petrophysical uncertainty on Bayesian hydrogeophysical inversion and model selection

NASA Astrophysics Data System (ADS)

Brunetti, Carlotta; Linde, Niklas

2018-01-01

Quantitative hydrogeophysical studies rely heavily on petrophysical relationships that link geophysical properties to hydrogeological properties and state variables. Coupled inversion studies are frequently based on the questionable assumption that these relationships are perfect (i.e., no scatter). Using synthetic examples and crosshole ground-penetrating radar (GPR) data from the South Oyster Bacterial Transport Site in Virginia, USA, we investigate the impact of spatially-correlated petrophysical uncertainty on inferred posterior porosity and hydraulic conductivity distributions and on Bayes factors used in Bayesian model selection. Our study shows that accounting for petrophysical uncertainty in the inversion (I) decreases bias of the inferred variance of hydrogeological subsurface properties, (II) provides more realistic uncertainty assessment and (III) reduces the overconfidence in the ability of geophysical data to falsify conceptual hydrogeological models.

Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

NASA Astrophysics Data System (ADS)

Fukuda, J.; Johnson, K. M.

2009-12-01

Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress drop.

Almost but not quite 2D, Non-linear Bayesian Inversion of CSEM Data

NASA Astrophysics Data System (ADS)

Ray, A.; Key, K.; Bodin, T.

2013-12-01

The geophysical inverse problem can be elegantly stated in a Bayesian framework where a probability distribution can be viewed as a statement of information regarding a random variable. After all, the goal of geophysical inversion is to provide information on the random variables of interest - physical properties of the earth's subsurface. However, though it may be simple to postulate, a practical difficulty of fully non-linear Bayesian inversion is the computer time required to adequately sample the model space and extract the information we seek. As a consequence, in geophysical problems where evaluation of a full 2D/3D forward model is computationally expensive, such as marine controlled source electromagnetic (CSEM) mapping of the resistivity of seafloor oil and gas reservoirs, Bayesian studies have largely been conducted with 1D forward models. While the 1D approximation is indeed appropriate for exploration targets with planar geometry and geological stratification, it only provides a limited, site-specific idea of uncertainty in resistivity with depth. In this work, we extend our fully non-linear 1D Bayesian inversion to a 2D model framework, without requiring the usual regularization of model resistivities in the horizontal or vertical directions used to stabilize quasi-2D inversions. In our approach, we use the reversible jump Markov-chain Monte-Carlo (RJ-MCMC) or trans-dimensional method and parameterize the subsurface in a 2D plane with Voronoi cells. The method is trans-dimensional in that the number of cells required to parameterize the subsurface is variable, and the cells dynamically move around and multiply or combine as demanded by the data being inverted. This approach allows us to expand our uncertainty analysis of resistivity at depth to more than a single site location, allowing for interactions between model resistivities at different horizontal locations along a traverse over an exploration target. While the model is parameterized in 2D, we efficiently evaluate the forward response using 1D profiles extracted from the model at the common-midpoints of the EM source-receiver pairs. Since the 1D approximation is locally valid at different midpoint locations, the computation time is far lower than is required by a full 2D or 3D simulation. We have applied this method to both synthetic and real CSEM survey data from the Scarborough gas field on the Northwest shelf of Australia, resulting in a spatially variable quantification of resistivity and its uncertainty in 2D. This Bayesian approach results in a large database of 2D models that comprise a posterior probability distribution, which we can subset to test various hypotheses about the range of model structures compatible with the data. For example, we can subset the model distributions to examine the hypothesis that a resistive reservoir extends overs a certain spatial extent. Depending on how this conditions other parts of the model space, light can be shed on the geological viability of the hypothesis. Since tackling spatially variable uncertainty and trade-offs in 2D and 3D is a challenging research problem, the insights gained from this work may prove valuable for subsequent full 2D and 3D Bayesian inversions.

Joint three-dimensional inversion of coupled groundwater flow and heat transfer based on automatic differentiation: sensitivity calculation, verification, and synthetic examples

NASA Astrophysics Data System (ADS)

Rath, V.; Wolf, A.; Bücker, H. M.

2006-10-01

Inverse methods are useful tools not only for deriving estimates of unknown parameters of the subsurface, but also for appraisal of the thus obtained models. While not being neither the most general nor the most efficient methods, Bayesian inversion based on the calculation of the Jacobian of a given forward model can be used to evaluate many quantities useful in this process. The calculation of the Jacobian, however, is computationally expensive and, if done by divided differences, prone to truncation error. Here, automatic differentiation can be used to produce derivative code by source transformation of an existing forward model. We describe this process for a coupled fluid flow and heat transport finite difference code, which is used in a Bayesian inverse scheme to estimate thermal and hydraulic properties and boundary conditions form measured hydraulic potentials and temperatures. The resulting derivative code was validated by comparison to simple analytical solutions and divided differences. Synthetic examples from different flow regimes demonstrate the use of the inverse scheme, and its behaviour in different configurations.

Inverse Modeling of Hydrologic Parameters Using Surface Flux and Runoff Observations in the Community Land Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Yu; Hou, Zhangshuan; Huang, Maoyi

2013-12-10

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) - Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find thatmore » using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent - as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to the different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.« less

Probabilistic inversion of expert assessments to inform projections about Antarctic ice sheet responses

PubMed Central

Wong, Tony E.; Keller, Klaus

2017-01-01

The response of the Antarctic ice sheet (AIS) to changing global temperatures is a key component of sea-level projections. Current projections of the AIS contribution to sea-level changes are deeply uncertain. This deep uncertainty stems, in part, from (i) the inability of current models to fully resolve key processes and scales, (ii) the relatively sparse available data, and (iii) divergent expert assessments. One promising approach to characterizing the deep uncertainty stemming from divergent expert assessments is to combine expert assessments, observations, and simple models by coupling probabilistic inversion and Bayesian inversion. Here, we present a proof-of-concept study that uses probabilistic inversion to fuse a simple AIS model and diverse expert assessments. We demonstrate the ability of probabilistic inversion to infer joint prior probability distributions of model parameters that are consistent with expert assessments. We then confront these inferred expert priors with instrumental and paleoclimatic observational data in a Bayesian inversion. These additional constraints yield tighter hindcasts and projections. We use this approach to quantify how the deep uncertainty surrounding expert assessments affects the joint probability distributions of model parameters and future projections. PMID:29287095

Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

PubMed

Rhodes, Kirsty M; Turner, Rebecca M; White, Ian R; Jackson, Dan; Spiegelhalter, David J; Higgins, Julian P T

2016-12-20

Many meta-analyses combine results from only a small number of studies, a situation in which the between-study variance is imprecisely estimated when standard methods are applied. Bayesian meta-analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta-analysis using data augmentation, in which we represent an informative conjugate prior for between-study variance by pseudo data and use meta-regression for estimation. To assist in this, we derive predictive inverse-gamma distributions for the between-study variance expected in future meta-analyses. These may serve as priors for heterogeneity in new meta-analyses. In a simulation study, we compare approximate Bayesian methods using meta-regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta-regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta-analysis is described. The proposed method facilitates Bayesian meta-analysis in a way that is accessible to applied researchers. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Resolution enhancement of robust Bayesian pre-stack inversion in the frequency domain

NASA Astrophysics Data System (ADS)

Yin, Xingyao; Li, Kun; Zong, Zhaoyun

2016-10-01

AVO/AVA (amplitude variation with an offset or angle) inversion is one of the most practical and useful approaches to estimating model parameters. So far, publications on AVO inversion in the Fourier domain have been quite limited in view of its poor stability and sensitivity to noise compared with time-domain inversion. For the resolution and stability of AVO inversion in the Fourier domain, a novel robust Bayesian pre-stack AVO inversion based on the mixed domain formulation of stationary convolution is proposed which could solve the instability and achieve superior resolution. The Fourier operator will be integrated into the objective equation and it avoids the Fourier inverse transform in our inversion process. Furthermore, the background constraints of model parameters are taken into consideration to improve the stability and reliability of inversion which could compensate for the low-frequency components of seismic signals. Besides, the different frequency components of seismic signals can realize decoupling automatically. This will help us to solve the inverse problem by means of multi-component successive iterations and the convergence precision of the inverse problem could be improved. So, superior resolution compared with the conventional time-domain pre-stack inversion could be achieved easily. Synthetic tests illustrate that the proposed method could achieve high-resolution results with a high degree of agreement with the theoretical model and verify the quality of anti-noise. Finally, applications on a field data case demonstrate that the proposed method could obtain stable inversion results of elastic parameters from pre-stack seismic data in conformity with the real logging data.

Greenhouse Gas Source Attribution: Measurements Modeling and Uncertainty Quantification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Zhen; Safta, Cosmin; Sargsyan, Khachik

2014-09-01

In this project we have developed atmospheric measurement capabilities and a suite of atmospheric modeling and analysis tools that are well suited for verifying emissions of green- house gases (GHGs) on an urban-through-regional scale. We have for the first time applied the Community Multiscale Air Quality (CMAQ) model to simulate atmospheric CO 2 . This will allow for the examination of regional-scale transport and distribution of CO 2 along with air pollutants traditionally studied using CMAQ at relatively high spatial and temporal resolution with the goal of leveraging emissions verification efforts for both air quality and climate. We have developedmore » a bias-enhanced Bayesian inference approach that can remedy the well-known problem of transport model errors in atmospheric CO 2 inversions. We have tested the approach using data and model outputs from the TransCom3 global CO 2 inversion comparison project. We have also performed two prototyping studies on inversion approaches in the generalized convection-diffusion context. One of these studies employed Polynomial Chaos Expansion to accelerate the evaluation of a regional transport model and enable efficient Markov Chain Monte Carlo sampling of the posterior for Bayesian inference. The other approach uses de- terministic inversion of a convection-diffusion-reaction system in the presence of uncertainty. These approaches should, in principle, be applicable to realistic atmospheric problems with moderate adaptation. We outline a regional greenhouse gas source inference system that integrates (1) two ap- proaches of atmospheric dispersion simulation and (2) a class of Bayesian inference and un- certainty quantification algorithms. We use two different and complementary approaches to simulate atmospheric dispersion. Specifically, we use a Eulerian chemical transport model CMAQ and a Lagrangian Particle Dispersion Model - FLEXPART-WRF. These two models share the same WRF assimilated meteorology fields, making it possible to perform a hybrid simulation, in which the Eulerian model (CMAQ) can be used to compute the initial condi- tion needed by the Lagrangian model, while the source-receptor relationships for a large state vector can be efficiently computed using the Lagrangian model in its backward mode. In ad- dition, CMAQ has a complete treatment of atmospheric chemistry of a suite of traditional air pollutants, many of which could help attribute GHGs from different sources. The inference of emissions sources using atmospheric observations is cast as a Bayesian model calibration problem, which is solved using a variety of Bayesian techniques, such as the bias-enhanced Bayesian inference algorithm, which accounts for the intrinsic model deficiency, Polynomial Chaos Expansion to accelerate model evaluation and Markov Chain Monte Carlo sampling, and Karhunen-Lo %60 eve (KL) Expansion to reduce the dimensionality of the state space. We have established an atmospheric measurement site in Livermore, CA and are collect- ing continuous measurements of CO 2 , CH 4 and other species that are typically co-emitted with these GHGs. Measurements of co-emitted species can assist in attributing the GHGs to different emissions sectors. Automatic calibrations using traceable standards are performed routinely for the gas-phase measurements. We are also collecting standard meteorological data at the Livermore site as well as planetary boundary height measurements using a ceilometer. The location of the measurement site is well suited to sample air transported between the San Francisco Bay area and the California Central Valley.« less

Bayesian inference in geomagnetism

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.

Waveform-based Bayesian full moment tensor inversion and uncertainty determination for the induced seismicity in an oil/gas field

NASA Astrophysics Data System (ADS)

Gu, Chen; Marzouk, Youssef M.; Toksöz, M. Nafi

2018-03-01

Small earthquakes occur due to natural tectonic motions and are induced by oil and gas production processes. In many oil/gas fields and hydrofracking processes, induced earthquakes result from fluid extraction or injection. The locations and source mechanisms of these earthquakes provide valuable information about the reservoirs. Analysis of induced seismic events has mostly assumed a double-couple source mechanism. However, recent studies have shown a non-negligible percentage of non-double-couple components of source moment tensors in hydraulic fracturing events, assuming a full moment tensor source mechanism. Without uncertainty quantification of the moment tensor solution, it is difficult to determine the reliability of these source models. This study develops a Bayesian method to perform waveform-based full moment tensor inversion and uncertainty quantification for induced seismic events, accounting for both location and velocity model uncertainties. We conduct tests with synthetic events to validate the method, and then apply our newly developed Bayesian inversion approach to real induced seismicity in an oil/gas field in the sultanate of Oman—determining the uncertainties in the source mechanism and in the location of that event.

A gradient-based model parametrization using Bernstein polynomials in Bayesian inversion of surface wave dispersion

NASA Astrophysics Data System (ADS)

Gosselin, Jeremy M.; Dosso, Stan E.; Cassidy, John F.; Quijano, Jorge E.; Molnar, Sheri; Dettmer, Jan

2017-10-01

This paper develops and applies a Bernstein-polynomial parametrization to efficiently represent general, gradient-based profiles in nonlinear geophysical inversion, with application to ambient-noise Rayleigh-wave dispersion data. Bernstein polynomials provide a stable parametrization in that small perturbations to the model parameters (basis-function coefficients) result in only small perturbations to the geophysical parameter profile. A fully nonlinear Bayesian inversion methodology is applied to estimate shear wave velocity (VS) profiles and uncertainties from surface wave dispersion data extracted from ambient seismic noise. The Bayesian information criterion is used to determine the appropriate polynomial order consistent with the resolving power of the data. Data error correlations are accounted for in the inversion using a parametric autoregressive model. The inversion solution is defined in terms of marginal posterior probability profiles for VS as a function of depth, estimated using Metropolis-Hastings sampling with parallel tempering. This methodology is applied to synthetic dispersion data as well as data processed from passive array recordings collected on the Fraser River Delta in British Columbia, Canada. Results from this work are in good agreement with previous studies, as well as with co-located invasive measurements. The approach considered here is better suited than `layered' modelling approaches in applications where smooth gradients in geophysical parameters are expected, such as soil/sediment profiles. Further, the Bernstein polynomial representation is more general than smooth models based on a fixed choice of gradient type (e.g. power-law gradient) because the form of the gradient is determined objectively by the data, rather than by a subjective parametrization choice.

Action Understanding as Inverse Planning

ERIC Educational Resources Information Center

Baker, Chris L.; Saxe, Rebecca; Tenenbaum, Joshua B.

2009-01-01

Humans are adept at inferring the mental states underlying other agents' actions, such as goals, beliefs, desires, emotions and other thoughts. We propose a computational framework based on Bayesian inverse planning for modeling human action understanding. The framework represents an intuitive theory of intentional agents' behavior based on the…

Adaptive framework to better characterize errors of apriori fluxes and observational residuals in a Bayesian setup for the urban flux inversions.

NASA Astrophysics Data System (ADS)

Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Karion, A.; Mueller, K.; Gourdji, S.; Martin, C.; Whetstone, J. R.

2017-12-01

The National Institute of Standards and Technology (NIST) supports the North-East Corridor Baltimore Washington (NEC-B/W) project and Indianapolis Flux Experiment (INFLUX) aiming to quantify sources of Greenhouse Gas (GHG) emissions as well as their uncertainties. These projects employ different flux estimation methods including top-down inversion approaches. The traditional Bayesian inversion method estimates emission distributions by updating prior information using atmospheric observations of Green House Gases (GHG) coupled to an atmospheric and dispersion model. The magnitude of the update is dependent upon the observed enhancement along with the assumed errors such as those associated with prior information and the atmospheric transport and dispersion model. These errors are specified within the inversion covariance matrices. The assumed structure and magnitude of the specified errors can have large impact on the emission estimates from the inversion. The main objective of this work is to build a data-adaptive model for these covariances matrices. We construct a synthetic data experiment using a Kalman Filter inversion framework (Lopez et al., 2017) employing different configurations of transport and dispersion model and an assumed prior. Unlike previous traditional Bayesian approaches, we estimate posterior emissions using regularized sample covariance matrices associated with prior errors to investigate whether the structure of the matrices help to better recover our hypothetical true emissions. To incorporate transport model error, we use ensemble of transport models combined with space-time analytical covariance to construct a covariance that accounts for errors in space and time. A Kalman Filter is then run using these covariances along with Maximum Likelihood Estimates (MLE) of the involved parameters. Preliminary results indicate that specifying sptio-temporally varying errors in the error covariances can improve the flux estimates and uncertainties. We also demonstrate that differences between the modeled and observed meteorology can be used to predict uncertainties associated with atmospheric transport and dispersion modeling which can help improve the skill of an inversion at urban scales.

Earth's core and inner-core resonances from analysis of VLBI nutation and superconducting gravimeter data

NASA Astrophysics Data System (ADS)

Rosat, S.; Lambert, S. B.; Gattano, C.; Calvo, M.

2017-01-01

Geophysical parameters of the deep Earth's interior can be evaluated through the resonance effects associated with the core and inner-core wobbles on the forced nutations of the Earth's figure axis, as observed by very long baseline interferometry (VLBI), or on the diurnal tidal waves, retrieved from the time-varying surface gravity recorded by superconducting gravimeters (SGs). In this paper, we inverse for the rotational mode parameters from both techniques to retrieve geophysical parameters of the deep Earth. We analyse surface gravity data from 15 SG stations and VLBI delays accumulated over the last 35 yr. We show existing correlations between several basic Earth parameters and then decide to inverse for the rotational modes parameters. We employ a Bayesian inversion based on the Metropolis-Hastings algorithm with a Markov-chain Monte Carlo method. We obtain estimates of the free core nutation resonant period and quality factor that are consistent for both techniques. We also attempt an inversion for the free inner-core nutation (FICN) resonant period from gravity data. The most probable solution gives a period close to the annual prograde term (or S1 tide). However the 95 per cent confidence interval extends the possible values between roughly 28 and 725 d for gravity, and from 362 to 414 d from nutation data, depending on the prior bounds. The precisions of the estimated long-period nutation and respective small diurnal tidal constituents are hence not accurate enough for a correct determination of the FICN complex frequency.

Application of Bayesian Approach in Cancer Clinical Trial

PubMed Central

Bhattacharjee, Atanu

2014-01-01

The application of Bayesian approach in clinical trials becomes more useful over classical method. It is beneficial from design to analysis phase. The straight forward statement is possible to obtain through Bayesian about the drug treatment effect. Complex computational problems are simple to handle with Bayesian techniques. The technique is only feasible to performing presence of prior information of the data. The inference is possible to establish through posterior estimates. However, some limitations are present in this method. The objective of this work was to explore the several merits and demerits of Bayesian approach in cancer research. The review of the technique will be helpful for the clinical researcher involved in the oncology to explore the limitation and power of Bayesian techniques. PMID:29147387

A comparative study of minimum norm inverse methods for MEG imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leahy, R.M.; Mosher, J.C.; Phillips, J.W.

1996-07-01

The majority of MEG imaging techniques currently in use fall into the general class of (weighted) minimum norm methods. The minimization of a norm is used as the basis for choosing one from a generally infinite set of solutions that provide an equally good fit to the data. This ambiguity in the solution arises from the inherent non- uniqueness of the continuous inverse problem and is compounded by the imbalance between the relatively small number of measurements and the large number of source voxels. Here we present a unified view of the minimum norm methods and describe how we canmore » use Tikhonov regularization to avoid instabilities in the solutions due to noise. We then compare the performance of regularized versions of three well known linear minimum norm methods with the non-linear iteratively reweighted minimum norm method and a Bayesian approach.« less

Transdimensional Bayesian tomography of the lowermost mantle from shear waves

NASA Astrophysics Data System (ADS)

Richardson, C.; Mousavi, S. S.; Tkalcic, H.; Masters, G.

2017-12-01

The lowermost layer of the mantle, known as D'', is a complex region that contains significant heterogeneities on different spatial scales and a wide range of physical and chemical features such as partial melting, seismic anisotropy, and variations in thermal and chemical composition. The most powerful tools we have to probe this region are seismic waves and corresponding imaging techniques such as tomography. Recently, we developed compressional velocity tomograms of D'' using a transdimensional Bayesian inversion, where the model parameterization is not explicit and regularization is not required. This has produced a far more nuanced P-wave velocity model of D'' than that from traditional S-wave tomography. We also note that P-wave models of D'' vary much more significantly among various research groups than the corresponding S-wave models. This study therefore seeks to develop a new S-wave velocity model of D'' underneath Australia by using predominantly ScS-S differential travel times measured through waveform correlation and Bayesian transdimensional inversion to further understand and characterize heterogeneities in D''. We used events at epicentral distances between 45 and 75 degrees from stations in Australia at depths of over 200 km and with magnitudes between 6.0 and 6.7. Because of globally incomplete coverage of station and earthquake locations, a major limitation of deep earth tomography has been the explicit parameterization of the region of interest. Explicit parameterization has been foundational in most studies, but faces inherent problems of either over-smoothing the data, or allowing for too much noise. To avoid this, we use spherical Voronoi polygons, which allow for a high level of flexibility as the polygons can grow, shrink, or be altogether deleted throughout a sequence of iterations. Our technique also yields highly desired model parameter uncertainties. While there is little doubt that D'' is heterogeneous, there is still much that is unclear about the extent and spatial distribution of different heterogeneous domains, as there are open questions about their dynamics and chemical interactions in the context of the surrounding mantle and outer core. In this context, our goal is also to quantify and understand the differences between S-wave and P-wave velocity tomographic models.

Quantifying the influences of spectral resolution on uncertainty in leaf trait estimates through a Bayesian approach to RTM inversion

DOE PAGES

Shiklomanov, Alexey N.; Dietze, Michael C.; Viskari, Toni; ...

2016-06-09

The remote monitoring of plant canopies is critically needed for understanding of terrestrial ecosystem mechanics and biodiversity as well as capturing the short- to long-term responses of vegetation to disturbance and climate change. A variety of orbital, sub-orbital, and field instruments have been used to retrieve optical spectral signals and to study different vegetation properties such as plant biochemistry, nutrient cycling, physiology, water status, and stress. Radiative transfer models (RTMs) provide a mechanistic link between vegetation properties and observed spectral features, and RTM spectral inversion is a useful framework for estimating these properties from spectral data. However, existing approaches tomore » RTM spectral inversion are typically limited by the inability to characterize uncertainty in parameter estimates. Here, we introduce a Bayesian algorithm for the spectral inversion of the PROSPECT 5 leaf RTM that is distinct from past approaches in two important ways: First, the algorithm only uses reflectance and does not require transmittance observations, which have been plagued by a variety of measurement and equipment challenges. Second, the output is not a point estimate for each parameter but rather the joint probability distribution that includes estimates of parameter uncertainties and covariance structure. We validated our inversion approach using a database of leaf spectra together with measurements of equivalent water thickness (EWT) and leaf dry mass per unit area (LMA). The parameters estimated by our inversion were able to accurately reproduce the observed reflectance (RMSE VIS = 0.0063, RMSE NIR-SWIR = 0.0098) and transmittance (RMSE VIS = 0.0404, RMSE NIR-SWIR = 0.0551) for both broadleaved and conifer species. Inversion estimates of EWT and LMA for broadleaved species agreed well with direct measurements (CV EWT = 18.8%, CV LMA = 24.5%), while estimates for conifer species were less accurate (CV EWT = 53.2%, CV LMA = 63.3%). To examine the influence of spectral resolution on parameter uncertainty, we simulated leaf reflectance as observed by ten common remote sensing platforms with varying spectral configurations and performed a Bayesian inversion on the resulting spectra. We found that full-range hyperspectral platforms were able to retrieve all parameters accurately and precisely, while the parameter estimates of multispectral platforms were much less precise and prone to bias at high and low values. We also observed that variations in the width and location of spectral bands influenced the shape of the covariance structure of parameter estimates. Lastly, our Bayesian spectral inversion provides a powerful and versatile framework for future RTM development and single- and multi-instrumental remote sensing of vegetation.« less

Quantifying the influences of spectral resolution on uncertainty in leaf trait estimates through a Bayesian approach to RTM inversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shiklomanov, Alexey N.; Dietze, Michael C.; Viskari, Toni

The remote monitoring of plant canopies is critically needed for understanding of terrestrial ecosystem mechanics and biodiversity as well as capturing the short- to long-term responses of vegetation to disturbance and climate change. A variety of orbital, sub-orbital, and field instruments have been used to retrieve optical spectral signals and to study different vegetation properties such as plant biochemistry, nutrient cycling, physiology, water status, and stress. Radiative transfer models (RTMs) provide a mechanistic link between vegetation properties and observed spectral features, and RTM spectral inversion is a useful framework for estimating these properties from spectral data. However, existing approaches tomore » RTM spectral inversion are typically limited by the inability to characterize uncertainty in parameter estimates. Here, we introduce a Bayesian algorithm for the spectral inversion of the PROSPECT 5 leaf RTM that is distinct from past approaches in two important ways: First, the algorithm only uses reflectance and does not require transmittance observations, which have been plagued by a variety of measurement and equipment challenges. Second, the output is not a point estimate for each parameter but rather the joint probability distribution that includes estimates of parameter uncertainties and covariance structure. We validated our inversion approach using a database of leaf spectra together with measurements of equivalent water thickness (EWT) and leaf dry mass per unit area (LMA). The parameters estimated by our inversion were able to accurately reproduce the observed reflectance (RMSE VIS = 0.0063, RMSE NIR-SWIR = 0.0098) and transmittance (RMSE VIS = 0.0404, RMSE NIR-SWIR = 0.0551) for both broadleaved and conifer species. Inversion estimates of EWT and LMA for broadleaved species agreed well with direct measurements (CV EWT = 18.8%, CV LMA = 24.5%), while estimates for conifer species were less accurate (CV EWT = 53.2%, CV LMA = 63.3%). To examine the influence of spectral resolution on parameter uncertainty, we simulated leaf reflectance as observed by ten common remote sensing platforms with varying spectral configurations and performed a Bayesian inversion on the resulting spectra. We found that full-range hyperspectral platforms were able to retrieve all parameters accurately and precisely, while the parameter estimates of multispectral platforms were much less precise and prone to bias at high and low values. We also observed that variations in the width and location of spectral bands influenced the shape of the covariance structure of parameter estimates. Lastly, our Bayesian spectral inversion provides a powerful and versatile framework for future RTM development and single- and multi-instrumental remote sensing of vegetation.« less

Decomposing Large Inverse Problems with an Augmented Lagrangian Approach: Application to Joint Inversion of Body-Wave Travel Times and Surface-Wave Dispersion Measurements

NASA Astrophysics Data System (ADS)

Reiter, D. T.; Rodi, W. L.

2015-12-01

Constructing 3D Earth models through the joint inversion of large geophysical data sets presents numerous theoretical and practical challenges, especially when diverse types of data and model parameters are involved. Among the challenges are the computational complexity associated with large data and model vectors and the need to unify differing model parameterizations, forward modeling methods and regularization schemes within a common inversion framework. The challenges can be addressed in part by decomposing the inverse problem into smaller, simpler inverse problems that can be solved separately, providing one knows how to merge the separate inversion results into an optimal solution of the full problem. We have formulated an approach to the decomposition of large inverse problems based on the augmented Lagrangian technique from optimization theory. As commonly done, we define a solution to the full inverse problem as the Earth model minimizing an objective function motivated, for example, by a Bayesian inference formulation. Our decomposition approach recasts the minimization problem equivalently as the minimization of component objective functions, corresponding to specified data subsets, subject to the constraints that the minimizing models be equal. A standard optimization algorithm solves the resulting constrained minimization problems by alternating between the separate solution of the component problems and the updating of Lagrange multipliers that serve to steer the individual solution models toward a common model solving the full problem. We are applying our inversion method to the reconstruction of the·crust and upper-mantle seismic velocity structure across Eurasia.· Data for the inversion comprise a large set of P and S body-wave travel times·and fundamental and first-higher mode Rayleigh-wave group velocities.

Bayesian inference of ice thickness from remote-sensing data

NASA Astrophysics Data System (ADS)

Werder, Mauro A.; Huss, Matthias

2017-04-01

Knowledge about ice thickness and volume is indispensable for studying ice dynamics, future sea-level rise due to glacier melt or their contribution to regional hydrology. Accurate measurements of glacier thickness require on-site work, usually employing radar techniques. However, these field measurements are time consuming, expensive and sometime downright impossible. Conversely, measurements of the ice surface, namely elevation and flow velocity, are becoming available world-wide through remote sensing. The model of Farinotti et al. (2009) calculates ice thicknesses based on a mass conservation approach paired with shallow ice physics using estimates of the surface mass balance. The presented work applies a Bayesian inference approach to estimate the parameters of a modified version of this forward model by fitting it to both measurements of surface flow speed and of ice thickness. The inverse model outputs ice thickness as well the distribution of the error. We fit the model to ten test glaciers and ice caps and quantify the improvements of thickness estimates through the usage of surface ice flow measurements.

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

Bowhead whale localization using time-difference-of-arrival data from asynchronous recorders.

PubMed

Warner, Graham A; Dosso, Stan E; Hannay, David E

2017-03-01

This paper estimates bowhead whale locations and uncertainties using nonlinear Bayesian inversion of the time-difference-of-arrival (TDOA) of low-frequency whale calls recorded on onmi-directional asynchronous recorders in the shallow waters of the northeastern Chukchi Sea, Alaska. A Y-shaped cluster of seven autonomous ocean-bottom hydrophones, separated by 0.5-9.2 km, was deployed for several months over which time their clocks drifted out of synchronization. Hundreds of recorded whale calls are manually associated between recorders. The TDOA between hydrophone pairs are calculated from filtered waveform cross correlations and depend on the whale locations, hydrophone locations, relative recorder clock offsets, and effective waveguide sound speed. A nonlinear Bayesian inversion estimates all of these parameters and their uncertainties as well as data error statistics. The problem is highly nonlinear and a linearized inversion did not produce physically realistic results. Whale location uncertainties from nonlinear inversion can be low enough to allow accurate tracking of migrating whales that vocalize repeatedly over several minutes. Estimates of clock drift rates are obtained from inversions of TDOA data over two weeks and agree with corresponding estimates obtained from long-time averaged ambient noise cross correlations. The inversion is suitable for application to large data sets of manually or automatically detected whale calls.

Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model

NASA Astrophysics Data System (ADS)

Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L. Ruby

2013-12-01

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Both deterministic least-square fitting and stochastic Markov-chain Monte Carlo (MCMC)-Bayesian inversion approaches are evaluated by applying them to CLM4 at selected sites with different climate and soil conditions. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the sampling-based stochastic inversion approaches provides significant improvements in the model simulations compared to using default CLM4 parameter values, and that as more information comes in, the predictive intervals (ranges of posterior distributions) of the calibrated parameters become narrower. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

A Bayesian analysis of redshifted 21-cm H I signal and foregrounds: simulations for LOFAR

NASA Astrophysics Data System (ADS)

Ghosh, Abhik; Koopmans, Léon V. E.; Chapman, E.; Jelić, V.

2015-09-01

Observations of the epoch of reionization (EoR) using the 21-cm hyperfine emission of neutral hydrogen (H I) promise to open an entirely new window on the formation of the first stars, galaxies and accreting black holes. In order to characterize the weak 21-cm signal, we need to develop imaging techniques that can reconstruct the extended emission very precisely. Here, we present an inversion technique for LOw Frequency ARray (LOFAR) baselines at the North Celestial Pole (NCP), based on a Bayesian formalism with optimal spatial regularization, which is used to reconstruct the diffuse foreground map directly from the simulated visibility data. We notice that the spatial regularization de-noises the images to a large extent, allowing one to recover the 21-cm power spectrum over a considerable k⊥-k∥ space in the range 0.03 Mpc-1 < k⊥ < 0.19 Mpc-1 and 0.14 Mpc-1 < k∥ < 0.35 Mpc-1 without subtracting the noise power spectrum. We find that, in combination with using generalized morphological component analysis (GMCA), a non-parametric foreground removal technique, we can mostly recover the spherical average power spectrum within 2σ statistical fluctuations for an input Gaussian random root-mean-square noise level of 60 mK in the maps after 600 h of integration over a 10-MHz bandwidth.

Bayesian image reconstruction for improving detection performance of muon tomography.

PubMed

Wang, Guobao; Schultz, Larry J; Qi, Jinyi

2009-05-01

Muon tomography is a novel technology that is being developed for detecting high-Z materials in vehicles or cargo containers. Maximum likelihood methods have been developed for reconstructing the scattering density image from muon measurements. However, the instability of maximum likelihood estimation often results in noisy images and low detectability of high-Z targets. In this paper, we propose using regularization to improve the image quality of muon tomography. We formulate the muon reconstruction problem in a Bayesian framework by introducing a prior distribution on scattering density images. An iterative shrinkage algorithm is derived to maximize the log posterior distribution. At each iteration, the algorithm obtains the maximum a posteriori update by shrinking an unregularized maximum likelihood update. Inverse quadratic shrinkage functions are derived for generalized Laplacian priors and inverse cubic shrinkage functions are derived for generalized Gaussian priors. Receiver operating characteristic studies using simulated data demonstrate that the Bayesian reconstruction can greatly improve the detection performance of muon tomography.

Superresolution radar imaging based on fast inverse-free sparse Bayesian learning for multiple measurement vectors

NASA Astrophysics Data System (ADS)

He, Xingyu; Tong, Ningning; Hu, Xiaowei

2018-01-01

Compressive sensing has been successfully applied to inverse synthetic aperture radar (ISAR) imaging of moving targets. By exploiting the block sparse structure of the target image, sparse solution for multiple measurement vectors (MMV) can be applied in ISAR imaging and a substantial performance improvement can be achieved. As an effective sparse recovery method, sparse Bayesian learning (SBL) for MMV involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size. To address this problem, we develop a fast inverse-free (IF) SBL method for MMV. A relaxed evidence lower bound (ELBO), which is computationally more amiable than the traditional ELBO used by SBL, is obtained by invoking fundamental property for smooth functions. A variational expectation-maximization scheme is then employed to maximize the relaxed ELBO, and a computationally efficient IF-MSBL algorithm is proposed. Numerical results based on simulated and real data show that the proposed method can reconstruct row sparse signal accurately and obtain clear superresolution ISAR images. Moreover, the running time and computational complexity are reduced to a great extent compared with traditional SBL methods.

Variational Bayesian Inversion of Quasi-Localized Seismic Attributes for the Spatial Distribution of Geological Facies

NASA Astrophysics Data System (ADS)

Nawaz, Muhammad Atif; Curtis, Andrew

2018-04-01

We introduce a new Bayesian inversion method that estimates the spatial distribution of geological facies from attributes of seismic data, by showing how the usual probabilistic inverse problem can be solved using an optimization framework still providing full probabilistic results. Our mathematical model consists of seismic attributes as observed data, which are assumed to have been generated by the geological facies. The method infers the post-inversion (posterior) probability density of the facies plus some other unknown model parameters, from the seismic attributes and geological prior information. Most previous research in this domain is based on the localized likelihoods assumption, whereby the seismic attributes at a location are assumed to depend on the facies only at that location. Such an assumption is unrealistic because of imperfect seismic data acquisition and processing, and fundamental limitations of seismic imaging methods. In this paper, we relax this assumption: we allow probabilistic dependence between seismic attributes at a location and the facies in any neighbourhood of that location through a spatial filter. We term such likelihoods quasi-localized.

A Bayesian inversion for slip distribution of 1 Apr 2007 Mw8.1 Solomon Islands Earthquake

NASA Astrophysics Data System (ADS)

Chen, T.; Luo, H.

2013-12-01

On 1 Apr 2007 the megathrust Mw8.1 Solomon Islands earthquake occurred in the southeast pacific along the New Britain subduction zone. 102 vertical displacement measurements over the southeastern end of the rupture zone from two field surveys after this event provide a unique constraint for slip distribution inversion. In conventional inversion method (such as bounded variable least squares) the smoothing parameter that determines the relative weight placed on fitting the data versus smoothing the slip distribution is often subjectively selected at the bend of the trade-off curve. Here a fully probabilistic inversion method[Fukuda,2008] is applied to estimate distributed slip and smoothing parameter objectively. The joint posterior probability density function of distributed slip and the smoothing parameter is formulated under a Bayesian framework and sampled with Markov chain Monte Carlo method. We estimate the spatial distribution of dip slip associated with the 1 Apr 2007 Solomon Islands earthquake with this method. Early results show a shallower dip angle than previous study and highly variable dip slip both along-strike and down-dip.

Bayesian model reduction and empirical Bayes for group (DCM) studies

PubMed Central

Friston, Karl J.; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E.; van Wijk, Bernadette C.M.; Ziegler, Gabriel; Zeidman, Peter

2016-01-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. PMID:26569570

Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.

PubMed

Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi

2015-02-01

We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.

An adaptive Bayesian inference algorithm to estimate the parameters of a hazardous atmospheric release

NASA Astrophysics Data System (ADS)

Rajaona, Harizo; Septier, François; Armand, Patrick; Delignon, Yves; Olry, Christophe; Albergel, Armand; Moussafir, Jacques

2015-12-01

In the eventuality of an accidental or intentional atmospheric release, the reconstruction of the source term using measurements from a set of sensors is an important and challenging inverse problem. A rapid and accurate estimation of the source allows faster and more efficient action for first-response teams, in addition to providing better damage assessment. This paper presents a Bayesian probabilistic approach to estimate the location and the temporal emission profile of a pointwise source. The release rate is evaluated analytically by using a Gaussian assumption on its prior distribution, and is enhanced with a positivity constraint to improve the estimation. The source location is obtained by the means of an advanced iterative Monte-Carlo technique called Adaptive Multiple Importance Sampling (AMIS), which uses a recycling process at each iteration to accelerate its convergence. The proposed methodology is tested using synthetic and real concentration data in the framework of the Fusion Field Trials 2007 (FFT-07) experiment. The quality of the obtained results is comparable to those coming from the Markov Chain Monte Carlo (MCMC) algorithm, a popular Bayesian method used for source estimation. Moreover, the adaptive processing of the AMIS provides a better sampling efficiency by reusing all the generated samples.

Bayesian model calibration of computational models in velocimetry diagnosed dynamic compression experiments.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Justin; Hund, Lauren

2017-02-01

Dynamic compression experiments are being performed on complicated materials using increasingly complex drivers. The data produced in these experiments are beginning to reach a regime where traditional analysis techniques break down; requiring the solution of an inverse problem. A common measurement in dynamic experiments is an interface velocity as a function of time, and often this functional output can be simulated using a hydrodynamics code. Bayesian model calibration is a statistical framework to estimate inputs into a computational model in the presence of multiple uncertainties, making it well suited to measurements of this type. In this article, we apply Bayesianmore » model calibration to high pressure (250 GPa) ramp compression measurements in tantalum. We address several issues speci c to this calibration including the functional nature of the output as well as parameter and model discrepancy identi ability. Speci cally, we propose scaling the likelihood function by an e ective sample size rather than modeling the autocorrelation function to accommodate the functional output and propose sensitivity analyses using the notion of `modularization' to assess the impact of experiment-speci c nuisance input parameters on estimates of material properties. We conclude that the proposed Bayesian model calibration procedure results in simple, fast, and valid inferences on the equation of state parameters for tantalum.« less

Bayesian probabilistic approach for inverse source determination from limited and noisy chemical or biological sensor concentration measurements

NASA Astrophysics Data System (ADS)

Yee, Eugene

2007-04-01

Although a great deal of research effort has been focused on the forward prediction of the dispersion of contaminants (e.g., chemical and biological warfare agents) released into the turbulent atmosphere, much less work has been directed toward the inverse prediction of agent source location and strength from the measured concentration, even though the importance of this problem for a number of practical applications is obvious. In general, the inverse problem of source reconstruction is ill-posed and unsolvable without additional information. It is demonstrated that a Bayesian probabilistic inferential framework provides a natural and logically consistent method for source reconstruction from a limited number of noisy concentration data. In particular, the Bayesian approach permits one to incorporate prior knowledge about the source as well as additional information regarding both model and data errors. The latter enables a rigorous determination of the uncertainty in the inference of the source parameters (e.g., spatial location, emission rate, release time, etc.), hence extending the potential of the methodology as a tool for quantitative source reconstruction. A model (or, source-receptor relationship) that relates the source distribution to the concentration data measured by a number of sensors is formulated, and Bayesian probability theory is used to derive the posterior probability density function of the source parameters. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source-receptor relationship, is described. Furthermore, we describe the application of efficient stochastic algorithms based on Markov chain Monte Carlo (MCMC) for sampling from the posterior distribution of the source parameters, the latter of which is required to undertake the Bayesian computation. The Bayesian inferential methodology for source reconstruction is validated against real dispersion data for two cases involving contaminant dispersion in highly disturbed flows over urban and complex environments where the idealizations of horizontal homogeneity and/or temporal stationarity in the flow cannot be applied to simplify the problem. Furthermore, the methodology is applied to the case of reconstruction of multiple sources.

Sharp Boundary Inversion of 2D Magnetotelluric Data using Bayesian Method.

NASA Astrophysics Data System (ADS)

Zhou, S.; Huang, Q.

2017-12-01

Normally magnetotelluric(MT) inversion method cannot show the distribution of underground resistivity with clear boundary, even if there are obviously different blocks. Aiming to solve this problem, we develop a Bayesian structure to inverse 2D MT sharp boundary data, using boundary location and inside resistivity as the random variables. Firstly, we use other MT inversion results, like ModEM, to analyze the resistivity distribution roughly. Then, we select the suitable random variables and change its data format to traditional staggered grid parameters, which can be used to do finite difference forward part. Finally, we can shape the posterior probability density(PPD), which contains all the prior information and model-data correlation, by Markov Chain Monte Carlo(MCMC) sampling from prior distribution. The depth, resistivity and their uncertainty can be valued. It also works for sensibility estimation. We applied the method to a synthetic case, which composes two large abnormal blocks in a trivial background. We consider the boundary smooth and the near true model weight constrains that mimic joint inversion or constrained inversion, then we find that the model results a more precise and focused depth distribution. And we also test the inversion without constrains and find that the boundary could also be figured, though not as well. Both inversions have a good valuation of resistivity. The constrained result has a lower root mean square than ModEM inversion result. The data sensibility obtained via PPD shows that the resistivity is the most sensible, center depth comes second and both sides are the worst.

Trans-Dimensional Bayesian Imaging of 3-D Crustal and Upper Mantle Structure in Northeast Asia

NASA Astrophysics Data System (ADS)

Kim, S.; Tkalcic, H.; Rhie, J.; Chen, Y.

2016-12-01

Imaging 3-D structures using stepwise inversions of ambient noise and receiver function data is now a routine work. Here, we carry out the inversion in the trans-dimensional and hierarchical extension of the Bayesian framework to obtain rigorous estimates of uncertainty and high-resolution images of crustal and upper mantle structures beneath Northeast (NE) Asia. The methods inherently account for data sensitivities by means of using adaptive parameterizations and treating data noise as free parameters. Therefore, parsimonious results from the methods are balanced out between model complexity and data fitting. This allows fully exploiting data information, preventing from over- or under-estimation of the data fit, and increases model resolution. In addition, the reliability of results is more rigorously checked through the use of Bayesian uncertainties. It is shown by various synthetic recovery tests that complex and spatially variable features are well resolved in our resulting images of NE Asia. Rayleigh wave phase and group velocity tomograms (8-70 s), a 3-D shear-wave velocity model from depth inversions of the estimated dispersion maps, and regional 3-D models (NE China, the Korean Peninsula, and the Japanese islands) from joint inversions with receiver function data of dense networks are presented. High-resolution models are characterized by a number of tectonically meaningful features. We focus our interpretation on complex patterns of sub-lithospheric low velocity structures that extend from back-arc regions to continental margins. We interpret the anomalies in conjunction with distal and distributed intraplate volcanoes in NE Asia. Further discussion on other imaged features will be presented.

Bayesian ISOLA: new tool for automated centroid moment tensor inversion

NASA Astrophysics Data System (ADS)

Vackář, Jiří; Burjánek, Jan; Gallovič, František; Zahradník, Jiří; Clinton, John

2017-04-01

Focal mechanisms are important for understanding seismotectonics of a region, and they serve as a basic input for seismic hazard assessment. Usually, the point source approximation and the moment tensor (MT) are used. We have developed a new, fully automated tool for the centroid moment tensor (CMT) inversion in a Bayesian framework. It includes automated data retrieval, data selection where station components with various instrumental disturbances and high signal-to-noise are rejected, and full-waveform inversion in a space-time grid around a provided hypocenter. The method is innovative in the following aspects: (i) The CMT inversion is fully automated, no user interaction is required, although the details of the process can be visually inspected latter on many figures which are automatically plotted.(ii) The automated process includes detection of disturbances based on MouseTrap code, so disturbed recordings do not affect inversion.(iii) A data covariance matrix calculated from pre-event noise yields an automated weighting of the station recordings according to their noise levels and also serves as an automated frequency filter suppressing noisy frequencies.(iv) Bayesian approach is used, so not only the best solution is obtained, but also the posterior probability density function.(v) A space-time grid search effectively combined with the least-squares inversion of moment tensor components speeds up the inversion and allows to obtain more accurate results compared to stochastic methods. The method has been tested on synthetic and observed data. It has been tested by comparison with manually processed moment tensors of all events greater than M≥3 in the Swiss catalogue over 16 years using data available at the Swiss data center (http://arclink.ethz.ch). The quality of the results of the presented automated process is comparable with careful manual processing of data. The software package programmed in Python has been designed to be as versatile as possible in order to be applicable in various networks ranging from local to regional. The method can be applied either to the everyday network data flow, or to process large previously existing earthquake catalogues and data sets.

Low frequency full waveform seismic inversion within a tree based Bayesian framework

NASA Astrophysics Data System (ADS)

Ray, Anandaroop; Kaplan, Sam; Washbourne, John; Albertin, Uwe

2018-01-01

Limited illumination, insufficient offset, noisy data and poor starting models can pose challenges for seismic full waveform inversion. We present an application of a tree based Bayesian inversion scheme which attempts to mitigate these problems by accounting for data uncertainty while using a mildly informative prior about subsurface structure. We sample the resulting posterior model distribution of compressional velocity using a trans-dimensional (trans-D) or Reversible Jump Markov chain Monte Carlo method in the wavelet transform domain of velocity. This allows us to attain rapid convergence to a stationary distribution of posterior models while requiring a limited number of wavelet coefficients to define a sampled model. Two synthetic, low frequency, noisy data examples are provided. The first example is a simple reflection + transmission inverse problem, and the second uses a scaled version of the Marmousi velocity model, dominated by reflections. Both examples are initially started from a semi-infinite half-space with incorrect background velocity. We find that the trans-D tree based approach together with parallel tempering for navigating rugged likelihood (i.e. misfit) topography provides a promising, easily generalized method for solving large-scale geophysical inverse problems which are difficult to optimize, but where the true model contains a hierarchy of features at multiple scales.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khosla, D.; Singh, M.

The estimation of three-dimensional dipole current sources on the cortical surface from the measured magnetoencephalogram (MEG) is a highly under determined inverse problem as there are many {open_quotes}feasible{close_quotes} images which are consistent with the MEG data. Previous approaches to this problem have concentrated on the use of weighted minimum norm inverse methods. While these methods ensure a unique solution, they often produce overly smoothed solutions and exhibit severe sensitivity to noise. In this paper we explore the maximum entropy approach to obtain better solutions to the problem. This estimation technique selects that image from the possible set of feasible imagesmore » which has the maximum entropy permitted by the information available to us. In order to account for the presence of noise in the data, we have also incorporated a noise rejection or likelihood term into our maximum entropy method. This makes our approach mirror a Bayesian maximum a posteriori (MAP) formulation. Additional information from other functional techniques like functional magnetic resonance imaging (fMRI) can be incorporated in the proposed method in the form of a prior bias function to improve solutions. We demonstrate the method with experimental phantom data from a clinical 122 channel MEG system.« less

Bayesian Techniques for Plasma Theory to Bridge the Gap Between Space and Lab Plasmas

NASA Astrophysics Data System (ADS)

Crabtree, Chris; Ganguli, Gurudas; Tejero, Erik

2017-10-01

We will show how Bayesian techniques provide a general data analysis methodology that is better suited to investigate phenomena that require a nonlinear theory for an explanation. We will provide short examples of how Bayesian techniques have been successfully used in the radiation belts to provide precise nonlinear spectral estimates of whistler mode chorus and how these techniques have been verified in laboratory plasmas. We will demonstrate how Bayesian techniques allow for the direct competition of different physical theories with data acting as the necessary arbitrator. This work is supported by the Naval Research Laboratory base program and by the National Aeronautics and Space Administration under Grant No. NNH15AZ90I.

Bayesian ISOLA: new tool for automated centroid moment tensor inversion

NASA Astrophysics Data System (ADS)

Vackář, Jiří; Burjánek, Jan; Gallovič, František; Zahradník, Jiří; Clinton, John

2017-08-01

We have developed a new, fully automated tool for the centroid moment tensor (CMT) inversion in a Bayesian framework. It includes automated data retrieval, data selection where station components with various instrumental disturbances are rejected and full-waveform inversion in a space-time grid around a provided hypocentre. A data covariance matrix calculated from pre-event noise yields an automated weighting of the station recordings according to their noise levels and also serves as an automated frequency filter suppressing noisy frequency ranges. The method is tested on synthetic and observed data. It is applied on a data set from the Swiss seismic network and the results are compared with the existing high-quality MT catalogue. The software package programmed in Python is designed to be as versatile as possible in order to be applicable in various networks ranging from local to regional. The method can be applied either to the everyday network data flow, or to process large pre-existing earthquake catalogues and data sets.

3D tomographic reconstruction using geometrical models

NASA Astrophysics Data System (ADS)

Battle, Xavier L.; Cunningham, Gregory S.; Hanson, Kenneth M.

1997-04-01

We address the issue of reconstructing an object of constant interior density in the context of 3D tomography where there is prior knowledge about the unknown shape. We explore the direct estimation of the parameters of a chosen geometrical model from a set of radiographic measurements, rather than performing operations (segmentation for example) on a reconstructed volume. The inverse problem is posed in the Bayesian framework. A triangulated surface describes the unknown shape and the reconstruction is computed with a maximum a posteriori (MAP) estimate. The adjoint differentiation technique computes the derivatives needed for the optimization of the model parameters. We demonstrate the usefulness of the approach and emphasize the techniques of designing forward and adjoint codes. We use the system response of the University of Arizona Fast SPECT imager to illustrate this method by reconstructing the shape of a heart phantom.

Bayesian model reduction and empirical Bayes for group (DCM) studies.

PubMed

Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter

2016-03-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biros, George

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. Thesemore » include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.« less

On uncertainty quantification in hydrogeology and hydrogeophysics

NASA Astrophysics Data System (ADS)

Linde, Niklas; Ginsbourger, David; Irving, James; Nobile, Fabio; Doucet, Arnaud

2017-12-01

Recent advances in sensor technologies, field methodologies, numerical modeling, and inversion approaches have contributed to unprecedented imaging of hydrogeological properties and detailed predictions at multiple temporal and spatial scales. Nevertheless, imaging results and predictions will always remain imprecise, which calls for appropriate uncertainty quantification (UQ). In this paper, we outline selected methodological developments together with pioneering UQ applications in hydrogeology and hydrogeophysics. The applied mathematics and statistics literature is not easy to penetrate and this review aims at helping hydrogeologists and hydrogeophysicists to identify suitable approaches for UQ that can be applied and further developed to their specific needs. To bypass the tremendous computational costs associated with forward UQ based on full-physics simulations, we discuss proxy-modeling strategies and multi-resolution (Multi-level Monte Carlo) methods. We consider Bayesian inversion for non-linear and non-Gaussian state-space problems and discuss how Sequential Monte Carlo may become a practical alternative. We also describe strategies to account for forward modeling errors in Bayesian inversion. Finally, we consider hydrogeophysical inversion, where petrophysical uncertainty is often ignored leading to overconfident parameter estimation. The high parameter and data dimensions encountered in hydrogeological and geophysical problems make UQ a complicated and important challenge that has only been partially addressed to date.

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond.

PubMed

Perdikaris, Paris; Karniadakis, George Em

2016-05-01

We present a computational framework for model inversion based on multi-fidelity information fusion and Bayesian optimization. The proposed methodology targets the accurate construction of response surfaces in parameter space, and the efficient pursuit to identify global optima while keeping the number of expensive function evaluations at a minimum. We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian optimization setting. This enables a smart adaptive sampling procedure that uses the predictive posterior variance to balance the exploration versus exploitation trade-off, and is a key enabler for practical computations under limited budgets. The effectiveness of the proposed framework is tested on three parameter estimation problems. The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one- and three-dimensional models, whereas the last one aims to identify the forcing term that generated a particular solution to an elliptic partial differential equation. © 2016 The Author(s).

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond

PubMed Central

Perdikaris, Paris; Karniadakis, George Em

2016-01-01

We present a computational framework for model inversion based on multi-fidelity information fusion and Bayesian optimization. The proposed methodology targets the accurate construction of response surfaces in parameter space, and the efficient pursuit to identify global optima while keeping the number of expensive function evaluations at a minimum. We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian optimization setting. This enables a smart adaptive sampling procedure that uses the predictive posterior variance to balance the exploration versus exploitation trade-off, and is a key enabler for practical computations under limited budgets. The effectiveness of the proposed framework is tested on three parameter estimation problems. The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one- and three-dimensional models, whereas the last one aims to identify the forcing term that generated a particular solution to an elliptic partial differential equation. PMID:27194481

Bayesian seismic tomography by parallel interacting Markov chains

NASA Astrophysics Data System (ADS)

Gesret, Alexandrine; Bottero, Alexis; Romary, Thomas; Noble, Mark; Desassis, Nicolas

2014-05-01

The velocity field estimated by first arrival traveltime tomography is commonly used as a starting point for further seismological, mineralogical, tectonic or similar analysis. In order to interpret quantitatively the results, the tomography uncertainty values as well as their spatial distribution are required. The estimated velocity model is obtained through inverse modeling by minimizing an objective function that compares observed and computed traveltimes. This step is often performed by gradient-based optimization algorithms. The major drawback of such local optimization schemes, beyond the possibility of being trapped in a local minimum, is that they do not account for the multiple possible solutions of the inverse problem. They are therefore unable to assess the uncertainties linked to the solution. Within a Bayesian (probabilistic) framework, solving the tomography inverse problem aims at estimating the posterior probability density function of velocity model using a global sampling algorithm. Markov chains Monte-Carlo (MCMC) methods are known to produce samples of virtually any distribution. In such a Bayesian inversion, the total number of simulations we can afford is highly related to the computational cost of the forward model. Although fast algorithms have been recently developed for computing first arrival traveltimes of seismic waves, the complete browsing of the posterior distribution of velocity model is hardly performed, especially when it is high dimensional and/or multimodal. In the latter case, the chain may even stay stuck in one of the modes. In order to improve the mixing properties of classical single MCMC, we propose to make interact several Markov chains at different temperatures. This method can make efficient use of large CPU clusters, without increasing the global computational cost with respect to classical MCMC and is therefore particularly suited for Bayesian inversion. The exchanges between the chains allow a precise sampling of the high probability zones of the model space while avoiding the chains to end stuck in a probability maximum. This approach supplies thus a robust way to analyze the tomography imaging uncertainties. The interacting MCMC approach is illustrated on two synthetic examples of tomography of calibration shots such as encountered in induced microseismic studies. On the second application, a wavelet based model parameterization is presented that allows to significantly reduce the dimension of the problem, making thus the algorithm efficient even for a complex velocity model.

Hierarchical Bayesian modeling of ionospheric TEC disturbances as non-stationary processes

NASA Astrophysics Data System (ADS)

Seid, Abdu Mohammed; Berhane, Tesfahun; Roininen, Lassi; Nigussie, Melessew

2018-03-01

We model regular and irregular variation of ionospheric total electron content as stationary and non-stationary processes, respectively. We apply the method developed to SCINDA GPS data set observed at Bahir Dar, Ethiopia (11.6 °N, 37.4 °E) . We use hierarchical Bayesian inversion with Gaussian Markov random process priors, and we model the prior parameters in the hyperprior. We use Matérn priors via stochastic partial differential equations, and use scaled Inv -χ2 hyperpriors for the hyperparameters. For drawing posterior estimates, we use Markov Chain Monte Carlo methods: Gibbs sampling and Metropolis-within-Gibbs for parameter and hyperparameter estimations, respectively. This allows us to quantify model parameter estimation uncertainties as well. We demonstrate the applicability of the method proposed using a synthetic test case. Finally, we apply the method to real GPS data set, which we decompose to regular and irregular variation components. The result shows that the approach can be used as an accurate ionospheric disturbance characterization technique that quantifies the total electron content variability with corresponding error uncertainties.

Bayesian performance metrics of binary sensors in homeland security applications

NASA Astrophysics Data System (ADS)

Jannson, Tomasz P.; Forrester, Thomas C.

2008-04-01

Bayesian performance metrics, based on such parameters, as: prior probability, probability of detection (or, accuracy), false alarm rate, and positive predictive value, characterizes the performance of binary sensors; i.e., sensors that have only binary response: true target/false target. Such binary sensors, very common in Homeland Security, produce an alarm that can be true, or false. They include: X-ray airport inspection, IED inspections, product quality control, cancer medical diagnosis, part of ATR, and many others. In this paper, we analyze direct and inverse conditional probabilities in the context of Bayesian inference and binary sensors, using X-ray luggage inspection statistical results as a guideline.

A Robust Deconvolution Method based on Transdimensional Hierarchical Bayesian Inference

NASA Astrophysics Data System (ADS)

Kolb, J.; Lekic, V.

2012-12-01

Analysis of P-S and S-P conversions allows us to map receiver side crustal and lithospheric structure. This analysis often involves deconvolution of the parent wave field from the scattered wave field as a means of suppressing source-side complexity. A variety of deconvolution techniques exist including damped spectral division, Wiener filtering, iterative time-domain deconvolution, and the multitaper method. All of these techniques require estimates of noise characteristics as input parameters. We present a deconvolution method based on transdimensional Hierarchical Bayesian inference in which both noise magnitude and noise correlation are used as parameters in calculating the likelihood probability distribution. Because the noise for P-S and S-P conversion analysis in terms of receiver functions is a combination of both background noise - which is relatively easy to characterize - and signal-generated noise - which is much more difficult to quantify - we treat measurement errors as an known quantity, characterized by a probability density function whose mean and variance are model parameters. This transdimensional Hierarchical Bayesian approach has been successfully used previously in the inversion of receiver functions in terms of shear and compressional wave speeds of an unknown number of layers [1]. In our method we used a Markov chain Monte Carlo (MCMC) algorithm to find the receiver function that best fits the data while accurately assessing the noise parameters. In order to parameterize the receiver function we model the receiver function as an unknown number of Gaussians of unknown amplitude and width. The algorithm takes multiple steps before calculating the acceptance probability of a new model, in order to avoid getting trapped in local misfit minima. Using both observed and synthetic data, we show that the MCMC deconvolution method can accurately obtain a receiver function as well as an estimate of the noise parameters given the parent and daughter components. Furthermore, we demonstrate that this new approach is far less susceptible to generating spurious features even at high noise levels. Finally, the method yields not only the most-likely receiver function, but also quantifies its full uncertainty. [1] Bodin, T., M. Sambridge, H. Tkalčić, P. Arroucau, K. Gallagher, and N. Rawlinson (2012), Transdimensional inversion of receiver functions and surface wave dispersion, J. Geophys. Res., 117, B02301

Bayesian inversion of a CRN depth profile to infer Quaternary erosion of the northwestern Campine Plateau (NE Belgium)

NASA Astrophysics Data System (ADS)

Laloy, Eric; Beerten, Koen; Vanacker, Veerle; Christl, Marcus; Rogiers, Bart; Wouters, Laurent

2017-07-01

The rate at which low-lying sandy areas in temperate regions, such as the Campine Plateau (NE Belgium), have been eroding during the Quaternary is a matter of debate. Current knowledge on the average pace of landscape evolution in the Campine area is largely based on geological inferences and modern analogies. We performed a Bayesian inversion of an in situ-produced 10Be concentration depth profile to infer the average long-term erosion rate together with two other parameters: the surface exposure age and the inherited 10Be concentration. Compared to the latest advances in probabilistic inversion of cosmogenic radionuclide (CRN) data, our approach has the following two innovative components: it (1) uses Markov chain Monte Carlo (MCMC) sampling and (2) accounts (under certain assumptions) for the contribution of model errors to posterior uncertainty. To investigate to what extent our approach differs from the state of the art in practice, a comparison against the Bayesian inversion method implemented in the CRONUScalc program is made. Both approaches identify similar maximum a posteriori (MAP) parameter values, but posterior parameter and predictive uncertainty derived using the method taken in CRONUScalc is moderately underestimated. A simple way for producing more consistent uncertainty estimates with the CRONUScalc-like method in the presence of model errors is therefore suggested. Our inferred erosion rate of 39 ± 8. 9 mm kyr-1 (1σ) is relatively large in comparison with landforms that erode under comparable (paleo-)climates elsewhere in the world. We evaluate this value in the light of the erodibility of the substrate and sudden base level lowering during the Middle Pleistocene. A denser sampling scheme of a two-nuclide concentration depth profile would allow for better inferred erosion rate resolution, and including more uncertain parameters in the MCMC inversion.

Sequential Bayesian Geostatistical Inversion and Evaluation of Combined Data Worth for Aquifer Characterization at the Hanford 300 Area

NASA Astrophysics Data System (ADS)

Murakami, H.; Chen, X.; Hahn, M. S.; Over, M. W.; Rockhold, M. L.; Vermeul, V.; Hammond, G. E.; Zachara, J. M.; Rubin, Y.

2010-12-01

Subsurface characterization for predicting groundwater flow and contaminant transport requires us to integrate large and diverse datasets in a consistent manner, and quantify the associated uncertainty. In this study, we sequentially assimilated multiple types of datasets for characterizing a three-dimensional heterogeneous hydraulic conductivity field at the Hanford 300 Area. The datasets included constant-rate injection tests, electromagnetic borehole flowmeter tests, lithology profile and tracer tests. We used the method of anchored distributions (MAD), which is a modular-structured Bayesian geostatistical inversion method. MAD has two major advantages over the other inversion methods. First, it can directly infer a joint distribution of parameters, which can be used as an input in stochastic simulations for prediction. In MAD, in addition to typical geostatistical structural parameters, the parameter vector includes multiple point values of the heterogeneous field, called anchors, which capture local trends and reduce uncertainty in the prediction. Second, MAD allows us to integrate the datasets sequentially in a Bayesian framework such that it updates the posterior distribution, as a new dataset is included. The sequential assimilation can decrease computational burden significantly. We applied MAD to assimilate different combinations of the datasets, and then compared the inversion results. For the injection and tracer test assimilation, we calculated temporal moments of pressure build-up and breakthrough curves, respectively, to reduce the data dimension. A massive parallel flow and transport code PFLOTRAN is used for simulating the tracer test. For comparison, we used different metrics based on the breakthrough curves not used in the inversion, such as mean arrival time, peak concentration and early arrival time. This comparison intends to yield the combined data worth, i.e. which combination of the datasets is the most effective for a certain metric, which will be useful for guiding the further characterization effort at the site and also the future characterization projects at the other sites.

Iterative updating of model error for Bayesian inversion

NASA Astrophysics Data System (ADS)

Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew

2018-02-01

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when optimization algorithms are used to find a single estimate, or to speed up Markov chain Monte Carlo (MCMC) calculations in the Bayesian framework. The use of an approximate model introduces a discrepancy, or modeling error, that may have a detrimental effect on the solution of the ill-posed inverse problem, or it may severely distort the estimate of the posterior distribution. In the Bayesian paradigm, the modeling error can be considered as a random variable, and by using an estimate of the probability distribution of the unknown, one may estimate the probability distribution of the modeling error and incorporate it into the inversion. We introduce an algorithm which iterates this idea to update the distribution of the model error, leading to a sequence of posterior distributions that are demonstrated empirically to capture the underlying truth with increasing accuracy. Since the algorithm is not based on rejections, it requires only limited full model evaluations. We show analytically that, in the linear Gaussian case, the algorithm converges geometrically fast with respect to the number of iterations when the data is finite dimensional. For more general models, we introduce particle approximations of the iteratively generated sequence of distributions; we also prove that each element of the sequence converges in the large particle limit under a simplifying assumption. We show numerically that, as in the linear case, rapid convergence occurs with respect to the number of iterations. Additionally, we show through computed examples that point estimates obtained from this iterative algorithm are superior to those obtained by neglecting the model error.

Bayesian seismic inversion based on rock-physics prior modeling for the joint estimation of acoustic impedance, porosity and lithofacies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Passos de Figueiredo, Leandro, E-mail: leandrop.fgr@gmail.com; Grana, Dario; Santos, Marcio

We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well datamore » multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.« less

Comparison of adjoint and analytical Bayesian inversion methods for constraining Asian sources of carbon monoxide using satellite (MOPITT) measurements of CO columns

NASA Astrophysics Data System (ADS)

Kopacz, Monika; Jacob, Daniel J.; Henze, Daven K.; Heald, Colette L.; Streets, David G.; Zhang, Qiang

2009-02-01

We apply the adjoint of an atmospheric chemical transport model (GEOS-Chem CTM) to constrain Asian sources of carbon monoxide (CO) with 2° × 2.5° spatial resolution using Measurement of Pollution in the Troposphere (MOPITT) satellite observations of CO columns in February-April 2001. Results are compared to the more common analytical method for solving the same Bayesian inverse problem and applied to the same data set. The analytical method is more exact but because of computational limitations it can only constrain emissions over coarse regions. We find that the correction factors to the a priori CO emission inventory from the adjoint inversion are generally consistent with those of the analytical inversion when averaged over the large regions of the latter. The adjoint solution reveals fine-scale variability (cities, political boundaries) that the analytical inversion cannot resolve, for example, in the Indian subcontinent or between Korea and Japan, and some of that variability is of opposite sign which points to large aggregation errors in the analytical solution. Upward correction factors to Chinese emissions from the prior inventory are largest in central and eastern China, consistent with a recent bottom-up revision of that inventory, although the revised inventory also sees the need for upward corrections in southern China where the adjoint and analytical inversions call for downward correction. Correction factors for biomass burning emissions derived from the adjoint and analytical inversions are consistent with a recent bottom-up inventory on the basis of MODIS satellite fire data.

Quantifying uncertainties of seismic Bayesian inversion of Northern Great Plains

NASA Astrophysics Data System (ADS)

Gao, C.; Lekic, V.

2017-12-01

Elastic waves excited by earthquakes are the fundamental observations of the seismological studies. Seismologists measure information such as travel time, amplitude, and polarization to infer the properties of earthquake source, seismic wave propagation, and subsurface structure. Across numerous applications, seismic imaging has been able to take advantage of complimentary seismic observables to constrain profiles and lateral variations of Earth's elastic properties. Moreover, seismic imaging plays a unique role in multidisciplinary studies of geoscience by providing direct constraints on the unreachable interior of the Earth. Accurate quantification of uncertainties of inferences made from seismic observations is of paramount importance for interpreting seismic images and testing geological hypotheses. However, such quantification remains challenging and subjective due to the non-linearity and non-uniqueness of geophysical inverse problem. In this project, we apply a reverse jump Markov chain Monte Carlo (rjMcMC) algorithm for a transdimensional Bayesian inversion of continental lithosphere structure. Such inversion allows us to quantify the uncertainties of inversion results by inverting for an ensemble solution. It also yields an adaptive parameterization that enables simultaneous inversion of different elastic properties without imposing strong prior information on the relationship between them. We present retrieved profiles of shear velocity (Vs) and radial anisotropy in Northern Great Plains using measurements from USArray stations. We use both seismic surface wave dispersion and receiver function data due to their complementary constraints of lithosphere structure. Furthermore, we analyze the uncertainties of both individual and joint inversion of those two data types to quantify the benefit of doing joint inversion. As an application, we infer the variation of Moho depths and crustal layering across the northern Great Plains.

Joint inversion for transponder localization and sound-speed profile temporal variation in high-precision acoustic surveys.

PubMed

Li, Zhao; Dosso, Stan E; Sun, Dajun

2016-07-01

This letter develops a Bayesian inversion for localizing underwater acoustic transponders using a surface ship which compensates for sound-speed profile (SSP) temporal variation during the survey. The method is based on dividing observed acoustic travel-time data into time segments and including depth-independent SSP variations for each segment as additional unknown parameters to approximate the SSP temporal variation. SSP variations are estimated jointly with transponder locations, rather than calculated separately as in existing two-step inversions. Simulation and sea-trial results show this localization/SSP joint inversion performs better than two-step inversion in terms of localization accuracy, agreement with measured SSP variations, and computational efficiency.

Technical Note: Approximate Bayesian parameterization of a process-based tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2014-02-01

Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistical inversion methods require a particular metric, the probability of observing the data given the model parameters, known as the likelihood. For technical and computational reasons, likelihoods for process-based stochastic models are usually based on general assumptions about variability in the observed data, and not on the stochasticity generated by the model. Only in recent years have new methods become available that allow the generation of likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional Markov chain Monte Carlo (MCMC) sampler, performs well in retrieving known parameter values from virtual inventory data generated by the forest model. We analyze the results of the parameter estimation, examine its sensitivity to the choice and aggregation of model outputs and observed data (summary statistics), and demonstrate the application of this method by fitting the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss how this approach differs from approximate Bayesian computation (ABC), another method commonly used to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can be successfully applied to process-based models of high complexity. The methodology is particularly suitable for heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models.

Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.

Estimation of Regional Carbon Balance from Atmospheric Observations

NASA Astrophysics Data System (ADS)

Denning, S.; Uliasz, M.; Skidmore, J.

2002-12-01

Variations in the concentration of CO2 and other trace gases in time and space contain information about sources and sinks at regional scales. Several methods have been developed to quantitatively extract this information from atmospheric measurements. Mass-balance techniques depend on the ability to repeatedly sample the same mass of air, which involves careful attention to airmass trajectories. Inverse and adjoint techniques rely on decomposition of the source field into quasi-independent "basis functions" that are propagated through transport models and then used to synthesize optimal linear combinations that best match observations. A recently proposed method for regional flux estimation from continuous measurements at tall towers relies on time-mean vertical gradients, and requires careful trajectory analysis to map the estimates onto regional ecosystems. Each of these techniques is likely to be applied to measurements made during the North American Carbon Program. We have also explored the use of Bayesian synthesis inversion at regional scales, using a Lagrangian particle dispersion model driven by mesoscale transport fields. Influence functions were calculated for each hypothetical observation in a realistic diurnally-varying flow. These influence functions were then treated as basis functions for the purpose of separate inversions for daytime photosynthesis and 24-hour mean ecosystem respiration. Our results highlight the importance of estimating CO2 fluxes through the lateral boundaries of the model. Respiration fluxes were well constrained by one or two hypothetical towers, regardless of inflow fluxes. Time-varying assimilation fluxes were less well constrained, and much more dependent on knowledge of inflow fluxes. The small net difference between respiration and photosynthesis was the most difficult to determine, being extremely sensitive to knowledge of inflow fluxes. Finally, we explored the feasibility of directly incorporating mid-day concentration values measured at surface-layer flux towers in global inversions for regional surface fluxes. We found that such data would substantially improve the observational constraint on current carbon cycle models, especially if applied selectively to a well-designed subset of the current network of flux towers.

GBIS (Geodetic Bayesian Inversion Software): Rapid Inversion of InSAR and GNSS Data to Estimate Surface Deformation Source Parameters and Uncertainties

NASA Astrophysics Data System (ADS)

Bagnardi, M.; Hooper, A. J.

2017-12-01

Inversions of geodetic observational data, such as Interferometric Synthetic Aperture Radar (InSAR) and Global Navigation Satellite System (GNSS) measurements, are often performed to obtain information about the source of surface displacements. Inverse problem theory has been applied to study magmatic processes, the earthquake cycle, and other phenomena that cause deformation of the Earth's interior and of its surface. Together with increasing improvements in data resolution, both spatial and temporal, new satellite missions (e.g., European Commission's Sentinel-1 satellites) are providing the unprecedented opportunity to access space-geodetic data within hours from their acquisition. To truly take advantage of these opportunities we must become able to interpret geodetic data in a rapid and robust manner. Here we present the open-source Geodetic Bayesian Inversion Software (GBIS; available for download at http://comet.nerc.ac.uk/gbis). GBIS is written in Matlab and offers a series of user-friendly and interactive pre- and post-processing tools. For example, an interactive function has been developed to estimate the characteristics of noise in InSAR data by calculating the experimental semi-variogram. The inversion software uses a Markov-chain Monte Carlo algorithm, incorporating the Metropolis-Hastings algorithm with adaptive step size, to efficiently sample the posterior probability distribution of the different source parameters. The probabilistic Bayesian approach allows the user to retrieve estimates of the optimal (best-fitting) deformation source parameters together with the associated uncertainties produced by errors in the data (and by scaling, errors in the model). The current version of GBIS (V1.0) includes fast analytical forward models for magmatic sources of different geometry (e.g., point source, finite spherical source, prolate spheroid source, penny-shaped sill-like source, and dipping-dike with uniform opening) and for dipping faults with uniform slip, embedded in a isotropic elastic half-space. However, the software architecture allows the user to easily add any other analytical or numerical forward models to calculate displacements at the surface. GBIS is delivered with a detailed user manual and three synthetic datasets for testing and practical training.

Reconstruction of Atmospheric Tracer Releases with Optimal Resolution Features: Concentration Data Assimilation

NASA Astrophysics Data System (ADS)

Singh, Sarvesh Kumar; Turbelin, Gregory; Issartel, Jean-Pierre; Kumar, Pramod; Feiz, Amir Ali

2015-04-01

The fast growing urbanization, industrialization and military developments increase the risk towards the human environment and ecology. This is realized in several past mortality incidents, for instance, Chernobyl nuclear explosion (Ukraine), Bhopal gas leak (India), Fukushima-Daichi radionuclide release (Japan), etc. To reduce the threat and exposure to the hazardous contaminants, a fast and preliminary identification of unknown releases is required by the responsible authorities for the emergency preparedness and air quality analysis. Often, an early detection of such contaminants is pursued by a distributed sensor network. However, identifying the origin and strength of unknown releases following the sensor reported concentrations is a challenging task. This requires an optimal strategy to integrate the measured concentrations with the predictions given by the atmospheric dispersion models. This is an inverse problem. The measured concentrations are insufficient and atmospheric dispersion models suffer from inaccuracy due to the lack of process understanding, turbulence uncertainties, etc. These lead to a loss of information in the reconstruction process and thus, affect the resolution, stability and uniqueness of the retrieved source. An additional well known issue is the numerical artifact arisen at the measurement locations due to the strong concentration gradient and dissipative nature of the concentration. Thus, assimilation techniques are desired which can lead to an optimal retrieval of the unknown releases. In general, this is facilitated within the Bayesian inference and optimization framework with a suitable choice of a priori information, regularization constraints, measurement and background error statistics. An inversion technique is introduced here for an optimal reconstruction of unknown releases using limited concentration measurements. This is based on adjoint representation of the source-receptor relationship and utilization of a weight function which exhibits a priori information about the unknown releases apparent to the monitoring network. The properties of the weight function provide an optimal data resolution and model resolution to the retrieved source estimates. The retrieved source estimates are proved theoretically to be stable against the random measurement errors and their reliability can be interpreted in terms of the distribution of the weight functions. Further, the same framework can be extended for the identification of the point type releases by utilizing the maximum of the retrieved source estimates. The inversion technique has been evaluated with the several diffusion experiments, like, Idaho low wind diffusion experiment (1974), IIT Delhi tracer experiment (1991), European Tracer Experiment (1994), Fusion Field Trials (2007), etc. In case of point release experiments, the source parameters are mostly retrieved close to the true source parameters with least error. Primarily, the proposed technique overcomes two major difficulties incurred in the source reconstruction: (i) The initialization of the source parameters as required by the optimization based techniques. The converged solution depends on their initialization. (ii) The statistical knowledge about the measurement and background errors as required by the Bayesian inference based techniques. These are hypothetically assumed in case of no prior knowledge.

Inverse and forward modeling under uncertainty using MRE-based Bayesian approach

NASA Astrophysics Data System (ADS)

Hou, Z.; Rubin, Y.

2004-12-01

A stochastic inverse approach for subsurface characterization is proposed and applied to shallow vadose zone at a winery field site in north California and to a gas reservoir at the Ormen Lange field site in the North Sea. The approach is formulated in a Bayesian-stochastic framework, whereby the unknown parameters are identified in terms of their statistical moments or their probabilities. Instead of the traditional single-valued estimation /prediction provided by deterministic methods, the approach gives a probability distribution for an unknown parameter. This allows calculating the mean, the mode, and the confidence interval, which is useful for a rational treatment of uncertainty and its consequences. The approach also allows incorporating data of various types and different error levels, including measurements of state variables as well as information such as bounds on or statistical moments of the unknown parameters, which may represent prior information. To obtain minimally subjective prior probabilities required for the Bayesian approach, the principle of Minimum Relative Entropy (MRE) is employed. The approach is tested in field sites for flow parameters identification and soil moisture estimation in the vadose zone and for gas saturation estimation at great depth below the ocean floor. Results indicate the potential of coupling various types of field data within a MRE-based Bayesian formalism for improving the estimation of the parameters of interest.

A Comparison of a Bayesian and a Maximum Likelihood Tailored Testing Procedure.

ERIC Educational Resources Information Center

McKinley, Robert L.; Reckase, Mark D.

A study was conducted to compare tailored testing procedures based on a Bayesian ability estimation technique and on a maximum likelihood ability estimation technique. The Bayesian tailored testing procedure selected items so as to minimize the posterior variance of the ability estimate distribution, while the maximum likelihood tailored testing…

Testing joint inversion techniques of gravity data and cosmic ray muon flux at a well-characterized site for use in the detection of subsurface density structures beneath volcanoes.

NASA Astrophysics Data System (ADS)

Cosburn, K.; Roy, M.; Rowe, C. A.; Guardincerri, E.

2017-12-01

Obtaining accurate static and time-dependent shallow subsurface density structure beneath volcanic, hydrogeologic, and tectonic targets can help illuminate active processes of fluid flow and magma transport. A limitation of using surface gravity measurements for such imaging is that these observations are vastly underdetermined and non-unique. In order to hone in on a more accurate solution, other data sets are needed to provide constraints, typically seismic or borehole observations. The spatial resolution of these techniques, however, is relatively poor, and a novel solution to this problem in recent years has been to use attenuation of the cosmic ray muon flux, which provides an independent constraint on density. In this study we present a joint inversion of gravity and cosmic ray muon flux observations to infer the density structure of a target rock volume at a well-characterized site near Los Alamos, New Mexico, USA. We investigate the shallow structure of a mesa formed by the Quaternary ash-flow tuffs on the Pajarito Plateau, flanking the Jemez volcano in New Mexico. Gravity measurements were made using a Lacoste and Romberg D meter on the surface of the mesa and inside a tunnel beneath the mesa. Muon flux measurements were also made at the mesa surface and at various points within the same tunnel using a muon detector having an acceptance region of 45 degrees from the vertical and a track resolution of several milliradians. We expect the combination of muon and gravity data to provide us with enhanced resolution as well as the ability to sense deeper structures in our region of interest. We use Bayesian joint inversion techniques on the gravity-muon dataset to test these ideas, building upon previous work using gravity inversion alone to resolve density structure in our study area. Both the regional geology and geometry of our study area is well-known and we assess the inferred density structure from our gravity-muon joint inversion within this known geologic framework.

Inverse problems biomechanical imaging (Conference Presentation)

NASA Astrophysics Data System (ADS)

Oberai, Assad A.

2016-03-01

It is now well recognized that a host of imaging modalities (a list that includes Ultrasound, MRI, Optical Coherence Tomography, and optical microscopy) can be used to "watch" tissue as it deforms in response to an internal or external excitation. The result is a detailed map of the deformation field in the interior of the tissue. This deformation field can be used in conjunction with a material mechanical response to determine the spatial distribution of material properties of the tissue by solving an inverse problem. Images of material properties thus obtained can be used to quantify the health of the tissue. Recently, they have been used to detect, diagnose and monitor cancerous lesions, detect vulnerable plaque in arteries, diagnose liver cirrhosis, and possibly detect the onset of Alzheimer's disease. In this talk I will describe the mathematical and computational aspects of solving this class of inverse problems, and their applications in biology and medicine. In particular, I will discuss the well-posedness of these problems and quantify the amount of displacement data necessary to obtain a unique property distribution. I will describe an efficient algorithm for solving the resulting inverse problem. I will also describe some recent developments based on Bayesian inference in estimating the variance in the estimates of material properties. I will conclude with the applications of these techniques in diagnosing breast cancer and in characterizing the mechanical properties of cells with sub-cellular resolution.

Unified Bayesian Estimator of EEG Reference at Infinity: rREST (Regularized Reference Electrode Standardization Technique).

PubMed

Hu, Shiang; Yao, Dezhong; Valdes-Sosa, Pedro A

2018-01-01

The choice of reference for the electroencephalogram (EEG) is a long-lasting unsolved issue resulting in inconsistent usages and endless debates. Currently, both the average reference (AR) and the reference electrode standardization technique (REST) are two primary, apparently irreconcilable contenders. We propose a theoretical framework to resolve this reference issue by formulating both (a) estimation of potentials at infinity, and (b) determination of the reference, as a unified Bayesian linear inverse problem, which can be solved by maximum a posterior estimation. We find that AR and REST are very particular cases of this unified framework: AR results from biophysically non-informative prior; while REST utilizes the prior based on the EEG generative model. To allow for simultaneous denoising and reference estimation, we develop the regularized versions of AR and REST, named rAR and rREST, respectively. Both depend on a regularization parameter that is the noise to signal variance ratio. Traditional and new estimators are evaluated with this framework, by both simulations and analysis of real resting EEGs. Toward this end, we leverage the MRI and EEG data from 89 subjects which participated in the Cuban Human Brain Mapping Project. Generated artificial EEGs-with a known ground truth, show that relative error in estimating the EEG potentials at infinity is lowest for rREST. It also reveals that realistic volume conductor models improve the performances of REST and rREST. Importantly, for practical applications, it is shown that an average lead field gives the results comparable to the individual lead field. Finally, it is shown that the selection of the regularization parameter with Generalized Cross-Validation (GCV) is close to the "oracle" choice based on the ground truth. When evaluated with the real 89 resting state EEGs, rREST consistently yields the lowest GCV. This study provides a novel perspective to the EEG reference problem by means of a unified inverse solution framework. It may allow additional principled theoretical formulations and numerical evaluation of performance.

Multilevel modeling of single-case data: A comparison of maximum likelihood and Bayesian estimation.

PubMed

Moeyaert, Mariola; Rindskopf, David; Onghena, Patrick; Van den Noortgate, Wim

2017-12-01

The focus of this article is to describe Bayesian estimation, including construction of prior distributions, and to compare parameter recovery under the Bayesian framework (using weakly informative priors) and the maximum likelihood (ML) framework in the context of multilevel modeling of single-case experimental data. Bayesian estimation results were found similar to ML estimation results in terms of the treatment effect estimates, regardless of the functional form and degree of information included in the prior specification in the Bayesian framework. In terms of the variance component estimates, both the ML and Bayesian estimation procedures result in biased and less precise variance estimates when the number of participants is small (i.e., 3). By increasing the number of participants to 5 or 7, the relative bias is close to 5% and more precise estimates are obtained for all approaches, except for the inverse-Wishart prior using the identity matrix. When a more informative prior was added, more precise estimates for the fixed effects and random effects were obtained, even when only 3 participants were included. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Bayesian resolution of TEM, CSEM and MT soundings: a comparative study

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Ray, A.; Key, K.

2017-12-01

We examine the resolution of three electromagnetic exploration methods commonly used to map the electrical conductivity of the shallow crust - the magnetotelluric (MT) method, the controlled-source electromagnetic (CSEM) method and the transient electromagnetic (TEM) method. TEM and CSEM utilize an artificial source of EM energy, while MT makes use of natural variations in the Earth's electromagnetic field. For a given geological setting and acquisition parameters, each of these methods will have a different resolution due to differences in the source field polarization and the frequency range of the measurements. For example, the MT and TEM methods primarily rely on induced horizontal currents and are most sensitive to conductive layers while the CSEM method generates vertical loops of current and is more sensitive to resistive features. Our study seeks to provide a robust resolution comparison that can help inform exploration geophysicists about which technique is best suited for a particular target. While it is possible to understand and describe a difference in resolution qualitatively, it remains challenging to fully describe it quantitatively using optimization based approaches. Part of the difficulty here stems from the standard electromagnetic inversion toolkit, which makes heavy use of regularization (often in the form of smoothing) to constrain the non-uniqueness inherent in the inverse problem. This regularization makes it difficult to accurately estimate the uncertainty in estimated model parameters - and therefore obscures their true resolution. To overcome this difficulty, we compare the resolution of CSEM, airborne TEM, and MT data quantitatively using a Bayesian trans-dimensional Markov chain Monte Carlo (McMC) inversion scheme. Noisy synthetic data for this study are computed from various representative 1D test models: a conductive anomaly under a conductive/resistive overburden; and a resistive anomaly under a conductive/resistive overburden. In addition to obtaining the full posterior probability density function of the model parameters, we develop a metric to more directly compare the resolution of each method as a function of depth.

Seismic velocity and crustal thickness inversions: Moon and Mars

NASA Astrophysics Data System (ADS)

Drilleau, Melanie; Blanchette-Guertin, Jean-François; Kawamura, Taichi; Lognonné, Philippe; Wieczorek, Mark

2017-04-01

We present results from new inversions of seismic data arrival times acquired by the Apollo active and passive experiments. Markov chain Monte Carlo inversions are used to constrain (i) 1-D lunar crustal and upper mantle velocity models and (ii) 3-D lateral crustal thickness models under the Apollo stations and the artificial and natural impact sites. A full 3-D model of the lunar crustal thickness is then obtained using the GRAIL gravimetric data, anchored by the crustal thicknesses under each Apollo station and impact site. To avoid the use of any seismic reference model, a Bayesian inversion technique is implemented. The advantage of such an approach is to obtain robust probability density functions of interior structure parameters governed by uncertainties on the seismic data arrival times. 1-D seismic velocities are parameterized using C1-Bézier curves, which allow the exploration of both smoothly varying models and first-order discontinuities. The parameters of the inversion include the seismic velocities of P and S waves as a function of depth, the thickness of the crust under each Apollo station and impact epicentre. The forward problem consists in a ray tracing method enabling both the relocation of the natural impact epicenters, and the computation of time corrections associated to the surface topography and the crustal thickness variations under the stations and impact sites. The results show geology-related differences between the different sites, which are due to contrasts in megaregolith thickness and to shallow subsurface composition and structure. Some of the finer structural elements might be difficult to constrain and might fall within the uncertainties of the dataset. However, we use the more precise LROC-located epicentral locations for the lunar modules and Saturn-IV upper stage artificial impacts, reducing some of the uncertainties observed in past studies. In the framework of the NASA InSight/SEIS mission to Mars, the method developed in this study will be used to constrain the Martian crustal thickness as soon as the first data will be available (late 2018). For Insight, impacts will be located by MRO data differential analysis, which provide a known location enabling the direct inversion of all differential travel times with respect to P arrival time. We have performed resolution tests to investigate to what extend impact events might help us to constrain the Martian crustal thickness. Due to the high flexibility of the Bayesian algorithm, the interior model will be refined each time a new event will be detected.

Trans-dimensional joint inversion of seabed scattering and reflection data.

PubMed

Steininger, Gavin; Dettmer, Jan; Dosso, Stan E; Holland, Charles W

2013-03-01

This paper examines joint inversion of acoustic scattering and reflection data to resolve seabed interface roughness parameters (spectral strength, exponent, and cutoff) and geoacoustic profiles. Trans-dimensional (trans-D) Bayesian sampling is applied with both the number of sediment layers and the order (zeroth or first) of auto-regressive parameters in the error model treated as unknowns. A prior distribution that allows fluid sediment layers over an elastic basement in a trans-D inversion is derived and implemented. Three cases are considered: Scattering-only inversion, joint scattering and reflection inversion, and joint inversion with the trans-D auto-regressive error model. Including reflection data improves the resolution of scattering and geoacoustic parameters. The trans-D auto-regressive model further improves scattering resolution and correctly differentiates between strongly and weakly correlated residual errors.

Development of microwave rainfall retrieval algorithm for climate applications

NASA Astrophysics Data System (ADS)

KIM, J. H.; Shin, D. B.

2014-12-01

With the accumulated satellite datasets for decades, it is possible that satellite-based data could contribute to sustained climate applications. Level-3 products from microwave sensors for climate applications can be obtained from several algorithms. For examples, the Microwave Emission brightness Temperature Histogram (METH) algorithm produces level-3 rainfalls directly, whereas the Goddard profiling (GPROF) algorithm first generates instantaneous rainfalls and then temporal and spatial averaging process leads to level-3 products. The rainfall algorithm developed in this study follows a similar approach to averaging instantaneous rainfalls. However, the algorithm is designed to produce instantaneous rainfalls at an optimal resolution showing reduced non-linearity in brightness temperature (TB)-rain rate(R) relations. It is found that the resolution tends to effectively utilize emission channels whose footprints are relatively larger than those of scattering channels. This algorithm is mainly composed of a-priori databases (DBs) and a Bayesian inversion module. The DB contains massive pairs of simulated microwave TBs and rain rates, obtained by WRF (version 3.4) and RTTOV (version 11.1) simulations. To improve the accuracy and efficiency of retrieval process, data mining technique is additionally considered. The entire DB is classified into eight types based on Köppen climate classification criteria using reanalysis data. Among these sub-DBs, only one sub-DB which presents the most similar physical characteristics is selected by considering the thermodynamics of input data. When the Bayesian inversion is applied to the selected DB, instantaneous rain rate with 6 hours interval is retrieved. The retrieved monthly mean rainfalls are statistically compared with CMAP and GPCP, respectively.

Measurement Uncertainty of Dew-Point Temperature in a Two-Pressure Humidity Generator

NASA Astrophysics Data System (ADS)

Martins, L. Lages; Ribeiro, A. Silva; Alves e Sousa, J.; Forbes, Alistair B.

2012-09-01

This article describes the measurement uncertainty evaluation of the dew-point temperature when using a two-pressure humidity generator as a reference standard. The estimation of the dew-point temperature involves the solution of a non-linear equation for which iterative solution techniques, such as the Newton-Raphson method, are required. Previous studies have already been carried out using the GUM method and the Monte Carlo method but have not discussed the impact of the approximate numerical method used to provide the temperature estimation. One of the aims of this article is to take this approximation into account. Following the guidelines presented in the GUM Supplement 1, two alternative approaches can be developed: the forward measurement uncertainty propagation by the Monte Carlo method when using the Newton-Raphson numerical procedure; and the inverse measurement uncertainty propagation by Bayesian inference, based on prior available information regarding the usual dispersion of values obtained by the calibration process. The measurement uncertainties obtained using these two methods can be compared with previous results. Other relevant issues concerning this research are the broad application to measurements that require hygrometric conditions obtained from two-pressure humidity generators and, also, the ability to provide a solution that can be applied to similar iterative models. The research also studied the factors influencing both the use of the Monte Carlo method (such as the seed value and the convergence parameter) and the inverse uncertainty propagation using Bayesian inference (such as the pre-assigned tolerance, prior estimate, and standard deviation) in terms of their accuracy and adequacy.

Variational Bayesian Learning for Wavelet Independent Component Analysis

NASA Astrophysics Data System (ADS)

Roussos, E.; Roberts, S.; Daubechies, I.

2005-11-01

In an exploratory approach to data analysis, it is often useful to consider the observations as generated from a set of latent generators or "sources" via a generally unknown mapping. For the noisy overcomplete case, where we have more sources than observations, the problem becomes extremely ill-posed. Solutions to such inverse problems can, in many cases, be achieved by incorporating prior knowledge about the problem, captured in the form of constraints. This setting is a natural candidate for the application of the Bayesian methodology, allowing us to incorporate "soft" constraints in a natural manner. The work described in this paper is mainly driven by problems in functional magnetic resonance imaging of the brain, for the neuro-scientific goal of extracting relevant "maps" from the data. This can be stated as a `blind' source separation problem. Recent experiments in the field of neuroscience show that these maps are sparse, in some appropriate sense. The separation problem can be solved by independent component analysis (ICA), viewed as a technique for seeking sparse components, assuming appropriate distributions for the sources. We derive a hybrid wavelet-ICA model, transforming the signals into a domain where the modeling assumption of sparsity of the coefficients with respect to a dictionary is natural. We follow a graphical modeling formalism, viewing ICA as a probabilistic generative model. We use hierarchical source and mixing models and apply Bayesian inference to the problem. This allows us to perform model selection in order to infer the complexity of the representation, as well as automatic denoising. Since exact inference and learning in such a model is intractable, we follow a variational Bayesian mean-field approach in the conjugate-exponential family of distributions, for efficient unsupervised learning in multi-dimensional settings. The performance of the proposed algorithm is demonstrated on some representative experiments.

Advances in the microrheology of complex fluids

NASA Astrophysics Data System (ADS)

Waigh, Thomas Andrew

2016-07-01

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

A statistical kinematic source inversion approach based on the QUESO library for uncertainty quantification and prediction

NASA Astrophysics Data System (ADS)

Zielke, Olaf; McDougall, Damon; Mai, Martin; Babuska, Ivo

2014-05-01

Seismic, often augmented with geodetic data, are frequently used to invert for the spatio-temporal evolution of slip along a rupture plane. The resulting images of the slip evolution for a single event, inferred by different research teams, often vary distinctly, depending on the adopted inversion approach and rupture model parameterization. This observation raises the question, which of the provided kinematic source inversion solutions is most reliable and most robust, and — more generally — how accurate are fault parameterization and solution predictions? These issues are not included in "standard" source inversion approaches. Here, we present a statistical inversion approach to constrain kinematic rupture parameters from teleseismic body waves. The approach is based a) on a forward-modeling scheme that computes synthetic (body-)waves for a given kinematic rupture model, and b) on the QUESO (Quantification of Uncertainty for Estimation, Simulation, and Optimization) library that uses MCMC algorithms and Bayes theorem for sample selection. We present Bayesian inversions for rupture parameters in synthetic earthquakes (i.e. for which the exact rupture history is known) in an attempt to identify the cross-over at which further model discretization (spatial and temporal resolution of the parameter space) is no longer attributed to a decreasing misfit. Identification of this cross-over is of importance as it reveals the resolution power of the studied data set (i.e. teleseismic body waves), enabling one to constrain kinematic earthquake rupture histories of real earthquakes at a resolution that is supported by data. In addition, the Bayesian approach allows for mapping complete posterior probability density functions of the desired kinematic source parameters, thus enabling us to rigorously assess the uncertainties in earthquake source inversions.

Sparse Bayesian Inference and the Temperature Structure of the Solar Corona

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warren, Harry P.; Byers, Jeff M.; Crump, Nicholas A.

Measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures. Unfortunately, the temperature of the upper atmosphere cannot be observed directly, but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures. Such observations are “inverted” to determine the distribution of plasma temperatures along the line of sight. This inversion is ill posed and, in the absence of regularization, tends to produce wildly oscillatory solutions. We introduce the application of sparse Bayesian inference to the problem of inferring the temperature structure of themore » solar corona. Within a Bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided. We demonstrate the efficacy of the Bayesian approach by considering a test library of 40 assumed temperature distributions.« less

An Inversion Analysis of Recent Variability in CO2 Fluxes Using GOSAT and In Situ Observations

NASA Astrophysics Data System (ADS)

Wang, J. S.; Kawa, S. R.; Baker, D. F.; Collatz, G. J.

2016-12-01

About one-half of the global CO2 emissions from fossil fuel combustion and deforestation accumulates in the atmosphere, where it contributes to global warming. The rest is taken up by vegetation and the ocean. The precise contribution of the two sinks and their location and year-to-year variability are not well understood. We use two different approaches, batch Bayesian synthesis inversion and variational data assimilation, to deduce the global spatiotemporal distributions of CO2 fluxes during 2009-2010. One of our objectives is to assess different sources of uncertainties in inferred fluxes, including uncertainties in prior flux estimates and observations, and differences in inversion techniques. For prior constraints, we utilize fluxes and uncertainties from the CASA-GFED model of the terrestrial biosphere and biomass burning driven by satellite observations. We also use measurement-based ocean flux estimates and fixed fossil CO2 emissions. Our inversions incorporate column CO2 measurements from the GOSAT satellite (ACOS retrieval, bias-corrected) and in situ observations (individual flask and afternoon-average continuous observations) to estimate fluxes in 108 regions over 8-day intervals for the batch inversion and at 3° x 3.75° weekly for the variational system. Relationships between fluxes and atmospheric concentrations are derived consistently for the two inversion systems using the PCTM transport model with MERRA meteorology. We compare the posterior fluxes and uncertainties derived using different data sets and the two inversion approaches, and evaluate the posterior atmospheric concentrations against independent data including aircraft measurements. The optimized fluxes generally resemble each other and those from other studies. For example, a GOSAT-only inversion suggests a shift in the global sink from the tropics/south to the north relative to the prior and to an in-situ-only inversion. The posterior fluxes of the GOSAT inversion are better constrained in most regions than those of the in situ inversion because of the greater spatial coverage of the GOSAT observations. The GOSAT inversion also indicates a significantly smaller terrestrial sink in higher-latitude northern regions in boreal summer of 2010 relative to 2009, consistent with observed drought conditions.

Bayesian soft X-ray tomography using non-stationary Gaussian Processes

NASA Astrophysics Data System (ADS)

Li, Dong; Svensson, J.; Thomsen, H.; Medina, F.; Werner, A.; Wolf, R.

2013-08-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

Bayesian soft X-ray tomography using non-stationary Gaussian Processes.

PubMed

Li, Dong; Svensson, J; Thomsen, H; Medina, F; Werner, A; Wolf, R

2013-08-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

A Bayesian Analysis of the Post-seismic Deformation of the Great 11 March 2011 Tohoku-Oki (Mw 9.0) Earthquake: Implications for Future Earthquake Occurrence

NASA Astrophysics Data System (ADS)

Ortega Culaciati, F. H.; Simons, M.; Minson, S. E.; Owen, S. E.; Moore, A. W.; Hetland, E. A.

2011-12-01

We aim to quantify the spatial distribution of after-slip following the Great 11 March 2011 Tohoku-Oki (Mw 9.0) earthquake and its implications for the occurrence of a future Great Earthquake, particularly in the Ibaraki region of Japan. We use a Bayesian approach (CATMIP algorithm), constrained by on-land Geonet GPS time series, to infer models of after-slip to date in the Japan megathrust. Unlike traditional inverse methods, in which a single optimum model is found, the Bayesian approach allows a complete characterization of the model parameter space by searching a-posteriori estimates of the range of plausible models. We use the Kullback-Liebler information divergence as a metric of the information gain on each subsurface slip patch, to quantify the extent to which land-based geodetic observations can constrain the upper parts of the megathrust, where the Great Tohoku-Oki earthquake took place. We aim to understand the relationships of spatial distribution of fault slip behavior in the different stages of the seismic cycle. We compare our post-seismic slip distributions to inter- and co-seismic slip distributions obtained through a Bayesian methodology as well as through traditional (optimization) inverse estimates in the published literature. We discuss implications of these analyses for the occurrence of a large earthquake in the Japan megathrust regions adjacent to the Great Tohoku-Oki earthquake.

Computational modelling of cellular level metabolism

NASA Astrophysics Data System (ADS)

Calvetti, D.; Heino, J.; Somersalo, E.

2008-07-01

The steady and stationary state inverse problems consist of estimating the reaction and transport fluxes, blood concentrations and possibly the rates of change of some of the concentrations based on data which are often scarce noisy and sampled over a population. The Bayesian framework provides a natural setting for the solution of this inverse problem, because a priori knowledge about the system itself and the unknown reaction fluxes and transport rates can compensate for the insufficiency of measured data, provided that the computational costs do not become prohibitive. This article identifies the computational challenges which have to be met when analyzing the steady and stationary states of multicompartment model for cellular metabolism and suggest stable and efficient ways to handle the computations. The outline of a computational tool based on the Bayesian paradigm for the simulation and analysis of complex cellular metabolic systems is also presented.

Source term identification in atmospheric modelling via sparse optimization

NASA Astrophysics Data System (ADS)

Adam, Lukas; Branda, Martin; Hamburger, Thomas

2015-04-01

Inverse modelling plays an important role in identifying the amount of harmful substances released into atmosphere during major incidents such as power plant accidents or volcano eruptions. Another possible application of inverse modelling lies in the monitoring the CO2 emission limits where only observations at certain places are available and the task is to estimate the total releases at given locations. This gives rise to minimizing the discrepancy between the observations and the model predictions. There are two standard ways of solving such problems. In the first one, this discrepancy is regularized by adding additional terms. Such terms may include Tikhonov regularization, distance from a priori information or a smoothing term. The resulting, usually quadratic, problem is then solved via standard optimization solvers. The second approach assumes that the error term has a (normal) distribution and makes use of Bayesian modelling to identify the source term. Instead of following the above-mentioned approaches, we utilize techniques from the field of compressive sensing. Such techniques look for a sparsest solution (solution with the smallest number of nonzeros) of a linear system, where a maximal allowed error term may be added to this system. Even though this field is a developed one with many possible solution techniques, most of them do not consider even the simplest constraints which are naturally present in atmospheric modelling. One of such examples is the nonnegativity of release amounts. We believe that the concept of a sparse solution is natural in both problems of identification of the source location and of the time process of the source release. In the first case, it is usually assumed that there are only few release points and the task is to find them. In the second case, the time window is usually much longer than the duration of the actual release. In both cases, the optimal solution should contain a large amount of zeros, giving rise to the concept of sparsity. In the paper, we summarize several optimization techniques which are used for finding sparse solutions and propose their modifications to handle selected constraints such as nonnegativity constraints and simple linear constraints, for example the minimal or maximal amount of total release. These techniques range from successive convex approximations to solution of one nonconvex problem. On simple examples, we explain these techniques and compare them from the point of implementation simplicity, approximation capability and convergence properties. Finally, these methods will be applied on the European Tracer Experiment (ETEX) data and the results will be compared with the current state of arts techniques such as regularized least squares or Bayesian approach. The obtained results show the surprisingly good results of these techniques. This research is supported by EEA/Norwegian Financial Mechanism under project 7F14287 STRADI.

Numerical convergence and validation of the DIMP inverse particle transport model

DOE PAGES

Nelson, Noel; Azmy, Yousry

2017-09-01

The data integration with modeled predictions (DIMP) model is a promising inverse radiation transport method for solving the special nuclear material (SNM) holdup problem. Unlike previous methods, DIMP is a completely passive nondestructive assay technique that requires no initial assumptions regarding the source distribution or active measurement time. DIMP predicts the most probable source location and distribution through Bayesian inference and quasi-Newtonian optimization of predicted detector re-sponses (using the adjoint transport solution) with measured responses. DIMP performs well with for-ward hemispherical collimation and unshielded measurements, but several considerations are required when using narrow-view collimated detectors. DIMP converged well to themore » correct source distribution as the number of synthetic responses increased. DIMP also performed well for the first experimental validation exercise after applying a collimation factor, and sufficiently reducing the source search vol-ume's extent to prevent the optimizer from getting stuck in local minima. DIMP's simple point detector response function (DRF) is being improved to address coplanar false positive/negative responses, and an angular DRF is being considered for integration with the next version of DIMP to account for highly collimated responses. Overall, DIMP shows promise for solving the SNM holdup inverse problem, especially once an improved optimization algorithm is implemented.« less

Ultra-Scalable Algorithms for Large-Scale Uncertainty Quantification in Inverse Wave Propagation

DTIC Science & Technology

2016-03-04

53] N. Petra , J. Martin , G. Stadler, and O. Ghattas, A computational framework for infinite-dimensional Bayesian inverse problems: Part II...positions: Alen Alexanderian (NC State), Tan Bui-Thanh (UT-Austin), Carsten Burstedde (University of Bonn), Noemi Petra (UC Merced), Georg Stalder (NYU), Hari...Baltimore, MD, Nov. 2002. SC2002 Best Technical Paper Award. [3] A. Alexanderian, N. Petra , G. Stadler, and O. Ghattas, A-optimal design of exper

Modeling the Absorbing Aerosol Index

NASA Technical Reports Server (NTRS)

Penner, Joyce; Zhang, Sophia

2003-01-01

We propose a scheme to model the absorbing aerosol index and improve the biomass carbon inventories by optimizing the difference between TOMS aerosol index (AI) and modeled AI with an inverse model. Two absorbing aerosol types are considered, including biomass carbon and mineral dust. A priori biomass carbon source was generated by Liousse et al [1996]. Mineral dust emission is parameterized according to surface wind and soil moisture using the method developed by Ginoux [2000]. In this initial study, the coupled CCM1 and GRANTOUR model was used to determine the aerosol spatial and temporal distribution. With modeled aerosol concentrations and optical properties, we calculate the radiance at the top of the atmosphere at 340 nm and 380 nm with a radiative transfer model. The contrast of radiance at these two wavelengths will be used to calculate AI. Then we compare the modeled AI with TOMS AI. This paper reports our initial modeling for AI and its comparison with TOMS Nimbus 7 AI. For our follow-on project we will model the global AI with aerosol spatial and temporal distribution recomputed from the IMPACT model and DAO GEOS-1 meteorology fields. Then we will build an inverse model, which applies a Bayesian inverse technique to optimize the agreement of between model and observational data. The inverse model will tune the biomass burning source strength to reduce the difference between modelled AI and TOMS AI. Further simulations with a posteriori biomass carbon sources from the inverse model will be carried out. Results will be compared to available observations such as surface concentration and aerosol optical depth.

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

Time series forecasting using ERNN and QR based on Bayesian model averaging

NASA Astrophysics Data System (ADS)

Pwasong, Augustine; Sathasivam, Saratha

2017-08-01

The Bayesian model averaging technique is a multi-model combination technique. The technique was employed to amalgamate the Elman recurrent neural network (ERNN) technique with the quadratic regression (QR) technique. The amalgamation produced a hybrid technique known as the hybrid ERNN-QR technique. The potentials of forecasting with the hybrid technique are compared with the forecasting capabilities of individual techniques of ERNN and QR. The outcome revealed that the hybrid technique is superior to the individual techniques in the mean square error sense.

Estimation of spatially varying heat transfer coefficient from a flat plate with flush mounted heat sources using Bayesian inference

NASA Astrophysics Data System (ADS)

Jakkareddy, Pradeep S.; Balaji, C.

2016-09-01

This paper employs the Bayesian based Metropolis Hasting - Markov Chain Monte Carlo algorithm to solve inverse heat transfer problem of determining the spatially varying heat transfer coefficient from a flat plate with flush mounted discrete heat sources with measured temperatures at the bottom of the plate. The Nusselt number is assumed to be of the form Nu = aReb(x/l)c . To input reasonable values of ’a’ and ‘b’ into the inverse problem, first limited two dimensional conjugate convection simulations were done with Comsol. Based on the guidance from this different values of ‘a’ and ‘b’ are input to a computationally less complex problem of conjugate conduction in the flat plate (15mm thickness) and temperature distributions at the bottom of the plate which is a more convenient location for measuring the temperatures without disturbing the flow were obtained. Since the goal of this work is to demonstrate the eficiacy of the Bayesian approach to accurately retrieve ‘a’ and ‘b’, numerically generated temperatures with known values of ‘a’ and ‘b’ are treated as ‘surrogate’ experimental data. The inverse problem is then solved by repeatedly using the forward solutions together with the MH-MCMC aprroach. To speed up the estimation, the forward model is replaced by an artificial neural network. The mean, maximum-a-posteriori and standard deviation of the estimated parameters ‘a’ and ‘b’ are reported. The robustness of the proposed method is examined, by synthetically adding noise to the temperatures.

Determining Crust and Upper Mantle Structure by Bayesian Joint Inversion of Receiver Functions and Surface Wave Dispersion at a Single Station: Preparation for Data from the InSight Mission

NASA Astrophysics Data System (ADS)

Jia, M.; Panning, M. P.; Lekic, V.; Gao, C.

2017-12-01

The InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission will deploy a geophysical station on Mars in 2018. Using seismology to explore the interior structure of the Mars is one of the main targets, and as part of the mission, we will use 3-component seismic data to constrain the crust and upper mantle structure including P and S wave velocities and densities underneath the station. We will apply a reversible jump Markov chain Monte Carlo algorithm in the transdimensional hierarchical Bayesian inversion framework, in which the number of parameters in the model space and the noise level of the observed data are also treated as unknowns in the inversion process. Bayesian based methods produce an ensemble of models which can be analyzed to quantify uncertainties and trade-offs of the model parameters. In order to get better resolution, we will simultaneously invert three different types of seismic data: receiver functions, surface wave dispersion (SWD), and ZH ratios. Because the InSight mission will only deliver a single seismic station to Mars, and both the source location and the interior structure will be unknown, we will jointly invert the ray parameter in our approach. In preparation for this work, we first verify our approach by using a set of synthetic data. We find that SWD can constrain the absolute value of velocities while receiver functions constrain the discontinuities. By joint inversion, the velocity structure in the crust and upper mantle is well recovered. Then, we apply our approach to real data from an earth-based seismic station BFO located in Black Forest Observatory in Germany, as already used in a demonstration study for single station location methods. From the comparison of the results, our hierarchical treatment shows its advantage over the conventional method in which the noise level of observed data is fixed as a prior.

Constraining mass anomalies in the interior of spherical bodies using Trans-dimensional Bayesian Hierarchical inference.

NASA Astrophysics Data System (ADS)

Izquierdo, K.; Lekic, V.; Montesi, L.

2017-12-01

Gravity inversions are especially important for planetary applications since measurements of the variations in gravitational acceleration are often the only constraint available to map out lateral density variations in the interiors of planets and other Solar system objects. Currently, global gravity data is available for the terrestrial planets and the Moon. Although several methods for inverting these data have been developed and applied, the non-uniqueness of global density models that fit the data has not yet been fully characterized. We make use of Bayesian inference and a Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach to develop a Trans-dimensional Hierarchical Bayesian (THB) inversion algorithm that yields a large sample of models that fit a gravity field. From this group of models, we can determine the most likely value of parameters of a global density model and a measure of the non-uniqueness of each parameter when the number of anomalies describing the gravity field is not fixed a priori. We explore the use of a parallel tempering algorithm and fast multipole method to reduce the number of iterations and computing time needed. We applied this method to a synthetic gravity field of the Moon and a long wavelength synthetic model of density anomalies in the Earth's lower mantle. We obtained a good match between the given gravity field and the gravity field produced by the most likely model in each inversion. The number of anomalies of the models showed parsimony of the algorithm, the value of the noise variance of the input data was retrieved, and the non-uniqueness of the models was quantified. Our results show that the ability to constrain the latitude and longitude of density anomalies, which is excellent at shallow locations (<200 km), decreases with increasing depth. With higher computational resources, this THB method for gravity inversion could give new information about the overall density distribution of celestial bodies even when there is no other geophysical data available.

Inferring Fault Frictional and Reservoir Hydraulic Properties From Injection-Induced Seismicity

NASA Astrophysics Data System (ADS)

Jagalur-Mohan, Jayanth; Jha, Birendra; Wang, Zheng; Juanes, Ruben; Marzouk, Youssef

2018-02-01

Characterizing the rheological properties of faults and the evolution of fault friction during seismic slip are fundamental problems in geology and seismology. Recent increases in the frequency of induced earthquakes have intensified the need for robust methods to estimate fault properties. Here we present a novel approach for estimation of aquifer and fault properties, which combines coupled multiphysics simulation of injection-induced seismicity with adaptive surrogate-based Bayesian inversion. In a synthetic 2-D model, we use aquifer pressure, ground displacements, and fault slip measurements during fluid injection to estimate the dynamic fault friction, the critical slip distance, and the aquifer permeability. Our forward model allows us to observe nonmonotonic evolutions of shear traction and slip on the fault resulting from the interplay of several physical mechanisms, including injection-induced aquifer expansion, stress transfer along the fault, and slip-induced stress relaxation. This interplay provides the basis for a successful joint inversion of induced seismicity, yielding well-informed Bayesian posterior distributions of dynamic friction and critical slip. We uncover an inverse relationship between dynamic friction and critical slip distance, which is in agreement with the small dynamic friction and large critical slip reported during seismicity on mature faults.

Estimating the periodic components of a biomedical signal through inverse problem modelling and Bayesian inference with sparsity enforcing prior

NASA Astrophysics Data System (ADS)

Dumitru, Mircea; Djafari, Ali-Mohammad

2015-01-01

The recent developments in chronobiology need a periodic components variation analysis for the signals expressing the biological rhythms. A precise estimation of the periodic components vector is required. The classical approaches, based on FFT methods, are inefficient considering the particularities of the data (short length). In this paper we propose a new method, using the sparsity prior information (reduced number of non-zero values components). The considered law is the Student-t distribution, viewed as a marginal distribution of a Infinite Gaussian Scale Mixture (IGSM) defined via a hidden variable representing the inverse variances and modelled as a Gamma Distribution. The hyperparameters are modelled using the conjugate priors, i.e. using Inverse Gamma Distributions. The expression of the joint posterior law of the unknown periodic components vector, hidden variables and hyperparameters is obtained and then the unknowns are estimated via Joint Maximum A Posteriori (JMAP) and Posterior Mean (PM). For the PM estimator, the expression of the posterior law is approximated by a separable one, via the Bayesian Variational Approximation (BVA), using the Kullback-Leibler (KL) divergence. Finally we show the results on synthetic data in cancer treatment applications.

Sequential Bayesian geoacoustic inversion for mobile and compact source-receiver configuration.

PubMed

Carrière, Olivier; Hermand, Jean-Pierre

2012-04-01

Geoacoustic characterization of wide areas through inversion requires easily deployable configurations including free-drifting platforms, underwater gliders and autonomous vehicles, typically performing repeated transmissions during their course. In this paper, the inverse problem is formulated as sequential Bayesian filtering to take advantage of repeated transmission measurements. Nonlinear Kalman filters implement a random-walk model for geometry and environment and an acoustic propagation code in the measurement model. Data from MREA/BP07 sea trials are tested consisting of multitone and frequency-modulated signals (bands: 0.25-0.8 and 0.8-1.6 kHz) received on a shallow vertical array of four hydrophones 5-m spaced drifting over 0.7-1.6 km range. Space- and time-coherent processing are applied to the respective signal types. Kalman filter outputs are compared to a sequence of global optimizations performed independently on each received signal. For both signal types, the sequential approach is more accurate but also more efficient. Due to frequency diversity, the processing of modulated signals produces a more stable tracking. Although an extended Kalman filter provides comparable estimates of the tracked parameters, the ensemble Kalman filter is necessary to properly assess uncertainty. In spite of mild range dependence and simplified bottom model, all tracked geoacoustic parameters are consistent with high-resolution seismic profiling, core logging P-wave velocity, and previous inversion results with fixed geometries.

Bayesian estimation of magma supply, storage, and eruption rates using a multiphysical volcano model: Kīlauea Volcano, 2000-2012

NASA Astrophysics Data System (ADS)

Anderson, Kyle R.; Poland, Michael P.

2016-08-01

Estimating rates of magma supply to the world's volcanoes remains one of the most fundamental aims of volcanology. Yet, supply rates can be difficult to estimate even at well-monitored volcanoes, in part because observations are noisy and are usually considered independently rather than as part of a holistic system. In this work we demonstrate a technique for probabilistically estimating time-variable rates of magma supply to a volcano through probabilistic constraint on storage and eruption rates. This approach utilizes Bayesian joint inversion of diverse datasets using predictions from a multiphysical volcano model, and independent prior information derived from previous geophysical, geochemical, and geological studies. The solution to the inverse problem takes the form of a probability density function which takes into account uncertainties in observations and prior information, and which we sample using a Markov chain Monte Carlo algorithm. Applying the technique to Kīlauea Volcano, we develop a model which relates magma flow rates with deformation of the volcano's surface, sulfur dioxide emission rates, lava flow field volumes, and composition of the volcano's basaltic magma. This model accounts for effects and processes mostly neglected in previous supply rate estimates at Kīlauea, including magma compressibility, loss of sulfur to the hydrothermal system, and potential magma storage in the volcano's deep rift zones. We jointly invert data and prior information to estimate rates of supply, storage, and eruption during three recent quasi-steady-state periods at the volcano. Results shed new light on the time-variability of magma supply to Kīlauea, which we find to have increased by 35-100% between 2001 and 2006 (from 0.11-0.17 to 0.18-0.28 km3/yr), before subsequently decreasing to 0.08-0.12 km3/yr by 2012. Changes in supply rate directly impact hazard at the volcano, and were largely responsible for an increase in eruption rate of 60-150% between 2001 and 2006, and subsequent decline by as much as 60% by 2012. We also demonstrate the occurrence of temporal changes in the proportion of Kīlauea's magma supply that is stored versus erupted, with the supply ;surge; in 2006 associated with increased accumulation of magma at the summit. Finally, we are able to place some constraints on sulfur concentrations in Kīlauea magma and the scrubbing of sulfur by the volcano's hydrothermal system. Multiphysical, Bayesian constraint on magma flow rates may be used to monitor evolving volcanic hazard not just at Kīlauea but at other volcanoes around the world.

Bayesian Travel Time Inversion adopting Gaussian Process Regression

NASA Astrophysics Data System (ADS)

Mauerberger, S.; Holschneider, M.

2017-12-01

A major application in seismology is the determination of seismic velocity models. Travel time measurements are putting an integral constraint on the velocity between source and receiver. We provide insight into travel time inversion from a correlation-based Bayesian point of view. Therefore, the concept of Gaussian process regression is adopted to estimate a velocity model. The non-linear travel time integral is approximated by a 1st order Taylor expansion. A heuristic covariance describes correlations amongst observations and a priori model. That approach enables us to assess a proxy of the Bayesian posterior distribution at ordinary computational costs. No multi dimensional numeric integration nor excessive sampling is necessary. Instead of stacking the data, we suggest to progressively build the posterior distribution. Incorporating only a single evidence at a time accounts for the deficit of linearization. As a result, the most probable model is given by the posterior mean whereas uncertainties are described by the posterior covariance.As a proof of concept, a synthetic purely 1d model is addressed. Therefore a single source accompanied by multiple receivers is considered on top of a model comprising a discontinuity. We consider travel times of both phases - direct and reflected wave - corrupted by noise. Left and right of the interface are assumed independent where the squared exponential kernel serves as covariance.

New Approaches For Asteroid Spin State and Shape Modeling From Delay-Doppler Radar Images

NASA Astrophysics Data System (ADS)

Raissi, Chedy; Lamee, Mehdi; Mosiane, Olorato; Vassallo, Corinne; Busch, Michael W.; Greenberg, Adam; Benner, Lance A. M.; Naidu, Shantanu P.; Duong, Nicholas

2016-10-01

Delay-Doppler radar imaging is a powerful technique to characterize the trajectories, shapes, and spin states of near-Earth asteroids; and has yielded detailed models of dozens of objects. Reconstructing objects' shapes and spins from delay-Doppler data is a computationally intensive inversion problem. Since the 1990s, delay-Doppler data has been analyzed using the SHAPE software. SHAPE performs sequential single-parameter fitting, and requires considerable computer runtime and human intervention (Hudson 1993, Magri et al. 2007). Recently, multiple-parameter fitting algorithms have been shown to more efficiently invert delay-Doppler datasets (Greenberg & Margot 2015) - decreasing runtime while improving accuracy. However, extensive human oversight of the shape modeling process is still required. We have explored two new techniques to better automate delay-Doppler shape modeling: Bayesian optimization and a machine-learning neural network.One of the most time-intensive steps of the shape modeling process is to perform a grid search to constrain the target's spin state. We have implemented a Bayesian optimization routine that uses SHAPE to autonomously search the space of spin-state parameters. To test the efficacy of this technique, we compared it to results with human-guided SHAPE for asteroids 1992 UY4, 2000 RS11, and 2008 EV5. Bayesian optimization yielded similar spin state constraints within a factor of 3 less computer runtime.The shape modeling process could be further accelerated using a deep neural network to replace iterative fitting. We have implemented a neural network with a variational autoencoder (VAE), using a subset of known asteroid shapes and a large set of synthetic radar images as inputs to train the network. Conditioning the VAE in this manner allows the user to give the network a set of radar images and get a 3D shape model as an output. Additional development will be required to train a network to reliably render shapes from delay-Doppler images.This work was supported by NASA Ames, NVIDIA, Autodesk and the SETI Institute as part of the NASA Frontier Development Lab program.

A default Bayesian hypothesis test for mediation.

PubMed

Nuijten, Michèle B; Wetzels, Ruud; Matzke, Dora; Dolan, Conor V; Wagenmakers, Eric-Jan

2015-03-01

In order to quantify the relationship between multiple variables, researchers often carry out a mediation analysis. In such an analysis, a mediator (e.g., knowledge of a healthy diet) transmits the effect from an independent variable (e.g., classroom instruction on a healthy diet) to a dependent variable (e.g., consumption of fruits and vegetables). Almost all mediation analyses in psychology use frequentist estimation and hypothesis-testing techniques. A recent exception is Yuan and MacKinnon (Psychological Methods, 14, 301-322, 2009), who outlined a Bayesian parameter estimation procedure for mediation analysis. Here we complete the Bayesian alternative to frequentist mediation analysis by specifying a default Bayesian hypothesis test based on the Jeffreys-Zellner-Siow approach. We further extend this default Bayesian test by allowing a comparison to directional or one-sided alternatives, using Markov chain Monte Carlo techniques implemented in JAGS. All Bayesian tests are implemented in the R package BayesMed (Nuijten, Wetzels, Matzke, Dolan, & Wagenmakers, 2014).

Some practical aspects of prestack waveform inversion using a genetic algorithm: An example from the east Texas Woodbine gas sand

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mallick, S.

1999-03-01

In this paper, a prestack inversion method using a genetic algorithm (GA) is presented, and issues relating to the implementation of prestack GA inversion in practice are discussed. GA is a Monte-Carlo type inversion, using a natural analogy to the biological evolution process. When GA is cast into a Bayesian framework, a priori information of the model parameters and the physics of the forward problem are used to compute synthetic data. These synthetic data can then be matched with observations to obtain approximate estimates of the marginal a posteriori probability density (PPD) functions in the model space. Plots of thesemore » PPD functions allow an interpreter to choose models which best describe the specific geologic setting and lead to an accurate prediction of seismic lithology. Poststack inversion and prestack GA inversion were applied to a Woodbine gas sand data set from East Texas. A comparison of prestack inversion with poststack inversion demonstrates that prestack inversion shows detailed stratigraphic features of the subsurface which are not visible on the poststack inversion.« less

Impact of meteorological inflow uncertainty on tracer transport and source estimation in urban atmospheres

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lucas, Donald D.; Gowardhan, Akshay; Cameron-Smith, Philip

2015-08-08

Here, a computational Bayesian inverse technique is used to quantify the effects of meteorological inflow uncertainty on tracer transport and source estimation in a complex urban environment. We estimate a probability distribution of meteorological inflow by comparing wind observations to Monte Carlo simulations from the Aeolus model. Aeolus is a computational fluid dynamics model that simulates atmospheric and tracer flow around buildings and structures at meter-scale resolution. Uncertainty in the inflow is propagated through forward and backward Lagrangian dispersion calculations to determine the impact on tracer transport and the ability to estimate the release location of an unknown source. Ourmore » uncertainty methods are compared against measurements from an intensive observation period during the Joint Urban 2003 tracer release experiment conducted in Oklahoma City.« less

Bayesian evidence computation for model selection in non-linear geoacoustic inference problems.

PubMed

Dettmer, Jan; Dosso, Stan E; Osler, John C

2010-12-01

This paper applies a general Bayesian inference approach, based on Bayesian evidence computation, to geoacoustic inversion of interface-wave dispersion data. Quantitative model selection is carried out by computing the evidence (normalizing constants) for several model parameterizations using annealed importance sampling. The resulting posterior probability density estimate is compared to estimates obtained from Metropolis-Hastings sampling to ensure consistent results. The approach is applied to invert interface-wave dispersion data collected on the Scotian Shelf, off the east coast of Canada for the sediment shear-wave velocity profile. Results are consistent with previous work on these data but extend the analysis to a rigorous approach including model selection and uncertainty analysis. The results are also consistent with core samples and seismic reflection measurements carried out in the area.

Fast model updating coupling Bayesian inference and PGD model reduction

NASA Astrophysics Data System (ADS)

Rubio, Paul-Baptiste; Louf, François; Chamoin, Ludovic

2018-04-01

The paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example.

Civil Engineering Applications of Ground Penetrating Radar Recent Advances @ the ELEDIA Research Center

NASA Astrophysics Data System (ADS)

Salucci, Marco; Tenuti, Lorenza; Nardin, Cristina; Oliveri, Giacomo; Viani, Federico; Rocca, Paolo; Massa, Andrea

2014-05-01

The application of non-destructive testing and evaluation (NDT/NDE) methodologies in civil engineering has raised a growing interest during the last years because of its potential impact in several different scenarios. As a consequence, Ground Penetrating Radar (GPR) technologies have been widely adopted as an instrument for the inspection of the structural stability of buildings and for the detection of cracks and voids. In this framework, the development and validation of GPR algorithms and methodologies represents one of the most active research areas within the ELEDIA Research Center of the University of Trento. More in detail, great efforts have been devoted towards the development of inversion techniques based on the integration of deterministic and stochastic search algorithms with multi-focusing strategies. These approaches proved to be effective in mitigating the effects of both nonlinearity and ill-posedness of microwave imaging problems, which represent the well-known issues arising in GPR inverse scattering formulations. More in detail, a regularized multi-resolution approach based on the Inexact Newton Method (INM) has been recently applied to subsurface prospecting, showing a remarkable advantage over a single-resolution implementation [1]. Moreover, the use of multi-frequency or frequency-hopping strategies to exploit the information coming from GPR data collected in time domain and transformed into its frequency components has been proposed as well. In this framework, the effectiveness of the multi-resolution multi-frequency techniques has been proven on synthetic data generated with numerical models such as GprMax [2]. The application of inversion algorithms based on Bayesian Compressive Sampling (BCS) [3][4] to GPR is currently under investigation, as well, in order to exploit their capability to provide satisfactory reconstructions in presence of single and multiple sparse scatterers [3][4]. Furthermore, multi-scaling approaches exploiting level-set-based optimization have been developed for the qualitative reconstruction of multiple and disconnected homogeneous scatterers [5]. Finally, the real-time detection and classification of subsurface scatterers has been investigated by means of learning-by-examples (LBE) techniques, such as Support Vector Machines (SVM) [6]. Acknowledgment - This work was partially supported by COST Action TU1208 'Civil Engineering Applications of Ground Penetrating Radar' References [1] M. Salucci, D. Sartori, N. Anselmi, A. Randazzo, G. Oliveri, and A. Massa, 'Imaging Buried Objects within the Second-Order Born Approximation through a Multiresolution Regularized Inexact-Newton Method', 2013 International Symposium on Electromagnetic Theory (EMTS), (Hiroshima, Japan), May 20-24 2013 (invited). [2] A. Giannopoulos, 'Modelling ground penetrating radar by GprMax', Construct. Build. Mater., vol. 19, no. 10, pp.755 -762 2005 [3] L. Poli, G. Oliveri, P. Rocca, and A. Massa, "Bayesian compressive sensing approaches for the reconstruction of two-dimensional sparse scatterers under TE illumination," IEEE Trans. Geosci. Remote Sensing, vol. 51, no. 5, pp. 2920-2936, May. 2013. [4] L. Poli, G. Oliveri, and A. Massa, "Imaging sparse metallic cylinders through a Local Shape Function Bayesian Compressive Sensing approach," Journal of Optical Society of America A, vol. 30, no. 6, pp. 1261-1272, 2013. [5] M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, "Multiple shapes reconstruction by means of multi-region level sets," IEEE Trans. Geosci. Remote Sensing, vol. 48, no. 5, pp. 2330-2342, May 2010. [6] L. Lizzi, F. Viani, P. Rocca, G. Oliveri, M. Benedetti and A. Massa, "Three-dimensional real-time localization of subsurface objects - From theory to experimental validation," 2009 IEEE International Geoscience and Remote Sensing Symposium, vol. 2, pp. II-121-II-124, 12-17 July 2009.

Localisation of an Unknown Number of Land Mines Using a Network of Vapour Detectors

PubMed Central

Chhadé, Hiba Haj; Abdallah, Fahed; Mougharbel, Imad; Gning, Amadou; Julier, Simon; Mihaylova, Lyudmila

2014-01-01

We consider the problem of localising an unknown number of land mines using concentration information provided by a wireless sensor network. A number of vapour sensors/detectors, deployed in the region of interest, are able to detect the concentration of the explosive vapours, emanating from buried land mines. The collected data is communicated to a fusion centre. Using a model for the transport of the explosive chemicals in the air, we determine the unknown number of sources using a Principal Component Analysis (PCA)-based technique. We also formulate the inverse problem of determining the positions and emission rates of the land mines using concentration measurements provided by the wireless sensor network. We present a solution for this problem based on a probabilistic Bayesian technique using a Markov chain Monte Carlo sampling scheme, and we compare it to the least squares optimisation approach. Experiments conducted on simulated data show the effectiveness of the proposed approach. PMID:25384008

Bayesian hierarchical model of ceftriaxone resistance proportions among Salmonella serotype Heidelberg infections.

PubMed

Gu, Weidong; Medalla, Felicita; Hoekstra, Robert M

2018-02-01

The National Antimicrobial Resistance Monitoring System (NARMS) at the Centers for Disease Control and Prevention tracks resistance among Salmonella infections. The annual number of Salmonella isolates of a particular serotype from states may be small, making direct estimation of resistance proportions unreliable. We developed a Bayesian hierarchical model to improve estimation by borrowing strength from relevant sampling units. We illustrate the models with different specifications of spatio-temporal interaction using 2004-2013 NARMS data for ceftriaxone-resistant Salmonella serotype Heidelberg. Our results show that Bayesian estimates of resistance proportions were smoother than observed values, and the difference between predicted and observed proportions was inversely related to the number of submitted isolates. The model with interaction allowed for tracking of annual changes in resistance proportions at the state level. We demonstrated that Bayesian hierarchical models provide a useful tool to examine spatio-temporal patterns of small sample size such as those found in NARMS. Published by Elsevier Ltd.

Bayesian Analysis of the Association between Family-Level Factors and Siblings' Dental Caries.

PubMed

Wen, A; Weyant, R J; McNeil, D W; Crout, R J; Neiswanger, K; Marazita, M L; Foxman, B

2017-07-01

We conducted a Bayesian analysis of the association between family-level socioeconomic status and smoking and the prevalence of dental caries among siblings (children from infant to 14 y) among children living in rural and urban Northern Appalachia using data from the Center for Oral Health Research in Appalachia (COHRA). The observed proportion of siblings sharing caries was significantly different from predicted assuming siblings' caries status was independent. Using a Bayesian hierarchical model, we found the inclusion of a household factor significantly improved the goodness of fit. Other findings showed an inverse association between parental education and siblings' caries and a positive association between households with smokers and siblings' caries. Our study strengthens existing evidence suggesting that increased parental education and decreased parental cigarette smoking are associated with reduced childhood caries in the household. Our results also demonstrate the value of a Bayesian approach, which allows us to include household as a random effect, thereby providing more accurate estimates than obtained using generalized linear mixed models.

Dependence of paracentric inversion rate on tract length.

PubMed

York, Thomas L; Durrett, Rick; Nielsen, Rasmus

2007-04-03

We develop a Bayesian method based on MCMC for estimating the relative rates of pericentric and paracentric inversions from marker data from two species. The method also allows estimation of the distribution of inversion tract lengths. We apply the method to data from Drosophila melanogaster and D. yakuba. We find that pericentric inversions occur at a much lower rate compared to paracentric inversions. The average paracentric inversion tract length is approx. 4.8 Mb with small inversions being more frequent than large inversions. If the two breakpoints defining a paracentric inversion tract are uniformly and independently distributed over chromosome arms there will be more short tract-length inversions than long; we find an even greater preponderance of short tract lengths than this would predict. Thus there appears to be a correlation between the positions of breakpoints which favors shorter tract lengths. The method developed in this paper provides the first statistical estimator for estimating the distribution of inversion tract lengths from marker data. Application of this method for a number of data sets may help elucidate the relationship between the length of an inversion and the chance that it will get accepted.

Dependence of paracentric inversion rate on tract length

PubMed Central

York, Thomas L; Durrett, Rick; Nielsen, Rasmus

2007-01-01

Background We develop a Bayesian method based on MCMC for estimating the relative rates of pericentric and paracentric inversions from marker data from two species. The method also allows estimation of the distribution of inversion tract lengths. Results We apply the method to data from Drosophila melanogaster and D. yakuba. We find that pericentric inversions occur at a much lower rate compared to paracentric inversions. The average paracentric inversion tract length is approx. 4.8 Mb with small inversions being more frequent than large inversions. If the two breakpoints defining a paracentric inversion tract are uniformly and independently distributed over chromosome arms there will be more short tract-length inversions than long; we find an even greater preponderance of short tract lengths than this would predict. Thus there appears to be a correlation between the positions of breakpoints which favors shorter tract lengths. Conclusion The method developed in this paper provides the first statistical estimator for estimating the distribution of inversion tract lengths from marker data. Application of this method for a number of data sets may help elucidate the relationship between the length of an inversion and the chance that it will get accepted. PMID:17407601

Analysis of the variability in ground-motion synthesis and inversion

USGS Publications Warehouse

Spudich, Paul A.; Cirella, Antonella; Scognamiglio, Laura; Tinti, Elisa

2017-12-07

In almost all past inversions of large-earthquake ground motions for rupture behavior, the goal of the inversion is to find the “best fitting” rupture model that predicts ground motions which optimize some function of the difference between predicted and observed ground motions. This type of inversion was pioneered in the linear-inverse sense by Olson and Apsel (1982), who minimized the square of the difference between observed and simulated motions (“least squares”) while simultaneously minimizing the rupture-model norm (by setting the null-space component of the rupture model to zero), and has been extended in many ways, one of which is the use of nonlinear inversion schemes such as simulated annealing algorithms that optimize some other misfit function. For example, the simulated annealing algorithm of Piatanesi and others (2007) finds the rupture model that minimizes a “cost” function which combines a least-squares and a waveform-correlation measure of misfit.All such inversions that look for a unique “best” model have at least three problems. (1) They have removed the null-space component of the rupture model—that is, an infinite family of rupture models that all fit the data equally well have been narrowed down to a single model. Some property of interest in the rupture model might have been discarded in this winnowing process. (2) Smoothing constraints are commonly used to yield a unique “best” model, in which case spatially rough rupture models will have been discarded, even if they provide a good fit to the data. (3) No estimate of confidence in the resulting rupture models can be given because the effects of unknown errors in the Green’s functions (“theory errors”) have not been assessed. In inversion for rupture behavior, these theory errors are generally larger than the data errors caused by ground noise and instrumental limitations, and so overfitting of the data is probably ubiquitous for such inversions.Recently, attention has turned to the inclusion of theory errors in the inversion process. Yagi and Fukahata (2011) made an important contribution by presenting a method to estimate the uncertainties in predicted large-earthquake ground motions due to uncertainties in the Green’s functions. Here we derive their result and compare it with the results of other recent studies that look at theory errors in a Bayesian inversion context particularly those by Bodin and others (2012), Duputel and others (2012), Dettmer and others (2014), and Minson and others (2014).Notably, in all these studies, the estimates of theory error were obtained from theoretical considerations alone; none of the investigators actually measured Green’s function errors. Large earthquakes typically have aftershocks, which, if their rupture surfaces are physically small enough, can be considered point evaluations of the real Green’s functions of the Earth. Here we simulate smallaftershock ground motions with (erroneous) theoretical Green’s functions. Taking differences between aftershock ground motions and simulated motions to be the “theory error,” we derive a statistical model of the sources of discrepancies between the theoretical and real Green’s functions. We use this model with an extended frequency-domain version of the time-domain theory of Yagi and Fukahata (2011) to determine the expected variance 2 τ caused by Green’s function error in ground motions from a larger (nonpoint) earthquake that we seek to model.We also differ from the above-mentioned Bayesian inversions in our handling of the nonuniqueness problem of seismic inversion. We follow the philosophy of Segall and Du (1993), who, instead of looking for a best-fitting model, looked for slip models that answered specific questions about the earthquakes they studied. In their Bayesian inversions, they inductively derived a posterior probability-density function (PDF) for every model parameter. We instead seek to find two extremal rupture models whose ground motions fit the data within the error bounds given by 2 τ , as quantified by using a chi-squared test described below. So, we can ask questions such as, “What are the rupture models with the highest and lowest average rupture speed consistent with the theory errors?” Having found those models, we can then say with confidence that the true rupture speed is somewhere between those values. Although the Bayesian approach gives a complete solution to the inverse problem, it is computationally demanding: Minson and others (2014) needed 1010 forward kinematic simulations to derive their posterior probability distribution. In our approach, only about107 simulations are needed. Moreover, in practical application, only a small set of rupture models may be needed to answer the relevant questions—for example, determining the maximum likelihood solution (achievable through standard inversion techniques) and the two rupture models bounding some property of interest.The specific property that we wish to investigate is the correlation between various rupturemodel parameters, such as peak slip velocity and rupture velocity, in models of real earthquakes. In some simulations of ground motions for hypothetical large earthquakes, such as those by Aagaard and others (2010) and the Southern California Earthquake Center Broadband Simulation Platform (Graves and Pitarka, 2015), rupture speed is assumed to correlate locally with peak slip, although there is evidence that rupture speed should correlate better with peak slip speed, owing to its dependence on local stress drop. We may be able to determine ways to modify Piatanesi and others’s (2007) inversion’s “cost” function to find rupture models with either high or low degrees of correlation between pairs of rupture parameters. We propose a cost function designed to find these two extremal models.

Hierarchical Bayesian method for mapping biogeochemical hot spots using induced polarization imaging

DOE PAGES

Wainwright, Haruko M.; Flores Orozco, Adrian; Bucker, Matthias; ...

2016-01-29

In floodplain environments, a naturally reduced zone (NRZ) is considered to be a common biogeochemical hot spot, having distinct microbial and geochemical characteristics. Although important for understanding their role in mediating floodplain biogeochemical processes, mapping the subsurface distribution of NRZs over the dimensions of a floodplain is challenging, as conventional wellbore data are typically spatially limited and the distribution of NRZs is heterogeneous. In this work, we present an innovative methodology for the probabilistic mapping of NRZs within a three-dimensional (3-D) subsurface domain using induced polarization imaging, which is a noninvasive geophysical technique. Measurements consist of surface geophysical surveys andmore » drilling-recovered sediments at the U.S. Department of Energy field site near Rifle, CO (USA). Inversion of surface time domain-induced polarization (TDIP) data yielded 3-D images of the complex electrical resistivity, in terms of magnitude and phase, which are associated with mineral precipitation and other lithological properties. By extracting the TDIP data values colocated with wellbore lithological logs, we found that the NRZs have a different distribution of resistivity and polarization from the other aquifer sediments. To estimate the spatial distribution of NRZs, we developed a Bayesian hierarchical model to integrate the geophysical and wellbore data. In addition, the resistivity images were used to estimate hydrostratigraphic interfaces under the floodplain. Validation results showed that the integration of electrical imaging and wellbore data using a Bayesian hierarchical model was capable of mapping spatially heterogeneous interfaces and NRZ distributions thereby providing a minimally invasive means to parameterize a hydrobiogeochemical model of the floodplain.« less

A probabilistic process model for pelagic marine ecosystems informed by Bayesian inverse analysis

EPA Science Inventory

Marine ecosystems are complex systems with multiple pathways that produce feedback cycles, which may lead to unanticipated effects. Models abstract this complexity and allow us to predict, understand, and hypothesize. In ecological models, however, the paucity of empirical data...

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

PubMed

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

2016-09-01

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

Logarithmic Laplacian Prior Based Bayesian Inverse Synthetic Aperture Radar Imaging.

PubMed

Zhang, Shuanghui; Liu, Yongxiang; Li, Xiang; Bi, Guoan

2016-04-28

This paper presents a novel Inverse Synthetic Aperture Radar Imaging (ISAR) algorithm based on a new sparse prior, known as the logarithmic Laplacian prior. The newly proposed logarithmic Laplacian prior has a narrower main lobe with higher tail values than the Laplacian prior, which helps to achieve performance improvement on sparse representation. The logarithmic Laplacian prior is used for ISAR imaging within the Bayesian framework to achieve better focused radar image. In the proposed method of ISAR imaging, the phase errors are jointly estimated based on the minimum entropy criterion to accomplish autofocusing. The maximum a posterior (MAP) estimation and the maximum likelihood estimation (MLE) are utilized to estimate the model parameters to avoid manually tuning process. Additionally, the fast Fourier Transform (FFT) and Hadamard product are used to minimize the required computational efficiency. Experimental results based on both simulated and measured data validate that the proposed algorithm outperforms the traditional sparse ISAR imaging algorithms in terms of resolution improvement and noise suppression.

Inverse problems and computational cell metabolic models: a statistical approach

NASA Astrophysics Data System (ADS)

Calvetti, D.; Somersalo, E.

2008-07-01

In this article, we give an overview of the Bayesian modelling of metabolic systems at the cellular and subcellular level. The models are based on detailed description of key biochemical reactions occurring in tissue, which may in turn be compartmentalized into cytosol and mitochondria, and of transports between the compartments. The classical deterministic approach which models metabolic systems as dynamical systems with Michaelis-Menten kinetics, is replaced by a stochastic extension where the model parameters are interpreted as random variables with an appropriate probability density. The inverse problem of cell metabolism in this setting consists of estimating the density of the model parameters. After discussing some possible approaches to solving the problem, we address the issue of how to assess the reliability of the predictions of a stochastic model by proposing an output analysis in terms of model uncertainties. Visualization modalities for organizing the large amount of information provided by the Bayesian dynamic sensitivity analysis are also illustrated.

Bayesian ionospheric multi-instrument 3D tomography

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Vierinen, Juha; Roininen, Lassi

2017-04-01

The tomographic reconstruction of ionospheric electron densities is an inverse problem that cannot be solved without relatively strong regularising additional information. % Especially the vertical electron density profile is determined predominantly by the regularisation. % %Often utilised regularisations in ionospheric tomography include smoothness constraints and iterative methods with initial ionospheric models. % Despite its crucial role, the regularisation is often hidden in the algorithm as a numerical procedure without physical understanding. % % The Bayesian methodology provides an interpretative approach for the problem, as the regularisation can be given in a physically meaningful and quantifiable prior probability distribution. % The prior distribution can be based on ionospheric physics, other available ionospheric measurements and their statistics. % Updating the prior with measurements results as the posterior distribution that carries all the available information combined. % From the posterior distribution, the most probable state of the ionosphere can then be solved with the corresponding probability intervals. % Altogether, the Bayesian methodology provides understanding on how strong the given regularisation is, what is the information gained with the measurements and how reliable the final result is. % In addition, the combination of different measurements and temporal development can be taken into account in a very intuitive way. However, a direct implementation of the Bayesian approach requires inversion of large covariance matrices resulting in computational infeasibility. % In the presented method, Gaussian Markov random fields are used to form a sparse matrix approximations for the covariances. % The approach makes the problem computationally feasible while retaining the probabilistic and physical interpretation. Here, the Bayesian method with Gaussian Markov random fields is applied for ionospheric 3D tomography over Northern Europe. % Multi-instrument measurements are utilised from TomoScand receiver network for Low Earth orbit beacon satellite signals, GNSS receiver networks, as well as from EISCAT ionosondes and incoherent scatter radars. % %The performance is demonstrated in three-dimensional spatial domain with temporal development also taken into account.

Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models

PubMed Central

Paz-Linares, Deirel; Vega-Hernández, Mayrim; Rojas-López, Pedro A.; Valdés-Hernández, Pedro A.; Martínez-Montes, Eduardo; Valdés-Sosa, Pedro A.

2017-01-01

The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods, Quality Measures and Visualization Routines are freely available in a public website. PMID:29200994

Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models.

PubMed

Paz-Linares, Deirel; Vega-Hernández, Mayrim; Rojas-López, Pedro A; Valdés-Hernández, Pedro A; Martínez-Montes, Eduardo; Valdés-Sosa, Pedro A

2017-01-01

The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods, Quality Measures and Visualization Routines are freely available in a public website.

An Inversion Analysis of Recent Variability in Natural CO2 Fluxes Using GOSAT and In Situ Observations

NASA Astrophysics Data System (ADS)

Wang, J. S.; Kawa, S. R.; Baker, D. F.; Collatz, G. J.; Ott, L. E.

2015-12-01

About one-half of the global CO2 emissions from fossil fuel combustion and deforestation accumulates in the atmosphere, where it contributes to global warming. The rest is taken up by vegetation and the ocean. The precise contribution of the two sinks, and their location and year-to-year variability are, however, not well understood. We use two different approaches, batch Bayesian synthesis inversion and variational data assimilation, to deduce the global spatiotemporal distributions of CO2 fluxes during 2009-2010. One of our objectives is to assess different sources of uncertainties in inferred fluxes, including uncertainties in prior flux estimates and observations, and differences in inversion techniques. For prior constraints, we utilize fluxes and uncertainties from the CASA-GFED model of the terrestrial biosphere and biomass burning driven by satellite observations and interannually varying meteorology. We also use measurement-based ocean flux estimates and two sets of fixed fossil CO2 emissions. Here, our inversions incorporate column CO2 measurements from the GOSAT satellite (ACOS retrieval, filtered and bias-corrected) and in situ observations (individual flask and afternoon-average continuous observations) to estimate fluxes in 108 regions over 8-day intervals for the batch inversion and at 3° x 3.75° weekly for the variational system. Relationships between fluxes and atmospheric concentrations are derived consistently for the two inversion systems using the PCTM atmospheric transport model driven by meteorology from the MERRA reanalysis. We compare the posterior fluxes and uncertainties derived using different data sets and the two inversion approaches, and evaluate the posterior atmospheric concentrations against independent data including aircraft measurements. The optimized fluxes generally resemble those from other studies. For example, the results indicate that the terrestrial biosphere is a net CO2 sink, and a GOSAT-only inversion suggests a shift in the global sink from the tropics/south to the north relative to the prior and to an in-situ-only inversion. We also find a smaller terrestrial sink in higher-latitude northern regions in boreal summer of 2010 relative to 2009.

Joint inversion of geophysical data using petrophysical clustering and facies deformation wth the level set technique

NASA Astrophysics Data System (ADS)

Revil, A.

2015-12-01

Geological expertise and petrophysical relationships can be brought together to provide prior information while inverting multiple geophysical datasets. The merging of such information can result in more realistic solution in the distribution of the model parameters, reducing ipse facto the non-uniqueness of the inverse problem. We consider two level of heterogeneities: facies, described by facies boundaries and heteroegenities inside each facies determined by a correlogram. In this presentation, we pose the geophysical inverse problem in terms of Gaussian random fields with mean functions controlled by petrophysical relationships and covariance functions controlled by a prior geological cross-section, including the definition of spatial boundaries for the geological facies. The petrophysical relationship problem is formulated as a regression problem upon each facies. The inversion of the geophysical data is performed in a Bayesian framework. We demonstrate the usefulness of this strategy using a first synthetic case for which we perform a joint inversion of gravity and galvanometric resistivity data with the stations located at the ground surface. The joint inversion is used to recover the density and resistivity distributions of the subsurface. In a second step, we consider the possibility that the facies boundaries are deformable and their shapes are inverted as well. We use the level set approach to perform such deformation preserving prior topological properties of the facies throughout the inversion. With the help of prior facies petrophysical relationships and topological characteristic of each facies, we make posterior inference about multiple geophysical tomograms based on their corresponding geophysical data misfits. The method is applied to a second synthetic case showing that we can recover the heterogeneities inside the facies, the mean values for the petrophysical properties, and, to some extent, the facies boundaries using the 2D joint inversion of gravity and galvanometric resistivity data. For this 2D synthetic example, we note that the position of the facies are well-recovered except far from the ground surfce where the sensitivity is too low. The figure shows the evolution of the shape of the facies during the inversion itertion by iteration.

An Inversion Analysis of Recent Variability in Natural CO2 Fluxes Using GOSAT and In Situ Observations

NASA Technical Reports Server (NTRS)

Wang, James S.; Kawa, S. Randolph; Collatz, G. James; Baker, David F.; Ott, Lesley

2015-01-01

About one-half of the global CO2 emissions from fossil fuel combustion and deforestation accumulates in the atmosphere, where it contributes to global warming. The rest is taken up by vegetation and the ocean. The precise contribution of the two sinks, and their location and year-to-year variability are, however, not well understood. We use two different approaches, batch Bayesian synthesis inversion and variational data assimilation, to deduce the global spatiotemporal distributions of CO2 fluxes during 2009-2010. One of our objectives is to assess different sources of uncertainties in inferred fluxes, including uncertainties in prior flux estimates and observations, and differences in inversion techniques. For prior constraints, we utilize fluxes and uncertainties from the CASA-GFED model of the terrestrial biosphere and biomass burning driven by satellite observations and interannually varying meteorology. We also use measurement-based ocean flux estimates and two sets of fixed fossil CO2 emissions. Here, our inversions incorporate column CO2 measurements from the GOSAT satellite (ACOS retrieval, filtered and bias-corrected) and in situ observations (individual flask and afternoon-average continuous observations) to estimate fluxes in 108 regions over 8-day intervals for the batch inversion and at 3 x 3.75 weekly for the variational system. Relationships between fluxes and atmospheric concentrations are derived consistently for the two inversion systems using the PCTM atmospheric transport model driven by meteorology from the MERRA reanalysis. We compare the posterior fluxes and uncertainties derived using different data sets and the two inversion approaches, and evaluate the posterior atmospheric concentrations against independent data including aircraft measurements. The optimized fluxes generally resemble those from other studies. For example, the results indicate that the terrestrial biosphere is a net CO2 sink, and a GOSAT-only inversion suggests a shift in the global sink from the tropics south to the north relative to the prior and to an in-situ-only inversion. We also find a smaller terrestrial sink in higher-latitude northern regions in boreal summer of 2010 relative to 2009.

Unified Bayesian Estimator of EEG Reference at Infinity: rREST (Regularized Reference Electrode Standardization Technique)

PubMed Central

Hu, Shiang; Yao, Dezhong; Valdes-Sosa, Pedro A.

2018-01-01

The choice of reference for the electroencephalogram (EEG) is a long-lasting unsolved issue resulting in inconsistent usages and endless debates. Currently, both the average reference (AR) and the reference electrode standardization technique (REST) are two primary, apparently irreconcilable contenders. We propose a theoretical framework to resolve this reference issue by formulating both (a) estimation of potentials at infinity, and (b) determination of the reference, as a unified Bayesian linear inverse problem, which can be solved by maximum a posterior estimation. We find that AR and REST are very particular cases of this unified framework: AR results from biophysically non-informative prior; while REST utilizes the prior based on the EEG generative model. To allow for simultaneous denoising and reference estimation, we develop the regularized versions of AR and REST, named rAR and rREST, respectively. Both depend on a regularization parameter that is the noise to signal variance ratio. Traditional and new estimators are evaluated with this framework, by both simulations and analysis of real resting EEGs. Toward this end, we leverage the MRI and EEG data from 89 subjects which participated in the Cuban Human Brain Mapping Project. Generated artificial EEGs—with a known ground truth, show that relative error in estimating the EEG potentials at infinity is lowest for rREST. It also reveals that realistic volume conductor models improve the performances of REST and rREST. Importantly, for practical applications, it is shown that an average lead field gives the results comparable to the individual lead field. Finally, it is shown that the selection of the regularization parameter with Generalized Cross-Validation (GCV) is close to the “oracle” choice based on the ground truth. When evaluated with the real 89 resting state EEGs, rREST consistently yields the lowest GCV. This study provides a novel perspective to the EEG reference problem by means of a unified inverse solution framework. It may allow additional principled theoretical formulations and numerical evaluation of performance. PMID:29780302

A Bayesian approach to earthquake source studies

NASA Astrophysics Data System (ADS)

Minson, Sarah

Bayesian sampling has several advantages over conventional optimization approaches to solving inverse problems. It produces the distribution of all possible models sampled proportionally to how much each model is consistent with the data and the specified prior information, and thus images the entire solution space, revealing the uncertainties and trade-offs in the model. Bayesian sampling is applicable to both linear and non-linear modeling, and the values of the model parameters being sampled can be constrained based on the physics of the process being studied and do not have to be regularized. However, these methods are computationally challenging for high-dimensional problems. Until now the computational expense of Bayesian sampling has been too great for it to be practicable for most geophysical problems. I present a new parallel sampling algorithm called CATMIP for Cascading Adaptive Tempered Metropolis In Parallel. This technique, based on Transitional Markov chain Monte Carlo, makes it possible to sample distributions in many hundreds of dimensions, if the forward model is fast, or to sample computationally expensive forward models in smaller numbers of dimensions. The design of the algorithm is independent of the model being sampled, so CATMIP can be applied to many areas of research. I use CATMIP to produce a finite fault source model for the 2007 Mw 7.7 Tocopilla, Chile earthquake. Surface displacements from the earthquake were recorded by six interferograms and twelve local high-rate GPS stations. Because of the wealth of near-fault data, the source process is well-constrained. I find that the near-field high-rate GPS data have significant resolving power above and beyond the slip distribution determined from static displacements. The location and magnitude of the maximum displacement are resolved. The rupture almost certainly propagated at sub-shear velocities. The full posterior distribution can be used not only to calculate source parameters but also to determine their uncertainties. So while kinematic source modeling and the estimation of source parameters is not new, with CATMIP I am able to use Bayesian sampling to determine which parts of the source process are well-constrained and which are not.

Joint time/frequency-domain inversion of reflection data for seabed geoacoustic profiles and uncertainties.

PubMed

Dettmer, Jan; Dosso, Stan E; Holland, Charles W

2008-03-01

This paper develops a joint time/frequency-domain inversion for high-resolution single-bounce reflection data, with the potential to resolve fine-scale profiles of sediment velocity, density, and attenuation over small seafloor footprints (approximately 100 m). The approach utilizes sequential Bayesian inversion of time- and frequency-domain reflection data, employing ray-tracing inversion for reflection travel times and a layer-packet stripping method for spherical-wave reflection-coefficient inversion. Posterior credibility intervals from the travel-time inversion are passed on as prior information to the reflection-coefficient inversion. Within the reflection-coefficient inversion, parameter information is passed from one layer packet inversion to the next in terms of marginal probability distributions rotated into principal components, providing an efficient approach to (partially) account for multi-dimensional parameter correlations with one-dimensional, numerical distributions. Quantitative geoacoustic parameter uncertainties are provided by a nonlinear Gibbs sampling approach employing full data error covariance estimation (including nonstationary effects) and accounting for possible biases in travel-time picks. Posterior examination of data residuals shows the importance of including data covariance estimates in the inversion. The joint inversion is applied to data collected on the Malta Plateau during the SCARAB98 experiment.

HARMONIZATION OF HUMAN AND ECOLOGICAL HEALTH ASSESSMENT: DEVELOPMENT OF BAYESIAN UPDATING TECHNIQUES TO INCORPORATE MECHANISTIC INFORMATION ACROSS SPECIES

EPA Science Inventory

Bayesian statistical techniques have proven useful in clinical and environmental epidemiological applications to evaluate and integrate available information, and in regulatory applications such as the National Ambient Air Quality Assessment for Nitrogen Oxides. A recent special...

Personalized Multi-Student Improvement Based on Bayesian Cybernetics

ERIC Educational Resources Information Center

Kaburlasos, Vassilis G.; Marinagi, Catherine C.; Tsoukalas, Vassilis Th.

2008-01-01

This work presents innovative cybernetics (feedback) techniques based on Bayesian statistics for drawing questions from an Item Bank towards personalized multi-student improvement. A novel software tool, namely "Module for Adaptive Assessment of Students" (or, "MAAS" for short), implements the proposed (feedback) techniques. In conclusion, a pilot…

A Bayesian method for characterizing distributed micro-releases: II. inference under model uncertainty with short time-series data.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef; Fast P.; Kraus, M.

2006-01-01

Terrorist attacks using an aerosolized pathogen preparation have gained credibility as a national security concern after the anthrax attacks of 2001. The ability to characterize such attacks, i.e., to estimate the number of people infected, the time of infection, and the average dose received, is important when planning a medical response. We address this question of characterization by formulating a Bayesian inverse problem predicated on a short time-series of diagnosed patients exhibiting symptoms. To be of relevance to response planning, we limit ourselves to 3-5 days of data. In tests performed with anthrax as the pathogen, we find that thesemore » data are usually sufficient, especially if the model of the outbreak used in the inverse problem is an accurate one. In some cases the scarcity of data may initially support outbreak characterizations at odds with the true one, but with sufficient data the correct inferences are recovered; in other words, the inverse problem posed and its solution methodology are consistent. We also explore the effect of model error-situations for which the model used in the inverse problem is only a partially accurate representation of the outbreak; here, the model predictions and the observations differ by more than a random noise. We find that while there is a consistent discrepancy between the inferred and the true characterizations, they are also close enough to be of relevance when planning a response.« less

Using Tranformation Group Priors and Maximum Relative Entropy for Bayesian Glaciological Inversions

NASA Astrophysics Data System (ADS)

Arthern, R. J.; Hindmarsh, R. C. A.; Williams, C. R.

2014-12-01

One of the key advances that has allowed better simulations of the large ice sheets of Greenland and Antarctica has been the use of inverse methods. These have allowed poorly known parameters such as the basal drag coefficient and ice viscosity to be constrained using a wide variety of satellite observations. Inverse methods used by glaciologists have broadly followed one of two related approaches. The first is minimization of a cost function that describes the misfit to the observations, often accompanied by some kind of explicit or implicit regularization that promotes smallness or smoothness in the inverted parameters. The second approach is a probabilistic framework that makes use of Bayes' theorem to update prior assumptions about the probability of parameters, making use of data with known error estimates. Both approaches have much in common and questions of regularization often map onto implicit choices of prior probabilities that are made explicit in the Bayesian framework. In both approaches questions can arise that seem to demand subjective input. What should the functional form of the cost function be if there are alternatives? What kind of regularization should be applied, and how much? How should the prior probability distribution for a parameter such as basal slipperiness be specified when we know so little about the details of the subglacial environment? Here we consider some approaches that have been used to address these questions and discuss ways that probabilistic prior information used for regularizing glaciological inversions might be specified with greater objectivity.

European emissions of HCFC-22 based on eleven years of high frequency atmospheric measurements and a Bayesian inversion method

NASA Astrophysics Data System (ADS)

Graziosi, F.; Arduini, J.; Furlani, F.; Giostra, U.; Kuijpers, L. J. M.; Montzka, S. A.; Miller, B. R.; O'Doherty, S. J.; Stohl, A.; Bonasoni, P.; Maione, M.

2015-07-01

HCFC-22 (CHClF2), a stratospheric ozone depleting substance and a powerful greenhouse gas, is the third most abundant anthropogenic halocarbon in the atmosphere. Primarily used in refrigeration and air conditioning systems, its global production and consumption have increased during the last 60 years, with the global increases in the last decade mainly attributable to developing countries. In 2007, an adjustment to the Montreal Protocol for Substances that Deplete the Ozone Layer called for an accelerated phase out of HCFCs, implying a 75% reduction (base year 1989) of HCFC production and consumption by 2010 in developed countries against the previous 65% reduction. In Europe HCFC-22 is continuously monitored at the two sites Mace Head (Ireland) and Monte Cimone (Italy). Combining atmospheric observations with a Bayesian inversion technique, we estimated fluxes of HCFC-22 from Europe and from eight macro-areas within it, over an 11-year period from January 2002 to December 2012, during which the accelerated restrictions on HCFCs production and consumption have entered into force. According to our study, the maximum emissions over the entire domain was in 2003 (38.2 ± 4.7 Gg yr-1), and the minimum in 2012 (12.1 ± 2.0 Gg yr-1); emissions continuously decreased between these years, except for secondary maxima in the 2008 and 2010. Despite such a decrease in regional emissions, background values of HCFC-22 measured at the two European stations over 2002-2012 are still increasing as a consequence of global emissions, in part from developing countries, with an average trend of ca 7.0 ppt yr-1. However, the observations at the two European stations show also that since 2008 a decrease in the global growth rate has occurred. In general, our European emission estimates are in good agreement with those reported by previous studies that used different techniques. Since the currently dominant emission source of HCFC-22 is from banks, we assess the banks' size and their contribution to the total European emissions up to 2030, and we project a fast decrease approaching negligible emissions in the last five years of the considered period. Finally, inversions conducted over three month periods showed evidence for a seasonal cycle in emissions in regions in the Mediterranean basin but not outside it. Emissions derived from regions in the Mediterranean basin were ca. 25% higher in warmer months than in colder months.

Prediction in Health Domain Using Bayesian Networks Optimization Based on Induction Learning Techniques

NASA Astrophysics Data System (ADS)

Felgaer, Pablo; Britos, Paola; García-Martínez, Ramón

A Bayesian network is a directed acyclic graph in which each node represents a variable and each arc a probabilistic dependency; they are used to provide: a compact form to represent the knowledge and flexible methods of reasoning. Obtaining it from data is a learning process that is divided in two steps: structural learning and parametric learning. In this paper we define an automatic learning method that optimizes the Bayesian networks applied to classification, using a hybrid method of learning that combines the advantages of the induction techniques of the decision trees (TDIDT-C4.5) with those of the Bayesian networks. The resulting method is applied to prediction in health domain.

Bayesian-based estimation of acoustic surface impedance: Finite difference frequency domain approach.

PubMed

Bockman, Alexander; Fackler, Cameron; Xiang, Ning

2015-04-01

Acoustic performance for an interior requires an accurate description of the boundary materials' surface acoustic impedance. Analytical methods may be applied to a small class of test geometries, but inverse numerical methods provide greater flexibility. The parameter estimation problem requires minimizing prediction vice observed acoustic field pressure. The Bayesian-network sampling approach presented here mitigates other methods' susceptibility to noise inherent to the experiment, model, and numerics. A geometry agnostic method is developed here and its parameter estimation performance is demonstrated for an air-backed micro-perforated panel in an impedance tube. Good agreement is found with predictions from the ISO standard two-microphone, impedance-tube method, and a theoretical model for the material. Data by-products exclusive to a Bayesian approach are analyzed to assess sensitivity of the method to nuisance parameters.

Detection of photosynthetic responses of cool-temperate forests following extreme climate events using Bayesian inversion

NASA Astrophysics Data System (ADS)

Toda, M.; Knohl, A.; Herbst, M.; Keenan, T. F.; Yokozawa, M.

2016-12-01

The increase in extreme climate events associated with ongoing global warming may create severe damage to terrestrial ecosystems, changing plant structure and the eco-physiological functions that regulate ecosystem carbon exchange. However, most damage is usually due to moderate, rather than catastrophic, disturbances. The nature of plant functional responses to such disturbances, and the resulting effects on the terrestrial carbon cycle, remain poorly understood. To unravel the scientific question, tower-based eddy covariance data in the cool-temperate forests were used to constrain plant eco-physiological parameters in a persimoneous ecosystem model that may have affected carbon dynamics following extreme climate events using the statistic Bayesian inversion approach. In the present study, we raised two types of extreme events relevant for cool-temperate regions, i.e. a typhoon with mechanistic foliage destraction and a heat wave with severe drought. With appropriate evaluation of parameter and predictive uncertainties, the inversion analysis shows annual trajectory of activated photosynthetic responses following climate extremes compared the pre-disturbance state in each forest. We address that forests with moderate disturbance show substantial and rapid photosynthetic recovery, enhanced productivity, and, thus, ecosystem carbon exchange, although the effect of extreme climatic events varies depending on the stand successional phase and the type, intensity, timing and legacy of the disturbance.

Detangling complex relationships in forensic data: principles and use of causal networks and their application to clinical forensic science.

PubMed

Lefèvre, Thomas; Lepresle, Aude; Chariot, Patrick

2015-09-01

The search for complex, nonlinear relationships and causality in data is hindered by the availability of techniques in many domains, including forensic science. Linear multivariable techniques are useful but present some shortcomings. In the past decade, Bayesian approaches have been introduced in forensic science. To date, authors have mainly focused on providing an alternative to classical techniques for quantifying effects and dealing with uncertainty. Causal networks, including Bayesian networks, can help detangle complex relationships in data. A Bayesian network estimates the joint probability distribution of data and graphically displays dependencies between variables and the circulation of information between these variables. In this study, we illustrate the interest in utilizing Bayesian networks for dealing with complex data through an application in clinical forensic science. Evaluating the functional impairment of assault survivors is a complex task for which few determinants are known. As routinely estimated in France, the duration of this impairment can be quantified by days of 'Total Incapacity to Work' ('Incapacité totale de travail,' ITT). In this study, we used a Bayesian network approach to identify the injury type, victim category and time to evaluation as the main determinants of the 'Total Incapacity to Work' (TIW). We computed the conditional probabilities associated with the TIW node and its parents. We compared this approach with a multivariable analysis, and the results of both techniques were converging. Thus, Bayesian networks should be considered a reliable means to detangle complex relationships in data.

Stochastic static fault slip inversion from geodetic data with non-negativity and bound constraints

NASA Astrophysics Data System (ADS)

Nocquet, J.-M.

2018-07-01

Despite surface displacements observed by geodesy are linear combinations of slip at faults in an elastic medium, determining the spatial distribution of fault slip remains a ill-posed inverse problem. A widely used approach to circumvent the illness of the inversion is to add regularization constraints in terms of smoothing and/or damping so that the linear system becomes invertible. However, the choice of regularization parameters is often arbitrary, and sometimes leads to significantly different results. Furthermore, the resolution analysis is usually empirical and cannot be made independently of the regularization. The stochastic approach of inverse problems provides a rigorous framework where the a priori information about the searched parameters is combined with the observations in order to derive posterior probabilities of the unkown parameters. Here, I investigate an approach where the prior probability density function (pdf) is a multivariate Gaussian function, with single truncation to impose positivity of slip or double truncation to impose positivity and upper bounds on slip for interseismic modelling. I show that the joint posterior pdf is similar to the linear untruncated Gaussian case and can be expressed as a truncated multivariate normal (TMVN) distribution. The TMVN form can then be used to obtain semi-analytical formulae for the single, 2-D or n-D marginal pdf. The semi-analytical formula involves the product of a Gaussian by an integral term that can be evaluated using recent developments in TMVN probabilities calculations. Posterior mean and covariance can also be efficiently derived. I show that the maximum posterior (MAP) can be obtained using a non-negative least-squares algorithm for the single truncated case or using the bounded-variable least-squares algorithm for the double truncated case. I show that the case of independent uniform priors can be approximated using TMVN. The numerical equivalence to Bayesian inversions using Monte Carlo Markov chain (MCMC) sampling is shown for a synthetic example and a real case for interseismic modelling in Central Peru. The TMVN method overcomes several limitations of the Bayesian approach using MCMC sampling. First, the need of computer power is largely reduced. Second, unlike Bayesian MCMC-based approach, marginal pdf, mean, variance or covariance are obtained independently one from each other. Third, the probability and cumulative density functions can be obtained with any density of points. Finally, determining the MAP is extremely fast.

Diagnosis and Reconfiguration using Bayesian Networks: An Electrical Power System Case Study

NASA Technical Reports Server (NTRS)

Knox, W. Bradley; Mengshoel, Ole

2009-01-01

Automated diagnosis and reconfiguration are important computational techniques that aim to minimize human intervention in autonomous systems. In this paper, we develop novel techniques and models in the context of diagnosis and reconfiguration reasoning using causal Bayesian networks (BNs). We take as starting point a successful diagnostic approach, using a static BN developed for a real-world electrical power system. We discuss in this paper the extension of this diagnostic approach along two dimensions, namely: (i) from a static BN to a dynamic BN; and (ii) from a diagnostic task to a reconfiguration task. More specifically, we discuss the auto-generation of a dynamic Bayesian network from a static Bayesian network. In addition, we discuss subtle, but important, differences between Bayesian networks when used for diagnosis versus reconfiguration. We discuss a novel reconfiguration agent, which models a system causally, including effects of actions through time, using a dynamic Bayesian network. Though the techniques we discuss are general, we demonstrate them in the context of electrical power systems (EPSs) for aircraft and spacecraft. EPSs are vital subsystems on-board aircraft and spacecraft, and many incidents and accidents of these vehicles have been attributed to EPS failures. We discuss a case study that provides initial but promising results for our approach in the setting of electrical power systems.

Integrating laboratory creep compaction data with numerical fault models: A Bayesian framework

USGS Publications Warehouse

Fitzenz, D.D.; Jalobeanu, A.; Hickman, S.H.

2007-01-01

We developed a robust Bayesian inversion scheme to plan and analyze laboratory creep compaction experiments. We chose a simple creep law that features the main parameters of interest when trying to identify rate-controlling mechanisms from experimental data. By integrating the chosen creep law or an approximation thereof, one can use all the data, either simultaneously or in overlapping subsets, thus making more complete use of the experiment data and propagating statistical variations in the data through to the final rate constants. Despite the nonlinearity of the problem, with this technique one can retrieve accurate estimates of both the stress exponent and the activation energy, even when the porosity time series data are noisy. Whereas adding observation points and/or experiments reduces the uncertainty on all parameters, enlarging the range of temperature or effective stress significantly reduces the covariance between stress exponent and activation energy. We apply this methodology to hydrothermal creep compaction data on quartz to obtain a quantitative, semiempirical law for fault zone compaction in the interseismic period. Incorporating this law into a simple direct rupture model, we find marginal distributions of the time to failure that are robust with respect to errors in the initial fault zone porosity. Copyright 2007 by the American Geophysical Union.

A Bayesian model averaging approach to examining changes in quality of life among returning Iraq and Afghanistan Veterans

PubMed Central

Stock, Eileen M.; Kimbrel, Nathan A.; Meyer, Eric C.; Copeland, Laurel A.; Monte, Ralph; Zeber, John E.; Gulliver, Suzy Bird; Morissette, Sandra B.

2016-01-01

Many Veterans from the conflicts in Iraq and Afghanistan return home with physical and psychological impairments that impact their ability to enjoy normal life activities and diminish their quality of life (QoL). The present research aimed to identify predictors of QoL over an 8-month period using Bayesian model averaging (BMA), which is a statistical technique useful for maximizing power with smaller sample sizes. A sample of 117 Iraq and Afghanistan Veterans receiving care in a southwestern healthcare system was recruited, and BMA examined the impact of key demographics (e.g., age, gender), diagnoses (e.g., depression), and treatment modalities (e.g., individual therapy, medication) on QoL over time. Multiple imputation based on Gibbs sampling was employed for incomplete data (6.4% missingness). Average follow-up QoL scores were significantly lower than at baseline (73.2 initial vs 69.5 4-month and 68.3 8-month). Employment was associated with increased QoL during each follow-up, while posttraumatic stress disorder and black race were inversely related. Additionally, predictive models indicated that depression, income, treatment for a medical condition, and group psychotherapy were strong negative predictors of 4-month QoL but not 8-month QoL. PMID:24942672

Large-Scale Optimization for Bayesian Inference in Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Willcox, Karen; Marzouk, Youssef

2013-11-12

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT--Sandia component of themore » SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas--Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as ``reduce then sample'' and ``sample then reduce.'' In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

Final Report: Large-Scale Optimization for Bayesian Inference in Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghattas, Omar

2013-10-15

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimiza- tion) Project focuses on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimiza- tion and inversion methods. Our research is directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. Our efforts are integrated in the context of a challenging testbed problem that considers subsurface reacting flow and transport. The MIT component of the SAGUAROmore » Project addresses the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas-Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to- observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

Lip-reading aids word recognition most in moderate noise: a Bayesian explanation using high-dimensional feature space.

PubMed

Ma, Wei Ji; Zhou, Xiang; Ross, Lars A; Foxe, John J; Parra, Lucas C

2009-01-01

Watching a speaker's facial movements can dramatically enhance our ability to comprehend words, especially in noisy environments. From a general doctrine of combining information from different sensory modalities (the principle of inverse effectiveness), one would expect that the visual signals would be most effective at the highest levels of auditory noise. In contrast, we find, in accord with a recent paper, that visual information improves performance more at intermediate levels of auditory noise than at the highest levels, and we show that a novel visual stimulus containing only temporal information does the same. We present a Bayesian model of optimal cue integration that can explain these conflicts. In this model, words are regarded as points in a multidimensional space and word recognition is a probabilistic inference process. When the dimensionality of the feature space is low, the Bayesian model predicts inverse effectiveness; when the dimensionality is high, the enhancement is maximal at intermediate auditory noise levels. When the auditory and visual stimuli differ slightly in high noise, the model makes a counterintuitive prediction: as sound quality increases, the proportion of reported words corresponding to the visual stimulus should first increase and then decrease. We confirm this prediction in a behavioral experiment. We conclude that auditory-visual speech perception obeys the same notion of optimality previously observed only for simple multisensory stimuli.

Elastic Properties of Novel Co- and CoNi-Based Superalloys Determined through Bayesian Inference and Resonant Ultrasound Spectroscopy

NASA Astrophysics Data System (ADS)

Goodlet, Brent R.; Mills, Leah; Bales, Ben; Charpagne, Marie-Agathe; Murray, Sean P.; Lenthe, William C.; Petzold, Linda; Pollock, Tresa M.

2018-06-01

Bayesian inference is employed to precisely evaluate single crystal elastic properties of novel γ -γ ' Co- and CoNi-based superalloys from simple and non-destructive resonant ultrasound spectroscopy (RUS) measurements. Nine alloys from three Co-, CoNi-, and Ni-based alloy classes were evaluated in the fully aged condition, with one alloy per class also evaluated in the solution heat-treated condition. Comparisons are made between the elastic properties of the three alloy classes and among the alloys of a single class, with the following trends observed. A monotonic rise in the c_{44} (shear) elastic constant by a total of 12 pct is observed between the three alloy classes as Co is substituted for Ni. Elastic anisotropy ( A) is also increased, with a large majority of the nearly 13 pct increase occurring after Co becomes the dominant constituent. Together the five CoNi alloys, with Co:Ni ratios from 1:1 to 1.5:1, exhibited remarkably similar properties with an average A 1.8 pct greater than the Ni-based alloy CMSX-4. Custom code demonstrating a substantial advance over previously reported methods for RUS inversion is also reported here for the first time. CmdStan-RUS is built upon the open-source probabilistic programing language of Stan and formulates the inverse problem using Bayesian methods. Bayesian posterior distributions are efficiently computed with Hamiltonian Monte Carlo (HMC), while initial parameterization is randomly generated from weakly informative prior distributions. Remarkably robust convergence behavior is demonstrated across multiple independent HMC chains in spite of initial parameterization often very far from actual parameter values. Experimental procedures are substantially simplified by allowing any arbitrary misorientation between the specimen and crystal axes, as elastic properties and misorientation are estimated simultaneously.

Unraveling multiple changes in complex climate time series using Bayesian inference

NASA Astrophysics Data System (ADS)

Berner, Nadine; Trauth, Martin H.; Holschneider, Matthias

2016-04-01

Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of observations. Unraveling such transitions yields essential information for the understanding of the observed system. The precise detection and basic characterization of underlying changes is therefore of particular importance in environmental sciences. We present a kernel-based Bayesian inference approach to investigate direct as well as indirect climate observations for multiple generic transition events. In order to develop a diagnostic approach designed to capture a variety of natural processes, the basic statistical features of central tendency and dispersion are used to locally approximate a complex time series by a generic transition model. A Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of such a transition. To systematically investigate time series for multiple changes occurring at different temporal scales, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. Thus, based on a generic transition model a probability expression is derived that is capable to indicate multiple changes within a complex time series. We discuss the method's performance by investigating direct and indirect climate observations. The approach is applied to environmental time series (about 100 a), from the weather station in Tuscaloosa, Alabama, and confirms documented instrumentation changes. Moreover, the approach is used to investigate a set of complex terrigenous dust records from the ODP sites 659, 721/722 and 967 interpreted as climate indicators of the African region of the Plio-Pleistocene period (about 5 Ma). The detailed inference unravels multiple transitions underlying the indirect climate observations coinciding with established global climate events.

Bayesian Modeling of Perceived Surface Slant from Actively-Generated and Passively-Observed Optic Flow

PubMed Central

Caudek, Corrado; Fantoni, Carlo; Domini, Fulvio

2011-01-01

We measured perceived depth from the optic flow (a) when showing a stationary physical or virtual object to observers who moved their head at a normal or slower speed, and (b) when simulating the same optic flow on a computer and presenting it to stationary observers. Our results show that perceived surface slant is systematically distorted, for both the active and the passive viewing of physical or virtual surfaces. These distortions are modulated by head translation speed, with perceived slant increasing directly with the local velocity gradient of the optic flow. This empirical result allows us to determine the relative merits of two alternative approaches aimed at explaining perceived surface slant in active vision: an “inverse optics” model that takes head motion information into account, and a probabilistic model that ignores extra-retinal signals. We compare these two approaches within the framework of the Bayesian theory. The “inverse optics” Bayesian model produces veridical slant estimates if the optic flow and the head translation velocity are measured with no error; because of the influence of a “prior” for flatness, the slant estimates become systematically biased as the measurement errors increase. The Bayesian model, which ignores the observer's motion, always produces distorted estimates of surface slant. Interestingly, the predictions of this second model, not those of the first one, are consistent with our empirical findings. The present results suggest that (a) in active vision perceived surface slant may be the product of probabilistic processes which do not guarantee the correct solution, and (b) extra-retinal signals may be mainly used for a better measurement of retinal information. PMID:21533197

Evaluating the impacts of different measurement and model configurations on top-down estimates of UK methane emissions

NASA Astrophysics Data System (ADS)

Lunt, Mark; Rigby, Matt; Manning, Alistair; O'Doherty, Simon; Stavert, Ann; Stanley, Kieran; Young, Dickon; Pitt, Joseph; Bauguitte, Stephane; Allen, Grant; Helfter, Carole; Palmer, Paul

2017-04-01

The Greenhouse gAs Uk and Global Emissions (GAUGE) project aims to quantify the magnitude and uncertainty of key UK greenhouse gas emissions more robustly than previously achieved. Measurements of methane have been taken from a number of tall-tower and surface sites as well as mobile measurement platforms such as a research aircraft and a ferry providing regular transects off the east coast of the UK. Using the UK Met Office's atmospheric transport model, NAME, and a novel Bayesian inversion technique we present estimates of methane emissions from the UK from a number of different combinations of sites to show the robustness of the UK total emissions to network configuration. The impact on uncertainties will be discussed, focusing on the usefulness of the various measurement platforms for constraining UK emissions. We will examine the effects of observation selection and how a priori assumptions about model uncertainty can affect the emission estimates, even within a data-driven hierarchical inversion framework. Finally, we will show the impact of the resolution of the meteorology used to drive the NAME model on emissions estimates, and how to rationalise our understanding of the ability of transport models to represent reality.

Bayesian linkage and segregation analysis: factoring the problem.

PubMed

Matthysse, S

2000-01-01

Complex segregation analysis and linkage methods are mathematical techniques for the genetic dissection of complex diseases. They are used to delineate complex modes of familial transmission and to localize putative disease susceptibility loci to specific chromosomal locations. The computational problem of Bayesian linkage and segregation analysis is one of integration in high-dimensional spaces. In this paper, three available techniques for Bayesian linkage and segregation analysis are discussed: Markov Chain Monte Carlo (MCMC), importance sampling, and exact calculation. The contribution of each to the overall integration will be explicitly discussed.

Source partitioning of methane emissions and its seasonality in the U.S. Midwest

USDA-ARS?s Scientific Manuscript database

The methane (CH4) budget and its source partitioning are poorly constrained in the Midwestern, United States. We used tall tower (185 m) aerodynamic flux measurements and atmospheric scale factor Bayesian inversions (SFBI) to constrain the monthly budget and to partition the total budget into natura...

A Non-linear Geodetic Data Inversion Using ABIC for Slip Distribution on a Fault With an Unknown dip Angle

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Wright, T. J.

2006-12-01

We developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. When fault geometry is unknown, the problem of geodetic data inversion is non-linear. A common strategy for obtaining slip distribution is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. In addition, in obtaining a uniform slip fault model, we have to simultaneously determine the values of the nine mutually dependent parameters, which is a highly non-linear, complicated process. Although the inverse problem is non-linear for cases with unknown fault geometries, the non-linearity of the problems is actually weak, when we can assume the fault surface to be flat. In particular, when a clear fault trace is observed on the EarthOs surface after an earthquake, we can precisely estimate the strike and the location of the fault. In this case only the dip angle has large ambiguity. In geodetic data inversion we usually need to introduce smoothness constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. Strictly speaking, the inverse problem with smoothness constraints is also non-linear, even if the fault geometry is known. The non-linearity has been dissolved by introducing AkaikeOs Bayesian Information Criterion (ABIC), with which the optimal value of the relative weight of observed data to smoothness constraints is objectively determined. In this study, using ABIC in determining the optimal dip angle, we dissolved the non-linearity of the inverse problem. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much shallower dip angle than before.

[Bayesian geostatistical prediction of soil organic carbon contents of solonchak soils in nor-thern Tarim Basin, Xinjiang, China.

PubMed

Wu, Wei Mo; Wang, Jia Qiang; Cao, Qi; Wu, Jia Ping

2017-02-01

Accurate prediction of soil organic carbon (SOC) distribution is crucial for soil resources utilization and conservation, climate change adaptation, and ecosystem health. In this study, we selected a 1300 m×1700 m solonchak sampling area in northern Tarim Basin, Xinjiang, China, and collected a total of 144 soil samples (5-10 cm). The objectives of this study were to build a Baye-sian geostatistical model to predict SOC content, and to assess the performance of the Bayesian model for the prediction of SOC content by comparing with other three geostatistical approaches [ordinary kriging (OK), sequential Gaussian simulation (SGS), and inverse distance weighting (IDW)]. In the study area, soil organic carbon contents ranged from 1.59 to 9.30 g·kg -1 with a mean of 4.36 g·kg -1 and a standard deviation of 1.62 g·kg -1 . Sample semivariogram was best fitted by an exponential model with the ratio of nugget to sill being 0.57. By using the Bayesian geostatistical approach, we generated the SOC content map, and obtained the prediction variance, upper 95% and lower 95% of SOC contents, which were then used to evaluate the prediction uncertainty. Bayesian geostatistical approach performed better than that of the OK, SGS and IDW, demonstrating the advantages of Bayesian approach in SOC prediction.

Estimating uncertainties in complex joint inverse problems

NASA Astrophysics Data System (ADS)

Afonso, Juan Carlos

2016-04-01

Sources of uncertainty affecting geophysical inversions can be classified either as reflective (i.e. the practitioner is aware of her/his ignorance) or non-reflective (i.e. the practitioner does not know that she/he does not know!). Although we should be always conscious of the latter, the former are the ones that, in principle, can be estimated either empirically (by making measurements or collecting data) or subjectively (based on the experience of the researchers). For complex parameter estimation problems in geophysics, subjective estimation of uncertainty is the most common type. In this context, probabilistic (aka Bayesian) methods are commonly claimed to offer a natural and realistic platform from which to estimate model uncertainties. This is because in the Bayesian approach, errors (whatever their nature) can be naturally included as part of the global statistical model, the solution of which represents the actual solution to the inverse problem. However, although we agree that probabilistic inversion methods are the most powerful tool for uncertainty estimation, the common claim that they produce "realistic" or "representative" uncertainties is not always justified. Typically, ALL UNCERTAINTY ESTIMATES ARE MODEL DEPENDENT, and therefore, besides a thorough characterization of experimental uncertainties, particular care must be paid to the uncertainty arising from model errors and input uncertainties. We recall here two quotes by G. Box and M. Gunzburger, respectively, of special significance for inversion practitioners and for this session: "…all models are wrong, but some are useful" and "computational results are believed by no one, except the person who wrote the code". In this presentation I will discuss and present examples of some problems associated with the estimation and quantification of uncertainties in complex multi-observable probabilistic inversions, and how to address them. Although the emphasis will be on sources of uncertainty related to the forward and statistical models, I will also address other uncertainties associated with data and uncertainty propagation.

Stochastic inversion of time-lapse geophysical data to characterize the vadose zone at the Arrenaes field site (Denmark)

NASA Astrophysics Data System (ADS)

Marie, S.; Irving, J. D.; Looms, M. C.; Nielsen, L.; Holliger, K.

2011-12-01

Geophysical methods such as ground-penetrating radar (GPR) can provide valuable information on the hydrological properties of the vadose zone. In particular, there is evidence to suggest that the stochastic inversion of such data may allow for significant reductions in uncertainty regarding subsurface van-Genuchten-Mualem (VGM) parameters, which characterize unsaturated hydrodynamic behaviour as defined by the combination of the water retention and hydraulic conductivity functions. A significant challenge associated with the use of geophysical methods in a hydrological context is that they generally exhibit an indirect and/or weak sensitivity to the hydraulic parameters of interest. A novel and increasingly popular means of addressing this issue involves the acquisition of geophysical data in a time-lapse fashion while changes occur in the hydrological condition of the probed subsurface region. Another significant challenge when attempting to use geophysical data for the estimation of subsurface hydrological properties is the inherent non-linearity and non-uniqueness of the corresponding inverse problems. Stochastic inversion approaches have the advantage of providing a comprehensive exploration of the model space, which makes them ideally suited for addressing such issues. In this work, we present the stochastic inversion of time-lapse zero-offset-profile (ZOP) crosshole GPR traveltime data, collected during a forced infiltration experiment at the Arreneas field site in Denmark, in order to estimate subsurface VGM parameters and their corresponding uncertainties. We do this using a Bayesian Markov-chain-Monte-Carlo (MCMC) inversion approach. We find that the Bayesian-MCMC methodology indeed allows for a substantial refinement in the inferred posterior parameter distributions of the VGM parameters as compared to the corresponding priors. To further understand the potential impact on capturing the underlying hydrological behaviour, we also explore how the posterior VGM parameter distributions affect the hydrodynamic characteristics. In doing so, we find clear evidence that the approach pursued in this study allows for effective characterization of the hydrological behaviour of the probed subsurface region.

On the limitations of standard statistical modeling in biological systems: a full Bayesian approach for biology.

PubMed

Gomez-Ramirez, Jaime; Sanz, Ricardo

2013-09-01

One of the most important scientific challenges today is the quantitative and predictive understanding of biological function. Classical mathematical and computational approaches have been enormously successful in modeling inert matter, but they may be inadequate to address inherent features of biological systems. We address the conceptual and methodological obstacles that lie in the inverse problem in biological systems modeling. We introduce a full Bayesian approach (FBA), a theoretical framework to study biological function, in which probability distributions are conditional on biophysical information that physically resides in the biological system that is studied by the scientist. Copyright © 2013 Elsevier Ltd. All rights reserved.

Bayesian historical earthquake relocation: an example from the 1909 Taipei earthquake

USGS Publications Warehouse

Minson, Sarah E.; Lee, William H.K.

2014-01-01

Locating earthquakes from the beginning of the modern instrumental period is complicated by the fact that there are few good-quality seismograms and what traveltimes do exist may be corrupted by both large phase-pick errors and clock errors. Here, we outline a Bayesian approach to simultaneous inference of not only the hypocentre location but also the clock errors at each station and the origin time of the earthquake. This methodology improves the solution for the source location and also provides an uncertainty analysis on all of the parameters included in the inversion. As an example, we applied this Bayesian approach to the well-studied 1909 Mw 7 Taipei earthquake. While our epicentre location and origin time for the 1909 Taipei earthquake are consistent with earlier studies, our focal depth is significantly shallower suggesting a higher seismic hazard to the populous Taipei metropolitan area than previously supposed.

Bayesian estimation of magma supply, storage, and eruption rates using a multiphysical volcano model: Kīlauea Volcano, 2000–2012

USGS Publications Warehouse

Anderson, Kyle R.; Poland, Michael

2016-01-01

Estimating rates of magma supply to the world's volcanoes remains one of the most fundamental aims of volcanology. Yet, supply rates can be difficult to estimate even at well-monitored volcanoes, in part because observations are noisy and are usually considered independently rather than as part of a holistic system. In this work we demonstrate a technique for probabilistically estimating time-variable rates of magma supply to a volcano through probabilistic constraint on storage and eruption rates. This approach utilizes Bayesian joint inversion of diverse datasets using predictions from a multiphysical volcano model, and independent prior information derived from previous geophysical, geochemical, and geological studies. The solution to the inverse problem takes the form of a probability density function which takes into account uncertainties in observations and prior information, and which we sample using a Markov chain Monte Carlo algorithm. Applying the technique to Kīlauea Volcano, we develop a model which relates magma flow rates with deformation of the volcano's surface, sulfur dioxide emission rates, lava flow field volumes, and composition of the volcano's basaltic magma. This model accounts for effects and processes mostly neglected in previous supply rate estimates at Kīlauea, including magma compressibility, loss of sulfur to the hydrothermal system, and potential magma storage in the volcano's deep rift zones. We jointly invert data and prior information to estimate rates of supply, storage, and eruption during three recent quasi-steady-state periods at the volcano. Results shed new light on the time-variability of magma supply to Kīlauea, which we find to have increased by 35–100% between 2001 and 2006 (from 0.11–0.17 to 0.18–0.28 km3/yr), before subsequently decreasing to 0.08–0.12 km3/yr by 2012. Changes in supply rate directly impact hazard at the volcano, and were largely responsible for an increase in eruption rate of 60–150% between 2001 and 2006, and subsequent decline by as much as 60% by 2012. We also demonstrate the occurrence of temporal changes in the proportion of Kīlauea's magma supply that is stored versus erupted, with the supply “surge” in 2006 associated with increased accumulation of magma at the summit. Finally, we are able to place some constraints on sulfur concentrations in Kīlauea magma and the scrubbing of sulfur by the volcano's hydrothermal system. Multiphysical, Bayesian constraint on magma flow rates may be used to monitor evolving volcanic hazard not just at Kīlauea but at other volcanoes around the world.

Bayesian Asymmetric Regression as a Means to Estimate and Evaluate Oral Reading Fluency Slopes

ERIC Educational Resources Information Center

Solomon, Benjamin G.; Forsberg, Ole J.

2017-01-01

Bayesian techniques have become increasingly present in the social sciences, fueled by advances in computer speed and the development of user-friendly software. In this paper, we forward the use of Bayesian Asymmetric Regression (BAR) to monitor intervention responsiveness when using Curriculum-Based Measurement (CBM) to assess oral reading…

Testing adaptive toolbox models: a Bayesian hierarchical approach.

PubMed

Scheibehenne, Benjamin; Rieskamp, Jörg; Wagenmakers, Eric-Jan

2013-01-01

Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox framework. How can a toolbox model be quantitatively specified? How can the number of toolbox strategies be limited to prevent uncontrolled strategy sprawl? How can a toolbox model be formally tested against alternative theories? The authors show how these challenges can be met by using Bayesian inference techniques. By means of parameter recovery simulations and the analysis of empirical data across a variety of domains (i.e., judgment and decision making, children's cognitive development, function learning, and perceptual categorization), the authors illustrate how Bayesian inference techniques allow toolbox models to be quantitatively specified, strategy sprawl to be contained, and toolbox models to be rigorously tested against competing theories. The authors demonstrate that their approach applies at the individual level but can also be generalized to the group level with hierarchical Bayesian procedures. The suggested Bayesian inference techniques represent a theoretical and methodological advancement for toolbox theories of cognition and behavior.

Towards national-scale greenhouse gas emissions evaluation with robust uncertainty estimates

NASA Astrophysics Data System (ADS)

Rigby, Matthew; Swallow, Ben; Lunt, Mark; Manning, Alistair; Ganesan, Anita; Stavert, Ann; Stanley, Kieran; O'Doherty, Simon

2016-04-01

Through the Deriving Emissions related to Climate Change (DECC) network and the Greenhouse gAs Uk and Global Emissions (GAUGE) programme, the UK's greenhouse gases are now monitored by instruments mounted on telecommunications towers and churches, on a ferry that performs regular transects of the North Sea, on-board a research aircraft and from space. When combined with information from high-resolution chemical transport models such as the Met Office Numerical Atmospheric dispersion Modelling Environment (NAME), these measurements are allowing us to evaluate emissions more accurately than has previously been possible. However, it has long been appreciated that current methods for quantifying fluxes using atmospheric data suffer from uncertainties, primarily relating to the chemical transport model, that have been largely ignored to date. Here, we use novel model reduction techniques for quantifying the influence of a set of potential systematic model errors on the outcome of a national-scale inversion. This new technique has been incorporated into a hierarchical Bayesian framework, which can be shown to reduce the influence of subjective choices on the outcome of inverse modelling studies. Using estimates of the UK's methane emissions derived from DECC and GAUGE tall-tower measurements as a case study, we will show that such model systematic errors have the potential to significantly increase the uncertainty on national-scale emissions estimates. Therefore, we conclude that these factors must be incorporated in national emissions evaluation efforts, if they are to be credible.

Markov chain Monte Carlo techniques and spatial-temporal modelling for medical EIT.

PubMed

West, Robert M; Aykroyd, Robert G; Meng, Sha; Williams, Richard A

2004-02-01

Many imaging problems such as imaging with electrical impedance tomography (EIT) can be shown to be inverse problems: that is either there is no unique solution or the solution does not depend continuously on the data. As a consequence solution of inverse problems based on measured data alone is unstable, particularly if the mapping between the solution distribution and the measurements is also nonlinear as in EIT. To deliver a practical stable solution, it is necessary to make considerable use of prior information or regularization techniques. The role of a Bayesian approach is therefore of fundamental importance, especially when coupled with Markov chain Monte Carlo (MCMC) sampling to provide information about solution behaviour. Spatial smoothing is a commonly used approach to regularization. In the human thorax EIT example considered here nonlinearity increases the difficulty of imaging, using only boundary data, leading to reconstructions which are often rather too smooth. In particular, in medical imaging the resistivity distribution usually contains substantial jumps at the boundaries of different anatomical regions. With spatial smoothing these boundaries can be masked by blurring. This paper focuses on the medical application of EIT to monitor lung and cardiac function and uses explicit geometric information regarding anatomical structure and incorporates temporal correlation. Some simple properties are assumed known, or at least reliably estimated from separate studies, whereas others are estimated from the voltage measurements. This structural formulation will also allow direct estimation of clinically important quantities, such as ejection fraction and residual capacity, along with assessment of precision.

Systematic evaluation of sequential geostatistical resampling within MCMC for posterior sampling of near-surface geophysical inverse problems

NASA Astrophysics Data System (ADS)

Ruggeri, Paolo; Irving, James; Holliger, Klaus

2015-08-01

We critically examine the performance of sequential geostatistical resampling (SGR) as a model proposal mechanism for Bayesian Markov-chain-Monte-Carlo (MCMC) solutions to near-surface geophysical inverse problems. Focusing on a series of simple yet realistic synthetic crosshole georadar tomographic examples characterized by different numbers of data, levels of data error and degrees of model parameter spatial correlation, we investigate the efficiency of three different resampling strategies with regard to their ability to generate statistically independent realizations from the Bayesian posterior distribution. Quite importantly, our results show that, no matter what resampling strategy is employed, many of the examined test cases require an unreasonably high number of forward model runs to produce independent posterior samples, meaning that the SGR approach as currently implemented will not be computationally feasible for a wide range of problems. Although use of a novel gradual-deformation-based proposal method can help to alleviate these issues, it does not offer a full solution. Further, we find that the nature of the SGR is found to strongly influence MCMC performance; however no clear rule exists as to what set of inversion parameters and/or overall proposal acceptance rate will allow for the most efficient implementation. We conclude that although the SGR methodology is highly attractive as it allows for the consideration of complex geostatistical priors as well as conditioning to hard and soft data, further developments are necessary in the context of novel or hybrid MCMC approaches for it to be considered generally suitable for near-surface geophysical inversions.

FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems

NASA Astrophysics Data System (ADS)

Vourc'h, Eric; Rodet, Thomas

2015-11-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2015 was a one-day workshop held in May 2015 which attracted around 70 attendees. Each of the submitted papers has been reviewed by two reviewers. There have been 15 accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks: GDR ISIS, GDR MIA, GDR MOA and GDR Ondes. The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA and SATIE.

Population forecasts for Bangladesh, using a Bayesian methodology.

PubMed

Mahsin, Md; Hossain, Syed Shahadat

2012-12-01

Population projection for many developing countries could be quite a challenging task for the demographers mostly due to lack of availability of enough reliable data. The objective of this paper is to present an overview of the existing methods for population forecasting and to propose an alternative based on the Bayesian statistics, combining the formality of inference. The analysis has been made using Markov Chain Monte Carlo (MCMC) technique for Bayesian methodology available with the software WinBUGS. Convergence diagnostic techniques available with the WinBUGS software have been applied to ensure the convergence of the chains necessary for the implementation of MCMC. The Bayesian approach allows for the use of observed data and expert judgements by means of appropriate priors, and a more realistic population forecasts, along with associated uncertainty, has been possible.

Trans-dimensional Bayesian inversion of airborne electromagnetic data for 2D conductivity profiles

NASA Astrophysics Data System (ADS)

Hawkins, Rhys; Brodie, Ross C.; Sambridge, Malcolm

2018-02-01

This paper presents the application of a novel trans-dimensional sampling approach to a time domain airborne electromagnetic (AEM) inverse problem to solve for plausible conductivities of the subsurface. Geophysical inverse field problems, such as time domain AEM, are well known to have a large degree of non-uniqueness. Common least-squares optimisation approaches fail to take this into account and provide a single solution with linearised estimates of uncertainty that can result in overly optimistic appraisal of the conductivity of the subsurface. In this new non-linear approach, the spatial complexity of a 2D profile is controlled directly by the data. By examining an ensemble of proposed conductivity profiles it accommodates non-uniqueness and provides more robust estimates of uncertainties.

On the null distribution of Bayes factors in linear regression

USDA-ARS?s Scientific Manuscript database

We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...

Quantitative estimation of the fluorescent parameters for crop leaves with the Bayesian inversion

USDA-ARS?s Scientific Manuscript database

In this study, the fluorescent parameters of crop leaves were retrieved from the leaf hyperspectral measurements by inverting the FluorMODleaf model, which is a leaf-level fluorescence model that is based on the widely used and validated PROSPECT (leaf optical properties) model and can simulate the ...

Algorithmic procedures for Bayesian MEG/EEG source reconstruction in SPM☆

PubMed Central

López, J.D.; Litvak, V.; Espinosa, J.J.; Friston, K.; Barnes, G.R.

2014-01-01

The MEG/EEG inverse problem is ill-posed, giving different source reconstructions depending on the initial assumption sets. Parametric Empirical Bayes allows one to implement most popular MEG/EEG inversion schemes (Minimum Norm, LORETA, etc.) within the same generic Bayesian framework. It also provides a cost-function in terms of the variational Free energy—an approximation to the marginal likelihood or evidence of the solution. In this manuscript, we revisit the algorithm for MEG/EEG source reconstruction with a view to providing a didactic and practical guide. The aim is to promote and help standardise the development and consolidation of other schemes within the same framework. We describe the implementation in the Statistical Parametric Mapping (SPM) software package, carefully explaining each of its stages with the help of a simple simulated data example. We focus on the Multiple Sparse Priors (MSP) model, which we compare with the well-known Minimum Norm and LORETA models, using the negative variational Free energy for model comparison. The manuscript is accompanied by Matlab scripts to allow the reader to test and explore the underlying algorithm. PMID:24041874

A Computationally-Efficient Inverse Approach to Probabilistic Strain-Based Damage Diagnosis

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.; Leser, William P.; Leser, Patrick E.; Newman, John A

2016-01-01

This work presents a computationally-efficient inverse approach to probabilistic damage diagnosis. Given strain data at a limited number of measurement locations, Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling are used to estimate probability distributions of the unknown location, size, and orientation of damage. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. The approach is experimentally validated on cracked test specimens where full field strains are determined using digital image correlation (DIC). Access to full field DIC data allows for testing of different hypothetical sensor arrangements, facilitating the study of strain-based diagnosis effectiveness as the distance between damage and measurement locations increases. The ability of the framework to effectively perform both probabilistic damage localization and characterization in cracked plates is demonstrated and the impact of measurement location on uncertainty in the predictions is shown. Furthermore, the analysis time to produce these predictions is orders of magnitude less than a baseline Bayesian approach with the FE method by utilizing surrogate modeling and effective numerical sampling approaches.

Seismic velocity structure of the forearc in northern Cascadia from Bayesian inversion of teleseismic data

NASA Astrophysics Data System (ADS)

Gosselin, J.; Audet, P.; Schaeffer, A. J.

2017-12-01

The seismic velocity structure in the forearc of subduction zones provides important constraints on material properties, with implications for seismogenesis. In Cascadia, previous studies have imaged a downgoing low-velocity zone (LVZ) characterized by an elevated P-to-S velocity ratio (Vp/Vs) down to 45 km depth, near the intersection with the mantle wedge corner, beyond which the signature of the LVZ disappears. These results, combined with the absence of a "normal" continental Moho, indicate that the down-going oceanic crust likely carries large amounts of overpressured free fluids that are released downdip at the onset of crustal eclogitization, and are further stored in the mantle wedge as serpentinite. These overpressured free fluids affect the stability of the plate interface and facilitate slow slip. These results are based on the inversion and migration of scattered teleseismic data for individual layer properties; a methodology which suffers from regularization and smoothing, non-uniqueness, and does not consider model uncertainty. This study instead applies trans-dimensional Bayesian inversion of teleseismic data collected in the forearc of northern Cascadia (the CAFÉ experiment in northern Washington) to provide rigorous, quantitative estimates of local velocity structure, and associated uncertainties (particularly Vp/Vs structure and depth to the plate interface). Trans-dimensional inversion is a generalization of fixed-dimensional inversion that includes the number (and type) of parameters required to describe the velocity model (or data error model) as unknown in the problem. This allows model complexity to be inherently determined by data information content, not by subjective regularization. The inversion is implemented here using the reversible-jump Markov chain Monte Carlo algorithm. The result is an ensemble set of candidate velocity-structure models which approximate the posterior probability density (PPD) of the model parameters. The solution to the inverse problem, and associated uncertainties, are described by properties of the PPD. The results obtained here will eventually be integrated with teleseismic data from OBS stations from the Cascadia Initiative to provide constraints across the entire seismogenic portion of the plate interface.

An Exploratory Study Examining the Feasibility of Using Bayesian Networks to Predict Circuit Analysis Understanding

ERIC Educational Resources Information Center

Chung, Gregory K. W. K.; Dionne, Gary B.; Kaiser, William J.

2006-01-01

Our research question was whether we could develop a feasible technique, using Bayesian networks, to diagnose gaps in student knowledge. Thirty-four college-age participants completed tasks designed to measure conceptual knowledge, procedural knowledge, and problem-solving skills related to circuit analysis. A Bayesian network was used to model…

Clay aquitards as archives of holocene paleoclimate: delta18O and thermal profiling.

PubMed

Hendry, M Jim; Woodbury, A D

2007-01-01

Paleoclimatic conditions in the Holocene were reconstructed from a detailed vertical profile of pore water delta(18)O and a series of downhole thermal profiles at a thick, hydrogeologically simple, aquitard research site in the Northern Great Plains of Saskatchewan. Reconstructions were obtained using the theory of one-dimensional diffusive transport and an empirical Bayesian inversion technique. Inversion of the delta(18)O profile shows that input signal consists of a sudden increase of +6 per thousand (corresponding to a temperature increase of about 18 degrees C) at about 12,000 years before present (BP), after which no measurable change in delta(18)O is apparent to present day. This research shows, at this location, that there is no evidence of large amplitude temperature shifts in the Holocene and supports the commonly used assumption in ground water studies of constant atmospheric delta(18)O values throughout the Holocene. Inversion of the temperature profiles suggests the ground surface temperature increased primarily in the last half of the 20th century, with a peak temperature (about 3 degrees C) circa 1990. For both profiles, the ability to resolve historical variability decays rapidly with time. For the temperature profiles, the decay in resolution precluded the development of reliable estimates of climatic conditions prior to about 1950 and, in the case of the delta(18)O profile, it prevented the precise definition of climate changes (e.g., Hypsithermal and Little Ice Age) in the Holocene.

A statistical assessment of seismic models of the U.S. continental crust using Bayesian inversion of ambient noise surface wave dispersion data

NASA Astrophysics Data System (ADS)

Olugboji, T. M.; Lekic, V.; McDonough, W.

2017-07-01

We present a new approach for evaluating existing crustal models using ambient noise data sets and its associated uncertainties. We use a transdimensional hierarchical Bayesian inversion approach to invert ambient noise surface wave phase dispersion maps for Love and Rayleigh waves using measurements obtained from Ekström (2014). Spatiospectral analysis shows that our results are comparable to a linear least squares inverse approach (except at higher harmonic degrees), but the procedure has additional advantages: (1) it yields an autoadaptive parameterization that follows Earth structure without making restricting assumptions on model resolution (regularization or damping) and data errors; (2) it can recover non-Gaussian phase velocity probability distributions while quantifying the sources of uncertainties in the data measurements and modeling procedure; and (3) it enables statistical assessments of different crustal models (e.g., CRUST1.0, LITHO1.0, and NACr14) using variable resolution residual and standard deviation maps estimated from the ensemble. These assessments show that in the stable old crust of the Archean, the misfits are statistically negligible, requiring no significant update to crustal models from the ambient noise data set. In other regions of the U.S., significant updates to regionalization and crustal structure are expected especially in the shallow sedimentary basins and the tectonically active regions, where the differences between model predictions and data are statistically significant.

Improved inference in Bayesian segmentation using Monte Carlo sampling: application to hippocampal subfield volumetry.

PubMed

Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen

2013-10-01

Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer's disease classification task. As an additional benefit, the technique also allows one to compute informative "error bars" on the volume estimates of individual structures. Copyright © 2013 Elsevier B.V. All rights reserved.

Improved Inference in Bayesian Segmentation Using Monte Carlo Sampling: Application to Hippocampal Subfield Volumetry

PubMed Central

Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Leemput, Koen Van

2013-01-01

Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer’s disease classification task. As an additional benefit, the technique also allows one to compute informative “error bars” on the volume estimates of individual structures. PMID:23773521

Applications of Bayesian Statistics to Problems in Gamma-Ray Bursts

NASA Technical Reports Server (NTRS)

Meegan, Charles A.

1997-01-01

This presentation will describe two applications of Bayesian statistics to Gamma Ray Bursts (GRBS). The first attempts to quantify the evidence for a cosmological versus galactic origin of GRBs using only the observations of the dipole and quadrupole moments of the angular distribution of bursts. The cosmological hypothesis predicts isotropy, while the galactic hypothesis is assumed to produce a uniform probability distribution over positive values for these moments. The observed isotropic distribution indicates that the Bayes factor for the cosmological hypothesis over the galactic hypothesis is about 300. Another application of Bayesian statistics is in the estimation of chance associations of optical counterparts with galaxies. The Bayesian approach is preferred to frequentist techniques here because the Bayesian approach easily accounts for galaxy mass distributions and because one can incorporate three disjoint hypotheses: (1) bursts come from galactic centers, (2) bursts come from galaxies in proportion to luminosity, and (3) bursts do not come from external galaxies. This technique was used in the analysis of the optical counterpart to GRB970228.

Invited commentary: Lost in estimation--searching for alternatives to markov chains to fit complex Bayesian models.

PubMed

Molitor, John

2012-03-01

Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.

Upper crustal structure of central Java, Indonesia, from transdimensional seismic ambient noise tomography

NASA Astrophysics Data System (ADS)

Zulfakriza, Z.; Saygin, E.; Cummins, P. R.; Widiyantoro, S.; Nugraha, A. D.; Lühr, B.-G.; Bodin, T.

2014-04-01

Delineating the crustal structure of central Java is crucial for understanding its complex tectonic setting. However, seismic imaging of the strong heterogeneity typical of such a tectonically active region can be challenging, particularly in the upper crust where velocity contrasts are strongest and steep body wave ray paths provide poor resolution. To overcome these difficulties, we apply the technique of ambient noise tomography (ANT) to data collected during the Merapi Amphibious Experiment (MERAMEX), which covered central Java with a temporary deployment of over 120 seismometers during 2004 May-October. More than 5000 Rayleigh wave Green's functions were extracted by cross-correlating the noise simultaneously recorded at available station pairs. We applied a fully non-linear 2-D Bayesian probabilistic inversion technique to the retrieved traveltimes. Features in the derived tomographic images correlate well with previous studies, and some shallow structures that were not evident in previous studies are clearly imaged with ANT. The Kendeng Basin and several active volcanoes appear with very low group velocities, and anomalies with relatively high velocities can be interpreted in terms of crustal sutures and/or surface geological features.

On the Implications of A Priori Constraints in Transdimensional Bayesian Inversion for Continental Lithospheric Layering

NASA Astrophysics Data System (ADS)

Roy, C.; Romanowicz, B. A.

2017-12-01

Monte Carlo methods are powerful approaches to solve nonlinear problems and are becoming very popular in Earth sciences. One reason being that, at first glance, no constraints or explicit regularization of model parameters are required. At second glance, one might realize that regularization is done through a prior. The choice of this prior, however, is subjective, and with its choice, unintended or undesired extra information can be injected into the problem. The principal criticism of Bayesian methods is that the prior can be "tuned" in order to get the expected solution. Consequently, detractors of the Bayesian method could easily argue that the solution is influenced by the form of the prior distribution, which choice is subjective. Hence, models obtained with Monte Carlo methods are still highly debated. Here we investigate the influence of a priori constraints (i.e., fixed crustal discontinuities) on the posterior probability distributions of estimated parameters, that is, vertical polarized shear velocity VSV and radial anisotropy ξ, in a transdimensional Bayesian inversion for continental lithospheric structure. We follow upon the work of Calò et al. (2016), who jointly inverted converted phases (P to S) without deconvolution and surface wave dispersion data, to obtain 1-D radial anisotropic shear wave velocity profiles in the North American craton. We aim at verifying whether the strong lithospheric layering found in the stable part of the craton is robust with respect to artifacts that might be caused by the methodology used. We test the hypothesis that the observed midlithospheric discontinuities result from (1) fixed crustal discontinuities in the reference model and (2) a fixed Vp/Vs ratio. The synthetic tests on two Earth models show that a fixed Vp/Vs ratio does not introduce artificial layering, even if the assumed value is slightly wrong. This is an important finding for real data inversion where the true value is not always available or accurate. However, fixing crustal discontinuities can lead to the introduction of spurious layering, and this is not recommended. Additionally, allowing the Vp/Vs ratio to vary does not help preventing that. Applying the modified approach resulting from these tests to two stations (FRB and FCC) in the North American craton, we confirm the presence of at least one midlithospheric low-velocity layer. We also confirm the difficulty of consistently detecting the lithosphere-asthenosphere boundary in the craton.

Information content of incubation experiments for inverse estimation of pools in the Rothamsted carbon model: a Bayesian approach

NASA Astrophysics Data System (ADS)

Scharnagl, Benedikt; Vrugt, Jasper A.; Vereecken, Harry; Herbst, Michael

2010-05-01

Turnover of soil organic matter is usually described with multi-compartment models. However, a major drawback of these models is that the conceptually defined compartments (or pools) do not necessarily correspond to measurable soil organic carbon (SOC) fractions in real practice. This not only impairs our ability to rigorously evaluate SOC models but also makes it difficult to derive accurate initial states. In this study, we tested the usefulness and applicability of inverse modeling to derive the various carbon pool sizes in the Rothamsted carbon model (ROTHC) using a synthetic time series of mineralization rates from laboratory incubation. To appropriately account for data and model uncertainty we considered a Bayesian approach using the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm. This Markov chain Monte Carlo scheme derives the posterior probability density distribution of the initial pool sizes at the start of incubation from observed mineralization rates. We used the Kullback-Leibler divergence to quantify the information contained in the data and to illustrate the effect of increasing incubation times on the reliability of the pool size estimates. Our results show that measured mineralization rates generally provide sufficient information to reliably estimate the sizes of all active pools in the ROTHC model. However, with about 900 days of incubation, these experiments are excessively long. The use of prior information on microbial biomass provided a way forward to significantly reduce uncertainty and required duration of incubation to about 600 days. Explicit consideration of model parameter uncertainty in the estimation process further impaired the identifiability of initial pools, especially for the more slowly decomposing pools. Our illustrative case studies show how Bayesian inverse modeling can be used to provide important insights into the information content of incubation experiments. Moreover, the outcome of this virtual experiment helps to explain the results of related real-world studies on SOC dynamics.

Revisiting the 2004 Sumatra-Andaman earthquake in a Bayesian framework

NASA Astrophysics Data System (ADS)

Bletery, Q.; Sladen, A.; Jiang, J.; Simons, M.

2015-12-01

The 2004 Mw 9.25 Sumatra-Andaman earthquake is the largest seismic event of the modern instrumental era. Despite considerable effort to analyze the characteristics of its rupture, the different available observations have proven difficult to simultaneously integrate jointly into a finite-fault slip model. In particular, the critical near-field geodetic records contain variable and significant post-seismic signal (between 2 weeks and 2 months) while the satellite altimetry records of the associated tsunami are affected by various sources of uncertainties (e.g. source rupture velocity, meso-scale oceanic currents). In this study, we investigate the quasi-static slip distribution of the Sumatra-Andaman earthquake by carefully accounting for the different sources of uncertainties in the joint inversion of an extended set of geodetic and tsunami data. To do so, we use non-diagonal covariance matrices reflecting both data and model uncertainties in a fully Bayesian inversion framework. As model errors are particularly large for mega-earthquakes, we also rely on advanced simulation codes (normal mode theory on a layered spherical Earth for the static displacement field and non-hydrostatic equations for the tsunami) and account for the 3D curvature of the megathrust interface to reduce the associated epistemic uncertainties. The fully Bayesian inversion framework then enables us to derive the families of possible models compatible with the unevenly distributed and sometimes ambiguous measurements. We find two regions of high slip at latitudes 3°-4°N and 7°-8°N with amplitudes that probably reached values as large as 40 m and possibly larger. Such amounts of slip were not proposed by previous studies, which might have been biased by smoothing regularizations. We also find significant slip (around 20 m) offshore Andaman islands absent in earlier studies. Furthermore, we find that the rupture very likely involved shallow slip, with the possibility of reaching the trench.

A Bayesian trans-dimensional approach for the fusion of multiple geophysical datasets

NASA Astrophysics Data System (ADS)

JafarGandomi, Arash; Binley, Andrew

2013-09-01

We propose a Bayesian fusion approach to integrate multiple geophysical datasets with different coverage and sensitivity. The fusion strategy is based on the capability of various geophysical methods to provide enough resolution to identify either subsurface material parameters or subsurface structure, or both. We focus on electrical resistivity as the target material parameter and electrical resistivity tomography (ERT), electromagnetic induction (EMI), and ground penetrating radar (GPR) as the set of geophysical methods. However, extending the approach to different sets of geophysical parameters and methods is straightforward. Different geophysical datasets are entered into a trans-dimensional Markov chain Monte Carlo (McMC) search-based joint inversion algorithm. The trans-dimensional property of the McMC algorithm allows dynamic parameterisation of the model space, which in turn helps to avoid bias of the post-inversion results towards a particular model. Given that we are attempting to develop an approach that has practical potential, we discretize the subsurface into an array of one-dimensional earth-models. Accordingly, the ERT data that are collected by using two-dimensional acquisition geometry are re-casted to a set of equivalent vertical electric soundings. Different data are inverted either individually or jointly to estimate one-dimensional subsurface models at discrete locations. We use Shannon's information measure to quantify the information obtained from the inversion of different combinations of geophysical datasets. Information from multiple methods is brought together via introducing joint likelihood function and/or constraining the prior information. A Bayesian maximum entropy approach is used for spatial fusion of spatially dispersed estimated one-dimensional models and mapping of the target parameter. We illustrate the approach with a synthetic dataset and then apply it to a field dataset. We show that the proposed fusion strategy is successful not only in enhancing the subsurface information but also as a survey design tool to identify the appropriate combination of the geophysical tools and show whether application of an individual method for further investigation of a specific site is beneficial.

Bayesian aggregation versus majority vote in the characterization of non-specific arm pain based on quantitative needle electromyography

PubMed Central

2010-01-01

Background Methods for the calculation and application of quantitative electromyographic (EMG) statistics for the characterization of EMG data detected from forearm muscles of individuals with and without pain associated with repetitive strain injury are presented. Methods A classification procedure using a multi-stage application of Bayesian inference is presented that characterizes a set of motor unit potentials acquired using needle electromyography. The utility of this technique in characterizing EMG data obtained from both normal individuals and those presenting with symptoms of "non-specific arm pain" is explored and validated. The efficacy of the Bayesian technique is compared with simple voting methods. Results The aggregate Bayesian classifier presented is found to perform with accuracy equivalent to that of majority voting on the test data, with an overall accuracy greater than 0.85. Theoretical foundations of the technique are discussed, and are related to the observations found. Conclusions Aggregation of motor unit potential conditional probability distributions estimated using quantitative electromyographic analysis, may be successfully used to perform electrodiagnostic characterization of "non-specific arm pain." It is expected that these techniques will also be able to be applied to other types of electrodiagnostic data. PMID:20156353

High-resolution gravity model of Venus

NASA Technical Reports Server (NTRS)

Reasenberg, R. D.; Goldberg, Z. M.

1992-01-01

The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter by means of a two-step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter-smoother. The Kalman filter has been evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography-gravity correlation previously reported. The topography-gravity scatter plots show two distinct trends.

Fifty years of levelling measurements at Askja volcano, Iceland: New Bayesian interpretations of a unique dataset

NASA Astrophysics Data System (ADS)

Barnie, Talfan; Sigmundsson, Freysteinn; Sturkell, Erik

2017-04-01

The year 2016 marks the 50th anniversary of the start of geodetic levelling surveys at Askja volcano in the Northern Volcanic Zone of Iceland. Askja has produced frequent basaltic fissural eruptions and rarer silicic caldera forming eruptions during the Holocene, the most recent of each type in 1961 and 1875 respectively. The potential for widespread disruption from larger eruptions and the popularity of the site with tourists makes Askja an important target for observation. Geodetic monitoring started in 1966 with the installation of a 12 station survey line on the 1961 lava flow, which provided a stable, extensive surface close to the putative source of magma. This was infilled and extended over the following two decades to give a finished levelling line of 35 stations spaced approximately 50 m apart (Tryggvason, Nordic Volcanological Institute, 1989). With the exception of the period 1972 to 1983, this line has been surveyed every year, providing a unique record of post eruptive deformation at a spreading rift segment capable of capturing magma motions at depth and any potential recharging in anticipation of future activity. The levelling has so far revealed that after an initial period of complicated inflations and deflations the volcano settled into a pattern of slowly decaying deflation from 1983 onwards (Sturkell and Sigmundsson, JGR, 105, 2000), a pattern that has been confirmed by newer geodetic techniques as they have become available (e.g. Pagli et al., JVGR, 152, 2005). The strength of the levelling data at Askja is its long time span, high accuracy and same measurement type over a period of 50 years. However, the small extent of the levelling line limits the power of the network to resolve changes in the magma plumbing system and requires the addition of constraints from other sources. This lends itself to Bayesian modelling techniques where assumptions are made explicit as priors and uncertainties in retrieved parameters can be comprehensibly modelled. Here we present a Bayesian inversion of the full dataset using the Stan probabilistic programming language that allows us to test a range of models of subsurface pressure changes and magma motions at depth.

An evaluation of Bayesian techniques for controlling model complexity and selecting inputs in a neural network for short-term load forecasting.

PubMed

Hippert, Henrique S; Taylor, James W

2010-04-01

Artificial neural networks have frequently been proposed for electricity load forecasting because of their capabilities for the nonlinear modelling of large multivariate data sets. Modelling with neural networks is not an easy task though; two of the main challenges are defining the appropriate level of model complexity, and choosing the input variables. This paper evaluates techniques for automatic neural network modelling within a Bayesian framework, as applied to six samples containing daily load and weather data for four different countries. We analyse input selection as carried out by the Bayesian 'automatic relevance determination', and the usefulness of the Bayesian 'evidence' for the selection of the best structure (in terms of number of neurones), as compared to methods based on cross-validation. Copyright 2009 Elsevier Ltd. All rights reserved.

A Novel Bayesian algorithm for Microwave Retrieval of Precipitation from Space: Applications in Snow and Coastal Hydrology

NASA Astrophysics Data System (ADS)

Foufoula, Efi; Ebtehaj, Ardeshir M.; Bras, Rafael L.

2015-04-01

Resolving accurately the space-time structure of precipitation over remote areas of the world where in-situ observations are not available is one of the biggest challenges in hydrology in view of the pressure to understand and mitigate climate and human-induced hydrologic and eco-geomorphologic changes. Two especially vulnerable areas are snow covered highlands (earlier snowmelt and changes in land-atmosphere feedbacks affecting storm dynamics and hydrologic response) and coastal areas (threats due to extreme storms and flooding in view of sea level rise and land-use changes affecting hazard potential in these overly populated low land areas). The GPM constellation of satellites offers the potential to retrieve precipitation over these complex surfaces but not without significant new ideas in the retrieval techniques for operational products. Here we present recent results from a new Bayesian inversion Passive Microwave Rainfall Retrieval algorithm (called ShARP) which introduces two main innovations: (1) a new distance metric in the space of retrieval (physically-derived or observational databases of brightness temperature and rainfall profiles) to create neighborhoods whose closeness is judged not on the basis of spatial averages but in terms of spatial structure in the space of spectral brightness temperatures, and (2) computes weights of those elements by minimizing a log-likelihood function plus a prior density of the spatial precipitation gradients. Both innovations rely on extending the typical Least squares (ℓ2) distance metric used in inverse problems to a mixed ℓ2 - ℓ1 metric (via regularization) and showing that this new metric is consistent with the localized small-scale spatial rainfall structure of sharp features embedded within more homogeneous domains. Using the data provided by the Tropical Rainfall Measuring Mission (TRMM) satellite, we demonstrate marked improvements in the ShARP rainfall retrievals in comparison with the standard TRMM-2A12 operational products by analysis of case studies in the Tibetan Highlands and the Ganges-Brahmaputra-Meghna river basin and its coastal delta.

A Bayesian approach to modeling 2D gravity data using polygon states

NASA Astrophysics Data System (ADS)

Titus, W. J.; Titus, S.; Davis, J. R.

2015-12-01

We present a Bayesian Markov chain Monte Carlo (MCMC) method for the 2D gravity inversion of a localized subsurface object with constant density contrast. Our models have four parameters: the density contrast, the number of vertices in a polygonal approximation of the object, an upper bound on the ratio of the perimeter squared to the area, and the vertices of a polygon container that bounds the object. Reasonable parameter values can be estimated prior to inversion using a forward model and geologic information. In addition, we assume that the field data have a common random uncertainty that lies between two bounds but that it has no systematic uncertainty. Finally, we assume that there is no uncertainty in the spatial locations of the measurement stations. For any set of model parameters, we use MCMC methods to generate an approximate probability distribution of polygons for the object. We then compute various probability distributions for the object, including the variance between the observed and predicted fields (an important quantity in the MCMC method), the area, the center of area, and the occupancy probability (the probability that a spatial point lies within the object). In addition, we compare probabilities of different models using parallel tempering, a technique which also mitigates trapping in local optima that can occur in certain model geometries. We apply our method to several synthetic data sets generated from objects of varying shape and location. We also analyze a natural data set collected across the Rio Grande Gorge Bridge in New Mexico, where the object (i.e. the air below the bridge) is known and the canyon is approximately 2D. Although there are many ways to view results, the occupancy probability proves quite powerful. We also find that the choice of the container is important. In particular, large containers should be avoided, because the more closely a container confines the object, the better the predictions match properties of object.

Stochastic static fault slip inversion from geodetic data with non-negativity and bounds constraints

NASA Astrophysics Data System (ADS)

Nocquet, J.-M.

2018-04-01

Despite surface displacements observed by geodesy are linear combinations of slip at faults in an elastic medium, determining the spatial distribution of fault slip remains a ill-posed inverse problem. A widely used approach to circumvent the illness of the inversion is to add regularization constraints in terms of smoothing and/or damping so that the linear system becomes invertible. However, the choice of regularization parameters is often arbitrary, and sometimes leads to significantly different results. Furthermore, the resolution analysis is usually empirical and cannot be made independently of the regularization. The stochastic approach of inverse problems (Tarantola & Valette 1982; Tarantola 2005) provides a rigorous framework where the a priori information about the searched parameters is combined with the observations in order to derive posterior probabilities of the unkown parameters. Here, I investigate an approach where the prior probability density function (pdf) is a multivariate Gaussian function, with single truncation to impose positivity of slip or double truncation to impose positivity and upper bounds on slip for interseismic modeling. I show that the joint posterior pdf is similar to the linear untruncated Gaussian case and can be expressed as a Truncated Multi-Variate Normal (TMVN) distribution. The TMVN form can then be used to obtain semi-analytical formulas for the single, two-dimensional or n-dimensional marginal pdf. The semi-analytical formula involves the product of a Gaussian by an integral term that can be evaluated using recent developments in TMVN probabilities calculations (e.g. Genz & Bretz 2009). Posterior mean and covariance can also be efficiently derived. I show that the Maximum Posterior (MAP) can be obtained using a Non-Negative Least-Squares algorithm (Lawson & Hanson 1974) for the single truncated case or using the Bounded-Variable Least-Squares algorithm (Stark & Parker 1995) for the double truncated case. I show that the case of independent uniform priors can be approximated using TMVN. The numerical equivalence to Bayesian inversions using Monte Carlo Markov Chain (MCMC) sampling is shown for a synthetic example and a real case for interseismic modeling in Central Peru. The TMVN method overcomes several limitations of the Bayesian approach using MCMC sampling. First, the need of computer power is largely reduced. Second, unlike Bayesian MCMC based approach, marginal pdf, mean, variance or covariance are obtained independently one from each other. Third, the probability and cumulative density functions can be obtained with any density of points. Finally, determining the Maximum Posterior (MAP) is extremely fast.

Probabilistic Inference: Task Dependency and Individual Differences of Probability Weighting Revealed by Hierarchical Bayesian Modeling

PubMed Central

Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno

2016-01-01

Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision. PMID:27303323

Probabilistic Prognosis of Non-Planar Fatigue Crack Growth

NASA Technical Reports Server (NTRS)

Leser, Patrick E.; Newman, John A.; Warner, James E.; Leser, William P.; Hochhalter, Jacob D.; Yuan, Fuh-Gwo

2016-01-01

Quantifying the uncertainty in model parameters for the purpose of damage prognosis can be accomplished utilizing Bayesian inference and damage diagnosis data from sources such as non-destructive evaluation or structural health monitoring. The number of samples required to solve the Bayesian inverse problem through common sampling techniques (e.g., Markov chain Monte Carlo) renders high-fidelity finite element-based damage growth models unusable due to prohibitive computation times. However, these types of models are often the only option when attempting to model complex damage growth in real-world structures. Here, a recently developed high-fidelity crack growth model is used which, when compared to finite element-based modeling, has demonstrated reductions in computation times of three orders of magnitude through the use of surrogate models and machine learning. The model is flexible in that only the expensive computation of the crack driving forces is replaced by the surrogate models, leaving the remaining parameters accessible for uncertainty quantification. A probabilistic prognosis framework incorporating this model is developed and demonstrated for non-planar crack growth in a modified, edge-notched, aluminum tensile specimen. Predictions of remaining useful life are made over time for five updates of the damage diagnosis data, and prognostic metrics are utilized to evaluate the performance of the prognostic framework. Challenges specific to the probabilistic prognosis of non-planar fatigue crack growth are highlighted and discussed in the context of the experimental results.

BATSE gamma-ray burst line search. 2: Bayesian consistency methodology

NASA Technical Reports Server (NTRS)

Band, D. L.; Ford, L. A.; Matteson, J. L.; Briggs, M.; Paciesas, W.; Pendleton, G.; Preece, R.; Palmer, D.; Teegarden, B.; Schaefer, B.

1994-01-01

We describe a Bayesian methodology to evaluate the consistency between the reported Ginga and Burst and Transient Source Experiment (BATSE) detections of absorption features in gamma-ray burst spectra. Currently no features have been detected by BATSE, but this methodology will still be applicable if and when such features are discovered. The Bayesian methodology permits the comparison of hypotheses regarding the two detectors' observations and makes explicit the subjective aspects of our analysis (e.g., the quantification of our confidence in detector performance). We also present non-Bayesian consistency statistics. Based on preliminary calculations of line detectability, we find that both the Bayesian and non-Bayesian techniques show that the BATSE and Ginga observations are consistent given our understanding of these detectors.

A Bayesian methodological framework for accommodating interannual variability of nutrient loading with the SPARROW model

NASA Astrophysics Data System (ADS)

Wellen, Christopher; Arhonditsis, George B.; Labencki, Tanya; Boyd, Duncan

2012-10-01

Regression-type, hybrid empirical/process-based models (e.g., SPARROW, PolFlow) have assumed a prominent role in efforts to estimate the sources and transport of nutrient pollution at river basin scales. However, almost no attempts have been made to explicitly accommodate interannual nutrient loading variability in their structure, despite empirical and theoretical evidence indicating that the associated source/sink processes are quite variable at annual timescales. In this study, we present two methodological approaches to accommodate interannual variability with the Spatially Referenced Regressions on Watershed attributes (SPARROW) nonlinear regression model. The first strategy uses the SPARROW model to estimate a static baseline load and climatic variables (e.g., precipitation) to drive the interannual variability. The second approach allows the source/sink processes within the SPARROW model to vary at annual timescales using dynamic parameter estimation techniques akin to those used in dynamic linear models. Model parameterization is founded upon Bayesian inference techniques that explicitly consider calibration data and model uncertainty. Our case study is the Hamilton Harbor watershed, a mixed agricultural and urban residential area located at the western end of Lake Ontario, Canada. Our analysis suggests that dynamic parameter estimation is the more parsimonious of the two strategies tested and can offer insights into the temporal structural changes associated with watershed functioning. Consistent with empirical and theoretical work, model estimated annual in-stream attenuation rates varied inversely with annual discharge. Estimated phosphorus source areas were concentrated near the receiving water body during years of high in-stream attenuation and dispersed along the main stems of the streams during years of low attenuation, suggesting that nutrient source areas are subject to interannual variability.

Family History as an Indicator of Risk for Reading Disability.

ERIC Educational Resources Information Center

Volger, George P.; And Others

1984-01-01

Self-reported reading ability of parents of 174 reading-disabled children and of 182 controls was used to estimate the probability that a child will become reading disabled. Using Bayesian inverse probability analysis, it was found that the risk for reading disability is increased substantially if either parent has had difficulty in learning to…

Source partitioning of methane emissions and its seasonality in the U.S. Midwest

Treesearch

Zichong Chen; Timothy J. Griffis; John M. Baker; Dylan B. Millet; Jeffrey D. Wood; Edward J. Dlugokencky; Arlyn E. Andrews; Colm Sweeney; Cheng Hu; Randall K. Kolka

2018-01-01

The methane (CH4) budget and its source partitioning are poorly constrained in the Midwestern United States. We used tall tower (185 m) aerodynamic flux measurements and atmospheric scale factor Bayesian inversions to constrain the monthly budget and to partition the total budget into natural (e.g., wetlands) and anthropogenic (e.g., livestock,...

Inversion Estimate of California Methane Emissions Using a Bayesian Inverse Model with Multi-Tower Greenhouse Gas Monitoring Network and Aircraft Measurements

NASA Astrophysics Data System (ADS)

Cui, Y.; Falk, M.; Chen, Y.; Herner, J.; Croes, B. E.; Vijayan, A.

2017-12-01

Methane (CH4) is an important short-lived climate pollutant (SLCP), and the second most important greenhouse gas (GHG) in California which accounts for 9% of the statewide GHG emissions inventory. Over the years, California has enacted several ambitious climate change mitigation goals, including the California Global Warming Solutions Act of 2006 which requires ARB to reduce statewide GHG emissions to 1990 emission level by 2020, as well as Assembly Bill 1383 which requires implementation of a climate mitigation program to reduce statewide methane emissions by 40% below the 2013 levels. In order to meet these requirements, ARB has proposed a comprehensive SLCP Strategy with goals to reduce oil and gas related emissions and capture methane emissions from dairy operations and organic waste. Achieving these goals will require accurate understanding of the sources of CH4 emissions. Since direct monitoring of CH4 emission sources in large spatial and temporal scales is challenging and resource intensive, we developed a complex inverse technique combined with atmospheric three-dimensional (3D) transport model and atmospheric observations of CH4 concentrations from a regional tower network and aircraft measurements, to gain insights into emission sources in California. In this study, develop a comprehensive inversion estimate using available aircraft measurements from CalNex airborne campaigns (May-June 2010) and three years of hourly continuous measurements from the ARB Statewide GHG Monitoring Network (2014-2016). The inversion analysis is conducted using two independent 3D Lagrangian models (WRF-STILT and WRF-FLEXPART), with a variety of bottom-up prior inputs from national and regional inventories, as well as two different probability density functions (Gaussian and Lognormal). Altogether, our analysis provides a detailed picture of the spatially resolved CH4 emission sources and their temporal variation over a multi-year period.

Information content of incubation experiments for inverse estimation of pools in the Rothamsted carbon model: a Bayesian perspective

NASA Astrophysics Data System (ADS)

Scharnagl, B.; Vrugt, J. A.; Vereecken, H.; Herbst, M.

2010-02-01

A major drawback of current soil organic carbon (SOC) models is that their conceptually defined pools do not necessarily correspond to measurable SOC fractions in real practice. This not only impairs our ability to rigorously evaluate SOC models but also makes it difficult to derive accurate initial states of the individual carbon pools. In this study, we tested the feasibility of inverse modelling for estimating pools in the Rothamsted carbon model (ROTHC) using mineralization rates observed during incubation experiments. This inverse approach may provide an alternative to existing SOC fractionation methods. To illustrate our approach, we used a time series of synthetically generated mineralization rates using the ROTHC model. We adopted a Bayesian approach using the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm to infer probability density functions of the various carbon pools at the start of incubation. The Kullback-Leibler divergence was used to quantify the information content of the mineralization rate data. Our results indicate that measured mineralization rates generally provided sufficient information to reliably estimate all carbon pools in the ROTHC model. The incubation time necessary to appropriately constrain all pools was about 900 days. The use of prior information on microbial biomass carbon significantly reduced the uncertainty of the initial carbon pools, decreasing the required incubation time to about 600 days. Simultaneous estimation of initial carbon pools and decomposition rate constants significantly increased the uncertainty of the carbon pools. This effect was most pronounced for the intermediate and slow pools. Altogether, our results demonstrate that it is particularly difficult to derive reasonable estimates of the humified organic matter pool and the inert organic matter pool from inverse modelling of mineralization rates observed during incubation experiments.

Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution

NASA Astrophysics Data System (ADS)

Saputro, D. R. S.; Amalia, F.; Widyaningsih, P.; Affan, R. C.

2018-05-01

Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques

NASA Technical Reports Server (NTRS)

Saha, Bhaskar; Goebel, kai

2007-01-01

Uncertainty management has always been the key hurdle faced by diagnostics and prognostics algorithms. A Bayesian treatment of this problem provides an elegant and theoretically sound approach to the modern Condition- Based Maintenance (CBM)/Prognostic Health Management (PHM) paradigm. The application of the Bayesian techniques to regression and classification in the form of Relevance Vector Machine (RVM), and to state estimation as in Particle Filters (PF), provides a powerful tool to integrate the diagnosis and prognosis of battery health. The RVM, which is a Bayesian treatment of the Support Vector Machine (SVM), is used for model identification, while the PF framework uses the learnt model, statistical estimates of noise and anticipated operational conditions to provide estimates of remaining useful life (RUL) in the form of a probability density function (PDF). This type of prognostics generates a significant value addition to the management of any operation involving electrical systems.

Multivariate Bayesian analysis of Gaussian, right censored Gaussian, ordered categorical and binary traits using Gibbs sampling

PubMed Central

Korsgaard, Inge Riis; Lund, Mogens Sandø; Sorensen, Daniel; Gianola, Daniel; Madsen, Per; Jensen, Just

2003-01-01

A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed. PMID:12633531

Monitoring fossil fuel sources of methane in Australia

NASA Astrophysics Data System (ADS)

Loh, Zoe; Etheridge, David; Luhar, Ashok; Hibberd, Mark; Thatcher, Marcus; Noonan, Julie; Thornton, David; Spencer, Darren; Gregory, Rebecca; Jenkins, Charles; Zegelin, Steve; Leuning, Ray; Day, Stuart; Barrett, Damian

2017-04-01

CSIRO has been active in identifying and quantifying methane emissions from a range of fossil fuel sources in Australia over the past decade. We present here a history of the development of our work in this domain. While we have principally focused on optimising the use of long term, fixed location, high precision monitoring, paired with both forward and inverse modelling techniques suitable either local or regional scales, we have also incorporated mobile ground surveys and flux calculations from plumes in some contexts. We initially developed leak detection methodologies for geological carbon storage at a local scale using a Bayesian probabilistic approach coupled to a backward Lagrangian particle dispersion model (Luhar et al. JGR, 2014), and single point monitoring with sector analysis (Etheridge et al. In prep.) We have since expanded our modelling techniques to regional scales using both forward and inverse approaches to constrain methane emissions from coal mining and coal seam gas (CSG) production. The Surat Basin (Queensland, Australia) is a region of rapidly expanding CSG production, in which we have established a pair of carefully located, well-intercalibrated monitoring stations. These data sets provide an almost continuous record of (i) background air arriving at the Surat Basin, and (ii) the signal resulting from methane emissions within the Basin, i.e. total downwind methane concentration (comprising emissions including natural geological seeps, agricultural and biogenic sources and fugitive emissions from CSG production) minus background or upwind concentration. We will present our latest results on monitoring from the Surat Basin and their application to estimating methane emissions.

Efficient hierarchical trans-dimensional Bayesian inversion of magnetotelluric data

NASA Astrophysics Data System (ADS)

Xiang, Enming; Guo, Rongwen; Dosso, Stan E.; Liu, Jianxin; Dong, Hao; Ren, Zhengyong

2018-06-01

This paper develops an efficient hierarchical trans-dimensional (trans-D) Bayesian algorithm to invert magnetotelluric (MT) data for subsurface geoelectrical structure, with unknown geophysical model parameterization (the number of conductivity-layer interfaces) and data-error models parameterized by an auto-regressive (AR) process to account for potential error correlations. The reversible-jump Markov-chain Monte Carlo algorithm, which adds/removes interfaces and AR parameters in birth/death steps, is applied to sample the trans-D posterior probability density for model parameterization, model parameters, error variance and AR parameters, accounting for the uncertainties of model dimension and data-error statistics in the uncertainty estimates of the conductivity profile. To provide efficient sampling over the multiple subspaces of different dimensions, advanced proposal schemes are applied. Parameter perturbations are carried out in principal-component space, defined by eigen-decomposition of the unit-lag model covariance matrix, to minimize the effect of inter-parameter correlations and provide effective perturbation directions and length scales. Parameters of new layers in birth steps are proposed from the prior, instead of focused distributions centred at existing values, to improve birth acceptance rates. Parallel tempering, based on a series of parallel interacting Markov chains with successively relaxed likelihoods, is applied to improve chain mixing over model dimensions. The trans-D inversion is applied in a simulation study to examine the resolution of model structure according to the data information content. The inversion is also applied to a measured MT data set from south-central Australia.

Estimating National-scale Emissions using Dense Monitoring Networks

NASA Astrophysics Data System (ADS)

Ganesan, A.; Manning, A.; Grant, A.; Young, D.; Oram, D.; Sturges, W. T.; Moncrieff, J. B.; O'Doherty, S.

2014-12-01

The UK's DECC (Deriving Emissions linked to Climate Change) network consists of four greenhouse gas measurement stations that are situated to constrain emissions from the UK and Northwest Europe. These four stations are located in Mace Head (West Coast of Ireland), and on telecommunication towers at Ridge Hill (Western England), Tacolneston (Eastern England) and Angus (Eastern Scotland). With the exception of Angus, which currently only measures carbon dioxide (CO2) and methane (CH4), the remaining sites are additionally equipped to monitor nitrous oxide (N2O). We present an analysis of the network's CH4 and N2O observations from 2011-2013 and compare derived top-down regional emissions with bottom-up inventories, including a recently produced high-resolution inventory (UK National Atmospheric Emissions Inventory). As countries are moving toward national-level emissions estimation, we also address some of the considerations that need to be made when designing these national networks. One of the novel aspects of this work is that we use a hierarchical Bayesian inversion framework. This methodology, which has newly been applied to greenhouse gas emissions estimation, is designed to estimate temporally and spatially varying model-measurement uncertainties and correlation scales, in addition to fluxes. Through this analysis, we demonstrate the importance of characterizing these covariance parameters in order to properly use data from high-density monitoring networks. This UK case study highlights the ways in which this new inverse framework can be used to address some of the limitations of traditional Bayesian inverse methods.

Bayesian inversion of marine CSEM data from the Scarborough gas field using a transdimensional 2-D parametrization

NASA Astrophysics Data System (ADS)

Ray, Anandaroop; Key, Kerry; Bodin, Thomas; Myer, David; Constable, Steven

2014-12-01

We apply a reversible-jump Markov chain Monte Carlo method to sample the Bayesian posterior model probability density function of 2-D seafloor resistivity as constrained by marine controlled source electromagnetic data. This density function of earth models conveys information on which parts of the model space are illuminated by the data. Whereas conventional gradient-based inversion approaches require subjective regularization choices to stabilize this highly non-linear and non-unique inverse problem and provide only a single solution with no model uncertainty information, the method we use entirely avoids model regularization. The result of our approach is an ensemble of models that can be visualized and queried to provide meaningful information about the sensitivity of the data to the subsurface, and the level of resolution of model parameters. We represent models in 2-D using a Voronoi cell parametrization. To make the 2-D problem practical, we use a source-receiver common midpoint approximation with 1-D forward modelling. Our algorithm is transdimensional and self-parametrizing where the number of resistivity cells within a 2-D depth section is variable, as are their positions and geometries. Two synthetic studies demonstrate the algorithm's use in the appraisal of a thin, segmented, resistive reservoir which makes for a challenging exploration target. As a demonstration example, we apply our method to survey data collected over the Scarborough gas field on the Northwest Australian shelf.

Uncertainty Estimation in Tsunami Initial Condition From Rapid Bayesian Finite Fault Modeling

NASA Astrophysics Data System (ADS)

Benavente, R. F.; Dettmer, J.; Cummins, P. R.; Urrutia, A.; Cienfuegos, R.

2017-12-01

It is well known that kinematic rupture models for a given earthquake can present discrepancies even when similar datasets are employed in the inversion process. While quantifying this variability can be critical when making early estimates of the earthquake and triggered tsunami impact, "most likely models" are normally used for this purpose. In this work, we quantify the uncertainty of the tsunami initial condition for the great Illapel earthquake (Mw = 8.3, 2015, Chile). We focus on utilizing data and inversion methods that are suitable to rapid source characterization yet provide meaningful and robust results. Rupture models from teleseismic body and surface waves as well as W-phase are derived and accompanied by Bayesian uncertainty estimates from linearized inversion under positivity constraints. We show that robust and consistent features about the rupture kinematics appear when working within this probabilistic framework. Moreover, by using static dislocation theory, we translate the probabilistic slip distributions into seafloor deformation which we interpret as a tsunami initial condition. After considering uncertainty, our probabilistic seafloor deformation models obtained from different data types appear consistent with each other providing meaningful results. We also show that selecting just a single "representative" solution from the ensemble of initial conditions for tsunami propagation may lead to overestimating information content in the data. Our results suggest that rapid, probabilistic rupture models can play a significant role during emergency response by providing robust information about the extent of the disaster.

FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)

NASA Astrophysics Data System (ADS)

2014-10-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2014 was a one-day workshop held in May 2014 which attracted around sixty attendees. Each of the submitted papers has been reviewed by two reviewers. There have been nine accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks (GDR ISIS, GDR MIA, GDR MOA, GDR Ondes). The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA, SATIE. Eric Vourc'h and Thomas Rodet

Clustering and Bayesian hierarchical modeling for the definition of informative prior distributions in hydrogeology

NASA Astrophysics Data System (ADS)

Cucchi, K.; Kawa, N.; Hesse, F.; Rubin, Y.

2017-12-01

In order to reduce uncertainty in the prediction of subsurface flow and transport processes, practitioners should use all data available. However, classic inverse modeling frameworks typically only make use of information contained in in-situ field measurements to provide estimates of hydrogeological parameters. Such hydrogeological information about an aquifer is difficult and costly to acquire. In this data-scarce context, the transfer of ex-situ information coming from previously investigated sites can be critical for improving predictions by better constraining the estimation procedure. Bayesian inverse modeling provides a coherent framework to represent such ex-situ information by virtue of the prior distribution and combine them with in-situ information from the target site. In this study, we present an innovative data-driven approach for defining such informative priors for hydrogeological parameters at the target site. Our approach consists in two steps, both relying on statistical and machine learning methods. The first step is data selection; it consists in selecting sites similar to the target site. We use clustering methods for selecting similar sites based on observable hydrogeological features. The second step is data assimilation; it consists in assimilating data from the selected similar sites into the informative prior. We use a Bayesian hierarchical model to account for inter-site variability and to allow for the assimilation of multiple types of site-specific data. We present the application and validation of the presented methods on an established database of hydrogeological parameters. Data and methods are implemented in the form of an open-source R-package and therefore facilitate easy use by other practitioners.

Remote sensing of suspended sediment water research: principles, methods, and progress

NASA Astrophysics Data System (ADS)

Shen, Ping; Zhang, Jing

2011-12-01

In this paper, we reviewed the principle, data, methods and steps in suspended sediment research by using remote sensing, summed up some representative models and methods, and analyzes the deficiencies of existing methods. Combined with the recent progress of remote sensing theory and application in water suspended sediment research, we introduced in some data processing methods such as atmospheric correction method, adjacent effect correction, and some intelligence algorithms such as neural networks, genetic algorithms, support vector machines into the suspended sediment inversion research, combined with other geographic information, based on Bayesian theory, we improved the suspended sediment inversion precision, and aim to give references to the related researchers.

Confidence set interference with a prior quadratic bound. [in geophysics

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

Multi-subject hierarchical inverse covariance modelling improves estimation of functional brain networks.

PubMed

Colclough, Giles L; Woolrich, Mark W; Harrison, Samuel J; Rojas López, Pedro A; Valdes-Sosa, Pedro A; Smith, Stephen M

2018-05-07

A Bayesian model for sparse, hierarchical, inver-covariance estimation is presented, and applied to multi-subject functional connectivity estimation in the human brain. It enables simultaneous inference of the strength of connectivity between brain regions at both subject and population level, and is applicable to fMRI, MEG and EEG data. Two versions of the model can encourage sparse connectivity, either using continuous priors to suppress irrelevant connections, or using an explicit description of the network structure to estimate the connection probability between each pair of regions. A large evaluation of this model, and thirteen methods that represent the state of the art of inverse covariance modelling, is conducted using both simulated and resting-state functional imaging datasets. Our novel Bayesian approach has similar performance to the best extant alternative, Ng et al.'s Sparse Group Gaussian Graphical Model algorithm, which also is based on a hierarchical structure. Using data from the Human Connectome Project, we show that these hierarchical models are able to reduce the measurement error in MEG beta-band functional networks by 10%, producing concomitant increases in estimates of the genetic influence on functional connectivity. Copyright © 2018. Published by Elsevier Inc.

Algorithmic procedures for Bayesian MEG/EEG source reconstruction in SPM.

PubMed

López, J D; Litvak, V; Espinosa, J J; Friston, K; Barnes, G R

2014-01-01

The MEG/EEG inverse problem is ill-posed, giving different source reconstructions depending on the initial assumption sets. Parametric Empirical Bayes allows one to implement most popular MEG/EEG inversion schemes (Minimum Norm, LORETA, etc.) within the same generic Bayesian framework. It also provides a cost-function in terms of the variational Free energy-an approximation to the marginal likelihood or evidence of the solution. In this manuscript, we revisit the algorithm for MEG/EEG source reconstruction with a view to providing a didactic and practical guide. The aim is to promote and help standardise the development and consolidation of other schemes within the same framework. We describe the implementation in the Statistical Parametric Mapping (SPM) software package, carefully explaining each of its stages with the help of a simple simulated data example. We focus on the Multiple Sparse Priors (MSP) model, which we compare with the well-known Minimum Norm and LORETA models, using the negative variational Free energy for model comparison. The manuscript is accompanied by Matlab scripts to allow the reader to test and explore the underlying algorithm. © 2013. Published by Elsevier Inc. All rights reserved.

Bayesian statistical ionospheric tomography improved by incorporating ionosonde measurements

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Virtanen, Ilkka I.; Roininen, Lassi; Vierinen, Juha; Orispää, Mikko; Kauristie, Kirsti; Lehtinen, Markku S.

2016-04-01

We validate two-dimensional ionospheric tomography reconstructions against EISCAT incoherent scatter radar measurements. Our tomography method is based on Bayesian statistical inversion with prior distribution given by its mean and covariance. We employ ionosonde measurements for the choice of the prior mean and covariance parameters and use the Gaussian Markov random fields as a sparse matrix approximation for the numerical computations. This results in a computationally efficient tomographic inversion algorithm with clear probabilistic interpretation. We demonstrate how this method works with simultaneous beacon satellite and ionosonde measurements obtained in northern Scandinavia. The performance is compared with results obtained with a zero-mean prior and with the prior mean taken from the International Reference Ionosphere 2007 model. In validating the results, we use EISCAT ultra-high-frequency incoherent scatter radar measurements as the ground truth for the ionization profile shape. We find that in comparison to the alternative prior information sources, ionosonde measurements improve the reconstruction by adding accurate information about the absolute value and the altitude distribution of electron density. With an ionosonde at continuous disposal, the presented method enhances stand-alone near-real-time ionospheric tomography for the given conditions significantly.

Bayesian inversion of the global present-day GIA signal uncertainty from RSL data

NASA Astrophysics Data System (ADS)

Caron, Lambert; Ivins, Erik R.; Adhikari, Surendra; Larour, Eric

2017-04-01

Various geophysical signals measured in the process of studying the present-day climate change (such as changes in the Earth gravitational potential, ocean altimery or GPS data) include a secular Glacial Isostatic Adjustment contribution that has to be corrected for. Yet, one of the current major challenges that Glacial Isostatic Adjustment modelling is currently struggling with is to accurately determine the uncertainty of the predicted present-day GIA signal. This is especially true at the global scale, where coupling between ice history and mantle rheology greatly contributes to the non-uniqueness of the solutions. Here we propose to use more than 11000 paleo sea level records to constrain a set of GIA Bayesian inversions and thoroughly explore its parameters space. We include two linearly relaxing models to represent the mantle rheology and couple them with a scalable ice history model in order to better assess the non-uniqueness of the solutions. From the resulting estimates of the Probability Density Function, we then extract maps of uncertainty affecting the present-day vertical land motion and geoid due to GIA at the global scale, and their associated expectation of the signal.

Bayesian or Laplacien inference, entropy and information theory and information geometry in data and signal processing

NASA Astrophysics Data System (ADS)

Mohammad-Djafari, Ali

2015-01-01

The main object of this tutorial article is first to review the main inference tools using Bayesian approach, Entropy, Information theory and their corresponding geometries. This review is focused mainly on the ways these tools have been used in data, signal and image processing. After a short introduction of the different quantities related to the Bayes rule, the entropy and the Maximum Entropy Principle (MEP), relative entropy and the Kullback-Leibler divergence, Fisher information, we will study their use in different fields of data and signal processing such as: entropy in source separation, Fisher information in model order selection, different Maximum Entropy based methods in time series spectral estimation and finally, general linear inverse problems.

Bayesian component separation: The Planck experience

NASA Astrophysics Data System (ADS)

Wehus, Ingunn Kathrine; Eriksen, Hans Kristian

2018-05-01

Bayesian component separation techniques have played a central role in the data reduction process of Planck. The most important strength of this approach is its global nature, in which a parametric and physical model is fitted to the data. Such physical modeling allows the user to constrain very general data models, and jointly probe cosmological, astrophysical and instrumental parameters. This approach also supports statistically robust goodness-of-fit tests in terms of data-minus-model residual maps, which are essential for identifying residual systematic effects in the data. The main challenges are high code complexity and computational cost. Whether or not these costs are justified for a given experiment depends on its final uncertainty budget. We therefore predict that the importance of Bayesian component separation techniques is likely to increase with time for intensity mapping experiments, similar to what has happened in the CMB field, as observational techniques mature, and their overall sensitivity improves.

Approximate Bayesian computation for spatial SEIR(S) epidemic models.

PubMed

Brown, Grant D; Porter, Aaron T; Oleson, Jacob J; Hinman, Jessica A

2018-02-01

Approximate Bayesia n Computation (ABC) provides an attractive approach to estimation in complex Bayesian inferential problems for which evaluation of the kernel of the posterior distribution is impossible or computationally expensive. These highly parallelizable techniques have been successfully applied to many fields, particularly in cases where more traditional approaches such as Markov chain Monte Carlo (MCMC) are impractical. In this work, we demonstrate the application of approximate Bayesian inference to spatially heterogeneous Susceptible-Exposed-Infectious-Removed (SEIR) stochastic epidemic models. These models have a tractable posterior distribution, however MCMC techniques nevertheless become computationally infeasible for moderately sized problems. We discuss the practical implementation of these techniques via the open source ABSEIR package for R. The performance of ABC relative to traditional MCMC methods in a small problem is explored under simulation, as well as in the spatially heterogeneous context of the 2014 epidemic of Chikungunya in the Americas. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

2014-06-01

Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

Dynamics of Mount Somma-Vesuvius edifice: from stress field inversion to analogue and numerical modelling

NASA Astrophysics Data System (ADS)

De Matteo, Ada; Massa, Bruno; D'Auria, Luca; Castaldo, Raffaele

2017-04-01

Geological processes are generally very complex and too slow to be directly observed in their completeness; modelling procedures overcome this limit. The state of stress in the upper lithosphere is the main responsible for driving geodynamical processes; in order to retrieve the active stress field in a rock volume, stress inversion techniques can be applied on both seismological and structural datasets. This approach has been successfully applied to active tectonics as well as volcanic areas. In this context the best approach in managing heterogeneous datasets in volcanic environments consists in the analysis of spatial variations of the stress field by applying robust techniques of inversion. The study of volcanic seismicity is an efficient tool to retrieve spatial and temporal pattern of the pre-, syn- and inter-eruptive stress field: magma migration as well as dynamics of magma chamber and hydrothermal system are directly connected to the volcanic seismicity. Additionally, analysis of the temporal variations of stress field pattern in volcanoes could be a useful monitoring tool. Recently the stress field acting on several active volcanoes has been investigated by using stress inversion techniques on seismological datasets (Massa et al., 2016). The Bayesian Right Trihedra Method (BRTM; D'Auria and Massa, 2015) is able to successfully manage heterogeneous datasets allowing the identification of regional fields locally overcame by the stress field due to volcano specific dynamics. In particular, the analysis of seismicity and stress field inversion at the Somma-Vesuvius highlighted the presence of two superposed volumes characterized by different behaviour and stress field pattern: a top volume dominated by an extensional stress field, in accordance with a gravitational spreading-style of deformation, and a bottom volume related to a regional extensional stress field. In addition, in order to evaluate the dynamics of deformation, both analogue and numerical modelling are being performed. Scaled analogue models of the Somma-Vesuvius are being built accordingly with the actual geometrical asymmetry of the volcano, varying just few parameters connected to the uncertainty of the depth and thickness of a buried decoupling layer. Experiments are being monitored by an optical stereo image system, useful to build a 3D time-lapsed models used to retrieve the model deformations. Simultaneously, a time-dependent 3D Finite Element model is being carried out in a fluid-dynamic context by fixing the same parameters of the proposed analogue model. Finally, a comparative analysis is being made between the model deformations and the DInSAR measurements derived from satellite data in order to estimate the uncertain parameters (i.e., thickness and viscosity of ductile layer). Preliminary results of the analogue models fit with the hypothesis of a spreading deformation active at the Somma-Vesuvius.

Bayesian Modeling of the Assimilative Capacity Component of Stream Nutrient Export

EPA Science Inventory

Implementing stream restoration techniques and best management practices to reduce nonpoint source nutrients implies enhancement of the assimilative capacity for the stream system. In this paper, a Bayesian method for evaluating this component of a TMDL load capacity is developed...

Combining historical eyewitness accounts on tsunami-induced waves and numerical simulations for getting insights in uncertainty of source parameters

NASA Astrophysics Data System (ADS)

Rohmer, Jeremy; Rousseau, Marie; Lemoine, Anne; Pedreros, Rodrigo; Lambert, Jerome; benki, Aalae

2017-04-01

Recent tsunami events including the 2004 Indian Ocean tsunami and the 2011 Tohoku tsunami have caused many casualties and damages to structures. Advances in numerical simulation of tsunami-induced wave processes have tremendously improved forecast, hazard and risk assessment and design of early warning for tsunamis. Among the major challenges, several studies have underlined uncertainties in earthquake slip distributions and rupture processes as major contributor on tsunami wave height and inundation extent. Constraining these uncertainties can be performed by taking advantage of observations either on tsunami waves (using network of water level gauge) or on inundation characteristics (using field evidence and eyewitness accounts). Despite these successful applications, combining tsunami observations and simulations still faces several limitations when the problem is addressed for past tsunamis events like 1755 Lisbon. 1) While recent inversion studies can benefit from current modern networks (e.g., tide gauges, sea bottom pressure gauges, GPS-mounted buoys), the number of tide gauges can be very scarce and testimonies on tsunami observations can be limited, incomplete and imprecise for past tsunamis events. These observations often restrict to eyewitness accounts on wave heights (e.g., maximum reached wave height at the coast) instead of the full observed waveforms; 2) Tsunami phenomena involve a large span of spatial scales (from ocean basin scales to local coastal wave interactions), which can make the modelling very demanding: the computation time cost of tsunami simulation can be very prohibitive; often reaching several hours. This often limits the number of allowable long-running simulations for performing the inversion, especially when the problem is addressed from a Bayesian inference perspective. The objective of the present study is to overcome both afore-described difficulties in the view to combine historical observations on past tsunami-induced waves and numerical simulations. In order to learn the uncertainty information on source parameters, we treat the problem within the Bayesian setting, which enables to incorporate in a flexible manner the different uncertainty sources. We propose to rely on an emerging technique called Approximate Bayesian Computation ABC, which has been developed to estimate the posterior distribution in modelling scenarios where the likelihood function is either unknown or cannot be explicitly defined. To overcome the computational issue, we combine ABC with statistical emulators (aka meta-model). We apply the proposed approach on the case study of Ligurian (North West of Italy) tsunami (1887) and discuss the results with a special attention paid to the impact of the observational error.

Deep Learning Neural Networks and Bayesian Neural Networks in Data Analysis

NASA Astrophysics Data System (ADS)

Chernoded, Andrey; Dudko, Lev; Myagkov, Igor; Volkov, Petr

2017-10-01

Most of the modern analyses in high energy physics use signal-versus-background classification techniques of machine learning methods and neural networks in particular. Deep learning neural network is the most promising modern technique to separate signal and background and now days can be widely and successfully implemented as a part of physical analysis. In this article we compare Deep learning and Bayesian neural networks application as a classifiers in an instance of top quark analysis.

Fully probabilistic earthquake source inversion on teleseismic scales

NASA Astrophysics Data System (ADS)

Stähler, Simon; Sigloch, Karin

2017-04-01

Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters but also estimates of their uncertainties are of great practical importance. We have developed a method of fully Bayesian inference for source parameters, based on measurements of waveform cross-correlation between broadband, teleseismic body-wave observations and their modelled counterparts. This approach yields not only depth and moment tensor estimates but also source time functions. These unknowns are parameterised efficiently by harnessing as prior knowledge solutions from a large number of non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 source time functions (STFs) by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits propagating these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible. A prerequisite for Bayesian inference is the proper characterisation of the noise afflicting the measurements. We show that, for realistic broadband body-wave seismograms, the systematic error due to an incomplete physical model affects waveform misfits more strongly than random, ambient background noise. In this situation, the waveform cross-correlation coefficient CC, or rather its decorrelation D = 1 - CC, performs more robustly as a misfit criterion than ℓp norms, more commonly used as sample-by-sample measures of misfit based on distances between individual time samples. From a set of over 900 user-supervised, deterministic earthquake source solutions treated as a quality-controlled reference, we derive the noise distribution on signal decorrelation D of the broadband seismogram fits between observed and modelled waveforms. The noise on D is found to approximately follow a log-normal distribution, a fortunate fact that readily accommodates the formulation of an empirical likelihood function for D for our multivariate problem. The first and second moments of this multivariate distribution are shown to depend mostly on the signal-to-noise ratio (SNR) of the CC measurements and on the back-azimuthal distances of seismic stations. References: Stähler, S. C. and Sigloch, K.: Fully probabilistic seismic source inversion - Part 1: Efficient parameterisation, Solid Earth, 5, 1055-1069, doi:10.5194/se-5-1055-2014, 2014. Stähler, S. C. and Sigloch, K.: Fully probabilistic seismic source inversion - Part 2: Modelling errors and station covariances, Solid Earth, 7, 1521-1536, doi:10.5194/se-7-1521-2016, 2016.

Practical differences among probabilities, possibilities, and credibilities

NASA Astrophysics Data System (ADS)

Grandin, Jean-Francois; Moulin, Caroline

2002-03-01

This paper presents some important differences that exist between theories, which allow the uncertainty management in data fusion. The main comparative results illustrated in this paper are the followings: Incompatibility between decisions got from probabilities and credibilities is highlighted. In the dynamic frame, as remarked in [19] or [17], belief and plausibility of Dempster-Shafer model do not frame the Bayesian probability. This framing can however be obtained by the Modified Dempster-Shafer approach. It also can be obtained in the Bayesian framework either by simulation techniques, or with a studentization. The uncommitted in the Dempster-Shafer way, e.g. the mass accorded to the ignorance, gives a mechanism similar to the reliability in the Bayesian model. Uncommitted mass in Dempster-Shafer theory or reliability in Bayes theory act like a filter that weakens extracted information, and improves robustness to outliners. So, it is logical to observe on examples like the one presented particularly by D.M. Buede, a faster convergence of a Bayesian method that doesn't take into account the reliability, in front of Dempster-Shafer method which uses uncommitted mass. But, on Bayesian masses, if reliability is taken into account, at the same level that the uncommited, e.g. F=1-m, we observe an equivalent rate for convergence. When Dempster-Shafer and Bayes operator are informed by uncertainty, faster or lower convergence can be exhibited on non Bayesian masses. This is due to positive or negative synergy between information delivered by sensors. This effect is a direct consequence of non additivity when considering non Bayesian masses. Unknowledge of the prior in bayesian techniques can be quickly compensated by information accumulated as time goes on by a set of sensors. All these results are presented on simple examples, and developed when necessary.

Confidence of compliance: a Bayesian approach for percentile standards.

PubMed

McBride, G B; Ellis, J C

2001-04-01

Rules for assessing compliance with percentile standards commonly limit the number of exceedances permitted in a batch of samples taken over a defined assessment period. Such rules are commonly developed using classical statistical methods. Results from alternative Bayesian methods are presented (using beta-distributed prior information and a binomial likelihood), resulting in "confidence of compliance" graphs. These allow simple reading of the consumer's risk and the supplier's risks for any proposed rule. The influence of the prior assumptions required by the Bayesian technique on the confidence results is demonstrated, using two reference priors (uniform and Jeffreys') and also using optimistic and pessimistic user-defined priors. All four give less pessimistic results than does the classical technique, because interpreting classical results as "confidence of compliance" actually invokes a Bayesian approach with an extreme prior distribution. Jeffreys' prior is shown to be the most generally appropriate choice of prior distribution. Cost savings can be expected using rules based on this approach.

An adaptive Gaussian process-based method for efficient Bayesian experimental design in groundwater contaminant source identification problems: ADAPTIVE GAUSSIAN PROCESS-BASED INVERSION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Jiangjiang; Li, Weixuan; Zeng, Lingzao

Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimations of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate approximation of the original model can be adaptively constructed with low computational cost. Based on this idea, we propose amore » Gaussian process (GP) surrogate-based Bayesian experimental design and parameter estimation approach for groundwater contaminant source identification problems. A major advantage of the GP surrogate is that it provides a convenient estimation of the approximation error, which can be incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work using two-stage MCMC.« less

Investigating different approaches to develop informative priors in hierarchical Bayesian safety performance functions.

PubMed

Yu, Rongjie; Abdel-Aty, Mohamed

2013-07-01

The Bayesian inference method has been frequently adopted to develop safety performance functions. One advantage of the Bayesian inference is that prior information for the independent variables can be included in the inference procedures. However, there are few studies that discussed how to formulate informative priors for the independent variables and evaluated the effects of incorporating informative priors in developing safety performance functions. This paper addresses this deficiency by introducing four approaches of developing informative priors for the independent variables based on historical data and expert experience. Merits of these informative priors have been tested along with two types of Bayesian hierarchical models (Poisson-gamma and Poisson-lognormal models). Deviance information criterion (DIC), R-square values, and coefficients of variance for the estimations were utilized as evaluation measures to select the best model(s). Comparison across the models indicated that the Poisson-gamma model is superior with a better model fit and it is much more robust with the informative priors. Moreover, the two-stage Bayesian updating informative priors provided the best goodness-of-fit and coefficient estimation accuracies. Furthermore, informative priors for the inverse dispersion parameter have also been introduced and tested. Different types of informative priors' effects on the model estimations and goodness-of-fit have been compared and concluded. Finally, based on the results, recommendations for future research topics and study applications have been made. Copyright © 2013 Elsevier Ltd. All rights reserved.

Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murakami, Haruko; Chen, X.; Hahn, Melanie S.

2010-10-21

This study presents a stochastic, three-dimensional characterization of a heterogeneous hydraulic conductivity field within DOE's Hanford 300 Area site, Washington, by assimilating large-scale, constant-rate injection test data with small-scale, three-dimensional electromagnetic borehole flowmeter (EBF) measurement data. We first inverted the injection test data to estimate the transmissivity field, using zeroth-order temporal moments of pressure buildup curves. We applied a newly developed Bayesian geostatistical inversion framework, the method of anchored distributions (MAD), to obtain a joint posterior distribution of geostatistical parameters and local log-transmissivities at multiple locations. The unique aspects of MAD that make it suitable for this purpose are itsmore » ability to integrate multi-scale, multi-type data within a Bayesian framework and to compute a nonparametric posterior distribution. After we combined the distribution of transmissivities with depth-discrete relative-conductivity profile from EBF data, we inferred the three-dimensional geostatistical parameters of the log-conductivity field, using the Bayesian model-based geostatistics. Such consistent use of the Bayesian approach throughout the procedure enabled us to systematically incorporate data uncertainty into the final posterior distribution. The method was tested in a synthetic study and validated using the actual data that was not part of the estimation. Results showed broader and skewed posterior distributions of geostatistical parameters except for the mean, which suggests the importance of inferring the entire distribution to quantify the parameter uncertainty.« less

Inverse modeling of the Chernobyl source term using atmospheric concentration and deposition measurements

NASA Astrophysics Data System (ADS)

Evangeliou, Nikolaos; Hamburger, Thomas; Cozic, Anne; Balkanski, Yves; Stohl, Andreas

2017-07-01

This paper describes the results of an inverse modeling study for the determination of the source term of the radionuclides 134Cs, 137Cs and 131I released after the Chernobyl accident. The accident occurred on 26 April 1986 in the Former Soviet Union and released about 1019 Bq of radioactive materials that were transported as far away as the USA and Japan. Thereafter, several attempts to assess the magnitude of the emissions were made that were based on the knowledge of the core inventory and the levels of the spent fuel. More recently, when modeling tools were further developed, inverse modeling techniques were applied to the Chernobyl case for source term quantification. However, because radioactivity is a sensitive topic for the public and attracts a lot of attention, high-quality measurements, which are essential for inverse modeling, were not made available except for a few sparse activity concentration measurements far from the source and far from the main direction of the radioactive fallout. For the first time, we apply Bayesian inversion of the Chernobyl source term using not only activity concentrations but also deposition measurements from the most recent public data set. These observations refer to a data rescue attempt that started more than 10 years ago, with a final goal to provide available measurements to anyone interested. In regards to our inverse modeling results, emissions of 134Cs were estimated to be 80 PBq or 30-50 % higher than what was previously published. From the released amount of 134Cs, about 70 PBq were deposited all over Europe. Similar to 134Cs, emissions of 137Cs were estimated as 86 PBq, on the same order as previously reported results. Finally, 131I emissions of 1365 PBq were found, which are about 10 % less than the prior total releases. The inversion pushes the injection heights of the three radionuclides to higher altitudes (up to about 3 km) than previously assumed (≈ 2.2 km) in order to better match both concentration and deposition observations over Europe. The results of the present inversion were confirmed using an independent Eulerian model, for which deposition patterns were also improved when using the estimated posterior releases. Although the independent model tends to underestimate deposition in countries that are not in the main direction of the plume, it reproduces country levels of deposition very efficiently. The results were also tested for robustness against different setups of the inversion through sensitivity runs. The source term data from this study are publicly available.

A New Paradigm for Satellite Retrieval of Hydrologic Variables: The CDRD Methodology

NASA Astrophysics Data System (ADS)

Smith, E. A.; Mugnai, A.; Tripoli, G. J.

2009-09-01

Historically, retrieval of thermodynamically active geophysical variables in the atmosphere (e.g., temperature, moisture, precipitation) involved some time of inversion scheme - embedded within the retrieval algorithm - to transform radiometric observations (a vector) to the desired geophysical parameter(s) (either a scalar or a vector). Inversion is fundamentally a mathematical operation involving some type of integral-differential radiative transfer equation - often resisting a straightforward algebraic solution - in which the integral side of the equation (typically the right-hand side) contains the desired geophysical vector, while the left-hand side contains the radiative measurement vector often free of operators. Inversion was considered more desirable than forward modeling because the forward model solution had to be selected from a generally unmanageable set of parameter-observation relationships. However, in the classical inversion problem for retrieval of temperature using multiple radiative frequencies along the wing of an absorption band (or line) of a well-mixed radiatively active gas, in either the infrared or microwave spectrums, the inversion equation to be solved consists of a Fredholm integral equation of the 2nd kind - a specific type of transform problem in which there are an infinite number of solutions. This meant that special treatment of the transform process was required in order to obtain a single solution. Inversion had become the method of choice for retrieval in the 1950s because it appealed to the use of mathematical elegance, and because the numerical approaches used to solve the problems (typically some type of relaxation or perturbation scheme) were computationally fast in an age when computers speeds were slow. Like many solution schemes, inversion has lingered on regardless of the fact that computer speeds have increased many orders of magnitude and forward modeling itself has become far more elegant in combination with Bayesian averaging procedures given that the a priori probabilities of occurrence in the true environment of the parameter(s) in question can be approximated (or are actually known). In this presentation, the theory of the more modern retrieval approach using a combination of cloud, radiation and other specialized forward models in conjunction with Bayesian weighted averaging will be reviewed in light of a brief history of inversion. The application of the theory will be cast in the framework of what we call the Cloud-Dynamics-Radiation-Database (CDRD) methodology - which we now use for the retrieval of precipitation from spaceborne passive microwave radiometers. In a companion presentation, we will specifically describe the CDRD methodology and present results for its application within the Mediterranean basin.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wainwright, Haruko M.; Flores Orozco, Adrian; Bucker, Matthias

In floodplain environments, a naturally reduced zone (NRZ) is considered to be a common biogeochemical hot spot, having distinct microbial and geochemical characteristics. Although important for understanding their role in mediating floodplain biogeochemical processes, mapping the subsurface distribution of NRZs over the dimensions of a floodplain is challenging, as conventional wellbore data are typically spatially limited and the distribution of NRZs is heterogeneous. In this work, we present an innovative methodology for the probabilistic mapping of NRZs within a three-dimensional (3-D) subsurface domain using induced polarization imaging, which is a noninvasive geophysical technique. Measurements consist of surface geophysical surveys andmore » drilling-recovered sediments at the U.S. Department of Energy field site near Rifle, CO (USA). Inversion of surface time domain-induced polarization (TDIP) data yielded 3-D images of the complex electrical resistivity, in terms of magnitude and phase, which are associated with mineral precipitation and other lithological properties. By extracting the TDIP data values colocated with wellbore lithological logs, we found that the NRZs have a different distribution of resistivity and polarization from the other aquifer sediments. To estimate the spatial distribution of NRZs, we developed a Bayesian hierarchical model to integrate the geophysical and wellbore data. In addition, the resistivity images were used to estimate hydrostratigraphic interfaces under the floodplain. Validation results showed that the integration of electrical imaging and wellbore data using a Bayesian hierarchical model was capable of mapping spatially heterogeneous interfaces and NRZ distributions thereby providing a minimally invasive means to parameterize a hydrobiogeochemical model of the floodplain.« less

Inversion of particle-size distribution from angular light-scattering data with genetic algorithms.

PubMed

Ye, M; Wang, S; Lu, Y; Hu, T; Zhu, Z; Xu, Y

1999-04-20

A stochastic inverse technique based on a genetic algorithm (GA) to invert particle-size distribution from angular light-scattering data is developed. This inverse technique is independent of any given a priori information of particle-size distribution. Numerical tests show that this technique can be successfully applied to inverse problems with high stability in the presence of random noise and low susceptibility to the shape of distributions. It has also been shown that the GA-based inverse technique is more efficient in use of computing time than the inverse Monte Carlo method recently developed by Ligon et al. [Appl. Opt. 35, 4297 (1996)].

Accelerated Bayesian model-selection and parameter-estimation in continuous gravitational-wave searches with pulsar-timing arrays

NASA Astrophysics Data System (ADS)

Taylor, Stephen; Ellis, Justin; Gair, Jonathan

2014-11-01

We describe several new techniques which accelerate Bayesian searches for continuous gravitational-wave emission from supermassive black-hole binaries using pulsar-timing arrays. These techniques mitigate the problematic increase of search dimensionality with the size of the pulsar array which arises from having to include an extra parameter per pulsar as the array is expanded. This extra parameter corresponds to searching over the phase of the gravitational wave as it propagates past each pulsar so that we can coherently include the pulsar term in our search strategies. Our techniques make the analysis tractable with powerful evidence-evaluation packages like MultiNest. We find good agreement of our techniques with the parameter-estimation and Bayes factor evaluation performed with full signal templates and conclude that these techniques make excellent first-cut tools for detection and characterization of continuous gravitational-wave signals with pulsar-timing arrays. Crucially, at low to moderate signal-to-noise ratios the factor by which the analysis is sped up can be ≳100 , permitting rigorous programs of systematic injection and recovery of signals to establish robust detection criteria within a Bayesian formalism.

Improving photoelectron counting and particle identification in scintillation detectors with Bayesian techniques

NASA Astrophysics Data System (ADS)

Akashi-Ronquest, M.; Amaudruz, P.-A.; Batygov, M.; Beltran, B.; Bodmer, M.; Boulay, M. G.; Broerman, B.; Buck, B.; Butcher, A.; Cai, B.; Caldwell, T.; Chen, M.; Chen, Y.; Cleveland, B.; Coakley, K.; Dering, K.; Duncan, F. A.; Formaggio, J. A.; Gagnon, R.; Gastler, D.; Giuliani, F.; Gold, M.; Golovko, V. V.; Gorel, P.; Graham, K.; Grace, E.; Guerrero, N.; Guiseppe, V.; Hallin, A. L.; Harvey, P.; Hearns, C.; Henning, R.; Hime, A.; Hofgartner, J.; Jaditz, S.; Jillings, C. J.; Kachulis, C.; Kearns, E.; Kelsey, J.; Klein, J. R.; Kuźniak, M.; LaTorre, A.; Lawson, I.; Li, O.; Lidgard, J. J.; Liimatainen, P.; Linden, S.; McFarlane, K.; McKinsey, D. N.; MacMullin, S.; Mastbaum, A.; Mathew, R.; McDonald, A. B.; Mei, D.-M.; Monroe, J.; Muir, A.; Nantais, C.; Nicolics, K.; Nikkel, J. A.; Noble, T.; O'Dwyer, E.; Olsen, K.; Orebi Gann, G. D.; Ouellet, C.; Palladino, K.; Pasuthip, P.; Perumpilly, G.; Pollmann, T.; Rau, P.; Retière, F.; Rielage, K.; Schnee, R.; Seibert, S.; Skensved, P.; Sonley, T.; Vázquez-Jáuregui, E.; Veloce, L.; Walding, J.; Wang, B.; Wang, J.; Ward, M.; Zhang, C.

2015-05-01

Many current and future dark matter and neutrino detectors are designed to measure scintillation light with a large array of photomultiplier tubes (PMTs). The energy resolution and particle identification capabilities of these detectors depend in part on the ability to accurately identify individual photoelectrons in PMT waveforms despite large variability in pulse amplitudes and pulse pileup. We describe a Bayesian technique that can identify the times of individual photoelectrons in a sampled PMT waveform without deconvolution, even when pileup is present. To demonstrate the technique, we apply it to the general problem of particle identification in single-phase liquid argon dark matter detectors. Using the output of the Bayesian photoelectron counting algorithm described in this paper, we construct several test statistics for rejection of backgrounds for dark matter searches in argon. Compared to simpler methods based on either observed charge or peak finding, the photoelectron counting technique improves both energy resolution and particle identification of low energy events in calibration data from the DEAP-1 detector and simulation of the larger MiniCLEAN dark matter detector.

Spectral line inversion for sounding of stratospheric minor constituents by infrared heterodyne technique from balloon altitudes

NASA Technical Reports Server (NTRS)

Abbas, M. M.; Shapiro, G. L.; Allario, F.; Alvarez, J. M.

1981-01-01

A combination of two different techniques for the inversion of infrared laser heterodyne measurements of tenuous gases in the stratosphere by solar occulation is presented which incorporates the advantages of each technique. An experimental approach and inversion technique are developed which optimize the retrieval of concentration profiles by incorporating the onion peel collection scheme into the spectral inversion technique. A description of an infrared heterodyne spectrometer and the mode of observations for solar occulation measurement is presented, and the results of inversions of some synthetic ClO spectral lines corresponding to solar occulation limb-scans of the stratosphere are examined. A comparison between the new techniques and one of the current techniques indicates that considerable improvement in the accuracy of the retrieved profiles can be achieved. It is found that noise affects the accuracy of both techniques but not in a straightforward manner since there is interaction between the noise level, noise propagation through inversion, and the number of scans leading to an optimum retrieval.

Advances in computer simulation of genome evolution: toward more realistic evolutionary genomics analysis by approximate bayesian computation.

PubMed

Arenas, Miguel

2015-04-01

NGS technologies present a fast and cheap generation of genomic data. Nevertheless, ancestral genome inference is not so straightforward due to complex evolutionary processes acting on this material such as inversions, translocations, and other genome rearrangements that, in addition to their implicit complexity, can co-occur and confound ancestral inferences. Recently, models of genome evolution that accommodate such complex genomic events are emerging. This letter explores these novel evolutionary models and proposes their incorporation into robust statistical approaches based on computer simulations, such as approximate Bayesian computation, that may produce a more realistic evolutionary analysis of genomic data. Advantages and pitfalls in using these analytical methods are discussed. Potential applications of these ancestral genomic inferences are also pointed out.

A semiparametric Bayesian proportional hazards model for interval censored data with frailty effects.

PubMed

Henschel, Volkmar; Engel, Jutta; Hölzel, Dieter; Mansmann, Ulrich

2009-02-10

Multivariate analysis of interval censored event data based on classical likelihood methods is notoriously cumbersome. Likelihood inference for models which additionally include random effects are not available at all. Developed algorithms bear problems for practical users like: matrix inversion, slow convergence, no assessment of statistical uncertainty. MCMC procedures combined with imputation are used to implement hierarchical models for interval censored data within a Bayesian framework. Two examples from clinical practice demonstrate the handling of clustered interval censored event times as well as multilayer random effects for inter-institutional quality assessment. The software developed is called survBayes and is freely available at CRAN. The proposed software supports the solution of complex analyses in many fields of clinical epidemiology as well as health services research.

Classification of Active Microwave and Passive Optical Data Based on Bayesian Theory and Mrf

NASA Astrophysics Data System (ADS)

Yu, F.; Li, H. T.; Han, Y. S.; Gu, H. Y.

2012-08-01

A classifier based on Bayesian theory and Markov random field (MRF) is presented to classify the active microwave and passive optical remote sensing data, which have demonstrated their respective advantages in inversion of surface soil moisture content. In the method, the VV, VH polarization of ASAR and all the 7 TM bands are taken as the input of the classifier to get the class labels of each pixel of the images. And the model is validated for the necessities of integration of TM and ASAR, it shows that, the total precision of classification in this paper is 89.4%. Comparing with the classification with single TM, the accuracy increase 11.5%, illustrating that synthesis of active and passive optical remote sensing data is efficient and potential in classification.

Bayesian Abel Inversion in Quantitative X-Ray Radiography

DOE PAGES

Howard, Marylesa; Fowler, Michael; Luttman, Aaron; ...

2016-05-19

A common image formation process in high-energy X-ray radiography is to have a pulsed power source that emits X-rays through a scene, a scintillator that absorbs X-rays and uoresces in the visible spectrum in response to the absorbed photons, and a CCD camera that images the visible light emitted from the scintillator. The intensity image is related to areal density, and, for an object that is radially symmetric about a central axis, the Abel transform then gives the object's volumetric density. Two of the primary drawbacks to classical variational methods for Abel inversion are their sensitivity to the type andmore » scale of regularization chosen and the lack of natural methods for quantifying the uncertainties associated with the reconstructions. In this work we cast the Abel inversion problem within a statistical framework in order to compute volumetric object densities from X-ray radiographs and to quantify uncertainties in the reconstruction. A hierarchical Bayesian model is developed with a likelihood based on a Gaussian noise model and with priors placed on the unknown density pro le, the data precision matrix, and two scale parameters. This allows the data to drive the localization of features in the reconstruction and results in a joint posterior distribution for the unknown density pro le, the prior parameters, and the spatial structure of the precision matrix. Results of the density reconstructions and pointwise uncertainty estimates are presented for both synthetic signals and real data from a U.S. Department of Energy X-ray imaging facility.« less

Action understanding as inverse planning.

PubMed

Baker, Chris L; Saxe, Rebecca; Tenenbaum, Joshua B

2009-12-01

Humans are adept at inferring the mental states underlying other agents' actions, such as goals, beliefs, desires, emotions and other thoughts. We propose a computational framework based on Bayesian inverse planning for modeling human action understanding. The framework represents an intuitive theory of intentional agents' behavior based on the principle of rationality: the expectation that agents will plan approximately rationally to achieve their goals, given their beliefs about the world. The mental states that caused an agent's behavior are inferred by inverting this model of rational planning using Bayesian inference, integrating the likelihood of the observed actions with the prior over mental states. This approach formalizes in precise probabilistic terms the essence of previous qualitative approaches to action understanding based on an "intentional stance" [Dennett, D. C. (1987). The intentional stance. Cambridge, MA: MIT Press] or a "teleological stance" [Gergely, G., Nádasdy, Z., Csibra, G., & Biró, S. (1995). Taking the intentional stance at 12 months of age. Cognition, 56, 165-193]. In three psychophysical experiments using animated stimuli of agents moving in simple mazes, we assess how well different inverse planning models based on different goal priors can predict human goal inferences. The results provide quantitative evidence for an approximately rational inference mechanism in human goal inference within our simplified stimulus paradigm, and for the flexible nature of goal representations that human observers can adopt. We discuss the implications of our experimental results for human action understanding in real-world contexts, and suggest how our framework might be extended to capture other kinds of mental state inferences, such as inferences about beliefs, or inferring whether an entity is an intentional agent.

A bayesian approach for determining velocity and uncertainty estimates from seismic cone penetrometer testing or vertical seismic profiling data

USGS Publications Warehouse

Pidlisecky, Adam; Haines, S.S.

2011-01-01

Conventional processing methods for seismic cone penetrometer data present several shortcomings, most notably the absence of a robust velocity model uncertainty estimate. We propose a new seismic cone penetrometer testing (SCPT) data-processing approach that employs Bayesian methods to map measured data errors into quantitative estimates of model uncertainty. We first calculate travel-time differences for all permutations of seismic trace pairs. That is, we cross-correlate each trace at each measurement location with every trace at every other measurement location to determine travel-time differences that are not biased by the choice of any particular reference trace and to thoroughly characterize data error. We calculate a forward operator that accounts for the different ray paths for each measurement location, including refraction at layer boundaries. We then use a Bayesian inversion scheme to obtain the most likely slowness (the reciprocal of velocity) and a distribution of probable slowness values for each model layer. The result is a velocity model that is based on correct ray paths, with uncertainty bounds that are based on the data error. ?? NRC Research Press 2011.

Earth Core and Inner Core: What Can We Learn From a Bayesian Inversion of Combined Nutation and Surface Gravimetry Data?

NASA Astrophysics Data System (ADS)

Lambert, S. B.; Ziegler, Y.; Rosat, S.; Bizouard, C.

2017-12-01

Nutation time series derived from very long baseline interferometry (VLBI) and time varying surface gravity data recorded by superconducting gravimeters (SG) have long been used separately to assess the Earth's interior via the estimation of the free core and inner core resonance effects on nutation or tidal gravity. The results obtained from these two techniques have shown recently to be consistent, making relevant the combination of VLBI and SG observables and the estimation of Earth's interior parameters in a single inversion. We present here the results of combining nutation and surface gravity time series to improve estimates of the Earth's core and inner core resonant frequencies. We use VLBI nutation time series spanning 1984-2016 derived by several analysis centers affiliated to the International VLBI Service for Geodesy and Astrometry, together with surface gravity data from about 15 SG stations. We address the resonance model used for describing the Earth's interior response to tidal excitation, the data preparation consisting of the error recalibration and amplitude fitting to nutation data, and processing of SG time-varying gravity to remove any gaps, spikes, steps and other disturbances, followed by the tidal analysis with the ETERNA 3.4 software package. New estimates of the resonant periods are proposed and correlations between the parameters are investigated.

Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pablant, N. A.; Bell, R. E.; Bitter, M.

2014-11-15

Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at the Large Helical Device. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy andmore » tomographic inversion, XICS can provide profile measurements of the local emissivity, temperature, and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modified Levenberg-Marquardt optimization scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example, geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.« less

Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaksa)

DOE PAGES

Pablant, N. A.; Bell, R. E.; Bitter, M.; ...

2014-08-08

Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at LHD. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy and tomographic inversion, XICSmore » can provide pro file measurements of the local emissivity, temperature and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modifi ed Levenberg-Marquardt optimization scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.« less

Period-dependent source rupture behavior of the 2011 Tohoku earthquake estimated by multi period-band Bayesian waveform inversion

NASA Astrophysics Data System (ADS)

Kubo, H.; Asano, K.; Iwata, T.; Aoi, S.

2014-12-01

Previous studies for the period-dependent source characteristics of the 2011 Tohoku earthquake (e.g., Koper et al., 2011; Lay et al., 2012) were based on the short and long period source models using different method. Kubo et al. (2013) obtained source models of the 2011 Tohoku earthquake using multi period-bands waveform data by a common inversion method and discussed its period-dependent source characteristics. In this study, to achieve more in detail spatiotemporal source rupture behavior of this event, we introduce a new fault surface model having finer sub-fault size and estimate the source models in multi period-bands using a Bayesian inversion method combined with a multi-time-window method. Three components of velocity waveforms at 25 stations of K-NET, KiK-net, and F-net of NIED are used in this analysis. The target period band is 10-100 s. We divide this period band into three period bands (10-25 s, 25-50 s, and 50-100 s) and estimate a kinematic source model in each period band using a Bayesian inversion method with MCMC sampling (e.g., Fukuda & Johnson, 2008; Minson et al., 2013, 2014). The parameterization of spatiotemporal slip distribution follows the multi-time-window method (Hartzell & Heaton, 1983). The Green's functions are calculated by the 3D FDM (GMS; Aoi & Fujiwara, 1999) using a 3D velocity structure model (JIVSM; Koketsu et al., 2012). The assumed fault surface model is based on the Pacific plate boundary of JIVSM and is divided into 384 subfaults of about 16 * 16 km^2. The estimated source models in multi period-bands show the following source image: (1) First deep rupture off Miyagi at 0-60 s toward down-dip mostly radiating relatively short period (10-25 s) seismic waves. (2) Shallow rupture off Miyagi at 45-90 s toward up-dip with long duration radiating long period (50-100 s) seismic wave. (3) Second deep rupture off Miyagi at 60-105 s toward down-dip radiating longer period seismic waves then that of the first deep rupture. (4) Deep rupture off Fukushima at 90-135 s. The dominant-period difference of the seismic-wave radiation between two deep ruptures off Miyagi may result from the mechanism that small-scale heterogeneities on the fault are removed by the first rupture. This difference can be also interpreted by the concept of multi-scale dynamic rupture (Ide & Aochi, 2005).

Top-down estimate of methane emissions in California using a mesoscale inverse modeling technique: The South Coast Air Basin

DOE PAGES

Cui, Yu Yan; Brioude, Jerome; McKeen, Stuart A.; ...

2015-07-28

Methane (CH 4) is the primary component of natural gas and has a larger global warming potential than CO 2. Some recent top-down studies based on observations showed CH 4 emissions in California's South Coast Air Basin (SoCAB) were greater than those expected from population-apportioned bottom-up state inventories. In this study, we quantify CH 4 emissions with an advanced mesoscale inverse modeling system at a resolution of 8 km × 8 km, using aircraft measurements in the SoCAB during the 2010 Nexus of Air Quality and Climate Change campaign to constrain the inversion. To simulate atmospheric transport, we use themore » FLEXible PARTicle-Weather Research and Forecasting (FLEXPART-WRF) Lagrangian particle dispersion model driven by three configurations of the Weather Research and Forecasting (WRF) mesoscale model. We determine surface fluxes of CH 4 using a Bayesian least squares method in a four-dimensional inversion. Simulated CH4 concentrations with the posterior emission inventory achieve much better correlations with the measurements (R2 = 0.7) than using the prior inventory (U.S. Environmental Protection Agency's National Emission Inventory 2005, R 2 = 0.5). The emission estimates for CH 4 in the posterior, 46.3 ± 9.2 Mg CH 4/h, are consistent with published observation-based estimates. Changes in the spatial distribution of CH 4 emissions in the SoCAB between the prior and posterior inventories are discussed. Missing or underestimated emissions from dairies, the oil/gas system, and landfills in the SoCAB seem to explain the differences between the prior and posterior inventories. Furthermore, we estimate that dairies contributed 5.9 ± 1.7 Mg CH 4/h and the two sectors of oil and gas industries (production and downstream) and landfills together contributed 39.6 ± 8.1 Mg CH 4/h in the SoCAB.« less

Real-time characterization of partially observed epidemics using surrogate models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Safta, Cosmin; Ray, Jaideep; Lefantzi, Sophia

We present a statistical method, predicated on the use of surrogate models, for the 'real-time' characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiologicalmore » parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also find that the number of projections required to construct a surrogate model is O(10)-O(10{sup 2}) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as observations from the 1918 influenza pandemic collected at Camp Custer, Michigan.« less

Accessing the uncertainties of seismic velocity and anisotropy structure of Northern Great Plains using a transdimensional Bayesian approach

NASA Astrophysics Data System (ADS)

Gao, C.; Lekic, V.

2017-12-01

Seismic imaging utilizing complementary seismic data provides unique insight on the formation, evolution and current structure of continental lithosphere. While numerous efforts have improved the resolution of seismic structure, the quantification of uncertainties remains challenging due to the non-linearity and the non-uniqueness of geophysical inverse problem. In this project, we use a reverse jump Markov chain Monte Carlo (rjMcMC) algorithm to incorporate seismic observables including Rayleigh and Love wave dispersion, Ps and Sp receiver function to invert for shear velocity (Vs), compressional velocity (Vp), density, and radial anisotropy of the lithospheric structure. The Bayesian nature and the transdimensionality of this approach allow the quantification of the model parameter uncertainties while keeping the models parsimonious. Both synthetic test and inversion of actual data for Ps and Sp receiver functions are performed. We quantify the information gained in different inversions by calculating the Kullback-Leibler divergence. Furthermore, we explore the ability of Rayleigh and Love wave dispersion data to constrain radial anisotropy. We show that when multiple types of model parameters (Vsv, Vsh, and Vp) are inverted simultaneously, the constraints on radial anisotropy are limited by relatively large data uncertainties and trade-off strongly with Vp. We then perform joint inversion of the surface wave dispersion (SWD) and Ps, Sp receiver functions, and show that the constraints on both isotropic Vs and radial anisotropy are significantly improved. To achieve faster convergence of the rjMcMC, we propose a progressive inclusion scheme, and invert SWD measurements and receiver functions from about 400 USArray stations in the Northern Great Plains. We start by only using SWD data due to its fast convergence rate. We then use the average of the ensemble as a starting model for the joint inversion, which is able to resolve distinct seismic signatures of geological structures including the trans-Hudson orogen, Wyoming craton and Yellowstone hotspot. Various analyses are done to access the uncertainties of the seismic velocities and Moho depths. We also address the importance of careful data processing of receiver functions by illustrating artifacts due to unmodelled sediment reverberations.

Bayesian Integrated Microbial Forensics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jarman, Kristin H.; Kreuzer-Martin, Helen W.; Wunschel, David S.

2008-06-01

In the aftermath of the 2001 anthrax letters, researchers have been exploring ways to predict the production environment of unknown source microorganisms. Different mass spectral techniques are being developed to characterize components of a microbe’s culture medium including water, carbon and nitrogen sources, metal ions added, and the presence of agar. Individually, each technique has the potential to identify one or two ingredients in a culture medium recipe. However, by integrating data from multiple mass spectral techniques, a more complete characterization is possible. We present a Bayesian statistical approach to integrated microbial forensics and illustrate its application on spores grownmore » in different culture media.« less

As-built design specification for proportion estimate software subsystem

NASA Technical Reports Server (NTRS)

Obrien, S. (Principal Investigator)

1980-01-01

The Proportion Estimate Processor evaluates four estimation techniques in order to get an improved estimate of the proportion of a scene that is planted in a selected crop. The four techniques to be evaluated were provided by the techniques development section and are: (1) random sampling; (2) proportional allocation, relative count estimate; (3) proportional allocation, Bayesian estimate; and (4) sequential Bayesian allocation. The user is given two options for computation of the estimated mean square error. These are referred to as the cluster calculation option and the segment calculation option. The software for the Proportion Estimate Processor is operational on the IBM 3031 computer.

Inferring the most probable maps of underground utilities using Bayesian mapping model

NASA Astrophysics Data System (ADS)

Bilal, Muhammad; Khan, Wasiq; Muggleton, Jennifer; Rustighi, Emiliano; Jenks, Hugo; Pennock, Steve R.; Atkins, Phil R.; Cohn, Anthony

2018-03-01

Mapping the Underworld (MTU), a major initiative in the UK, is focused on addressing social, environmental and economic consequences raised from the inability to locate buried underground utilities (such as pipes and cables) by developing a multi-sensor mobile device. The aim of MTU device is to locate different types of buried assets in real time with the use of automated data processing techniques and statutory records. The statutory records, even though typically being inaccurate and incomplete, provide useful prior information on what is buried under the ground and where. However, the integration of information from multiple sensors (raw data) with these qualitative maps and their visualization is challenging and requires the implementation of robust machine learning/data fusion approaches. An approach for automated creation of revised maps was developed as a Bayesian Mapping model in this paper by integrating the knowledge extracted from sensors raw data and available statutory records. The combination of statutory records with the hypotheses from sensors was for initial estimation of what might be found underground and roughly where. The maps were (re)constructed using automated image segmentation techniques for hypotheses extraction and Bayesian classification techniques for segment-manhole connections. The model consisting of image segmentation algorithm and various Bayesian classification techniques (segment recognition and expectation maximization (EM) algorithm) provided robust performance on various simulated as well as real sites in terms of predicting linear/non-linear segments and constructing refined 2D/3D maps.

How to Detect the Location and Time of a Covert Chemical Attack: A Bayesian Approach

DTIC Science & Technology

2009-12-01

Inverse Problems, Design and Optimization Symposium 2004. Rio de Janeiro , Brazil. Chan, R., and Yee, E. (1997). A simple model for the probability...sensor interpretation applications and has been successfully applied, for example, to estimate the source strength of pollutant releases in multi...coagulation, and second-order pollutant diffusion in sorption- desorption, are not linear. Furthermore, wide uncertainty bounds exist for several of

An adaptive Bayesian inversion for upper-mantle structure using surface waves and scattered body waves

NASA Astrophysics Data System (ADS)

Eilon, Zachary; Fischer, Karen M.; Dalton, Colleen A.

2018-07-01

We present a methodology for 1-D imaging of upper-mantle structure using a Bayesian approach that incorporates a novel combination of seismic data types and an adaptive parametrization based on piecewise discontinuous splines. Our inversion algorithm lays the groundwork for improved seismic velocity models of the lithosphere and asthenosphere by harnessing the recent expansion of large seismic arrays and computational power alongside sophisticated data analysis. Careful processing of P- and S-wave arrivals isolates converted phases generated at velocity gradients between the mid-crust and 300 km depth. This data is allied with ambient noise and earthquake Rayleigh wave phase velocities to obtain detailed VS and VP velocity models. Synthetic tests demonstrate that converted phases are necessary to accurately constrain velocity gradients, and S-p phases are particularly important for resolving mantle structure, while surface waves are necessary for capturing absolute velocities. We apply the method to several stations in the northwest and north-central United States, finding that the imaged structure improves upon existing models by sharpening the vertical resolution of absolute velocity profiles, offering robust uncertainty estimates, and revealing mid-lithospheric velocity gradients indicative of thermochemical cratonic layering. This flexible method holds promise for increasingly detailed understanding of the upper mantle.

Recent global methane trends: an investigation using hierarchical Bayesian methods

NASA Astrophysics Data System (ADS)

Rigby, M. L.; Stavert, A.; Ganesan, A.; Lunt, M. F.

2014-12-01

Following a decade with little growth, methane concentrations began to increase across the globe in 2007, and have continued to rise ever since. The reasons for this renewed growth are currently the subject of much debate. Here, we discuss the recent observed trends, and highlight some of the strengths and weaknesses in current "inverse" methods for quantifying fluxes using observations. In particular, we focus on the outstanding problems of accurately quantifying uncertainties in inverse frameworks. We examine to what extent the recent methane changes can be explained by the current generation of flux models and inventories. We examine the major modes of variability in wetland models along with the Global Fire Emissions Database (GFED) and the Emissions Database for Global Atmospheric Research (EDGAR). Using the Model for Ozone and Related Tracers (MOZART), we determine whether the spatial and temporal atmospheric trends predicted using these emissions can be brought into consistency with in situ atmospheric observations. We use a novel hierarchical Bayesian methodology in which scaling factors applied to the principal components of the flux fields are estimated simultaneously with the uncertainties associated with the a priori fluxes and with model representations of the observations. Using this method, we examine the predictive power of methane flux models for explaining recent fluctuations.

Bayesian multiple-source localization in an uncertain ocean environment.

PubMed

Dosso, Stan E; Wilmut, Michael J

2011-06-01

This paper considers simultaneous localization of multiple acoustic sources when properties of the ocean environment (water column and seabed) are poorly known. A Bayesian formulation is developed in which the environmental parameters, noise statistics, and locations and complex strengths (amplitudes and phases) of multiple sources are considered to be unknown random variables constrained by acoustic data and prior information. Two approaches are considered for estimating source parameters. Focalization maximizes the posterior probability density (PPD) over all parameters using adaptive hybrid optimization. Marginalization integrates the PPD using efficient Markov-chain Monte Carlo methods to produce joint marginal probability distributions for source ranges and depths, from which source locations are obtained. This approach also provides quantitative uncertainty analysis for all parameters, which can aid in understanding of the inverse problem and may be of practical interest (e.g., source-strength probability distributions). In both approaches, closed-form maximum-likelihood expressions for source strengths and noise variance at each frequency allow these parameters to be sampled implicitly, substantially reducing the dimensionality and difficulty of the inversion. Examples are presented of both approaches applied to single- and multi-frequency localization of multiple sources in an uncertain shallow-water environment, and a Monte Carlo performance evaluation study is carried out. © 2011 Acoustical Society of America

Transdimensional inversion of scattered body waves for 1D S-wave velocity structure - Application to the Tengchong volcanic area, Southwestern China

NASA Astrophysics Data System (ADS)

Li, Mengkui; Zhang, Shuangxi; Bodin, Thomas; Lin, Xu; Wu, Tengfei

2018-06-01

Inversion of receiver functions is commonly used to recover the S-wave velocity structure beneath seismic stations. Traditional approaches are based on deconvolved waveforms, where the horizontal component of P-wave seismograms is deconvolved by the vertical component. Deconvolution of noisy seismograms is a numerically unstable process that needs to be stabilized by regularization parameters. This biases noise statistics, making it difficult to estimate uncertainties in observed receiver functions for Bayesian inference. This study proposes a method to directly invert observed radial waveforms and to better account for data noise in a Bayesian formulation. We illustrate its feasibility with two synthetic tests having different types of noises added to seismograms. Then, a real site application is performed to obtain the 1-D S-wave velocity structure beneath a seismic station located in the Tengchong volcanic area, Southwestern China. Surface wave dispersion measurements spanning periods from 8 to 65 s are jointly inverted with P waveforms. The results show a complex S-wave velocity structure, as two low velocity zones are observed in the crust and uppermost mantle, suggesting the existence of magma chambers, or zones of partial melt. The upper magma chambers may be the heart source that cause the thermal activity on the surface.

An adaptive Bayesian inversion for upper mantle structure using surface waves and scattered body waves

NASA Astrophysics Data System (ADS)

Eilon, Zachary; Fischer, Karen M.; Dalton, Colleen A.

2018-04-01

We present a methodology for 1-D imaging of upper mantle structure using a Bayesian approach that incorporates a novel combination of seismic data types and an adaptive parameterisation based on piecewise discontinuous splines. Our inversion algorithm lays the groundwork for improved seismic velocity models of the lithosphere and asthenosphere by harnessing the recent expansion of large seismic arrays and computational power alongside sophisticated data analysis. Careful processing of P- and S-wave arrivals isolates converted phases generated at velocity gradients between the mid-crust and 300 km depth. This data is allied with ambient noise and earthquake Rayleigh wave phase velocities to obtain detailed VS and VP velocity models. Synthetic tests demonstrate that converted phases are necessary to accurately constrain velocity gradients, and S-p phases are particularly important for resolving mantle structure, while surface waves are necessary for capturing absolute velocities. We apply the method to several stations in the northwest and north-central United States, finding that the imaged structure improves upon existing models by sharpening the vertical resolution of absolute velocity profiles, offering robust uncertainty estimates, and revealing mid-lithospheric velocity gradients indicative of thermochemical cratonic layering. This flexible method holds promise for increasingly detailed understanding of the upper mantle.

Detection of Natural Fractures from Observed Surface Seismic Data Based on a Linear-Slip Model

NASA Astrophysics Data System (ADS)

Chen, Huaizhen; Zhang, Guangzhi

2018-03-01

Natural fractures play an important role in migration of hydrocarbon fluids. Based on a rock physics effective model, the linear-slip model, which defines fracture parameters (fracture compliances) for quantitatively characterizing the effects of fractures on rock total compliance, we propose a method to detect natural fractures from observed seismic data via inversion for the fracture compliances. We first derive an approximate PP-wave reflection coefficient in terms of fracture compliances. Using the approximate reflection coefficient, we derive azimuthal elastic impedance as a function of fracture compliances. An inversion method to estimate fracture compliances from seismic data is presented based on a Bayesian framework and azimuthal elastic impedance, which is implemented in a two-step procedure: a least-squares inversion for azimuthal elastic impedance and an iterative inversion for fracture compliances. We apply the inversion method to synthetic and real data to verify its stability and reasonability. Synthetic tests confirm that the method can make a stable estimation of fracture compliances in the case of seismic data containing a moderate signal-to-noise ratio for Gaussian noise, and the test on real data reveals that reasonable fracture compliances are obtained using the proposed method.

Fully probabilistic seismic source inversion - Part 2: Modelling errors and station covariances

NASA Astrophysics Data System (ADS)

Stähler, Simon C.; Sigloch, Karin

2016-11-01

Seismic source inversion, a central task in seismology, is concerned with the estimation of earthquake source parameters and their uncertainties. Estimating uncertainties is particularly challenging because source inversion is a non-linear problem. In a companion paper, Stähler and Sigloch (2014) developed a method of fully Bayesian inference for source parameters, based on measurements of waveform cross-correlation between broadband, teleseismic body-wave observations and their modelled counterparts. This approach yields not only depth and moment tensor estimates but also source time functions. A prerequisite for Bayesian inference is the proper characterisation of the noise afflicting the measurements, a problem we address here. We show that, for realistic broadband body-wave seismograms, the systematic error due to an incomplete physical model affects waveform misfits more strongly than random, ambient background noise. In this situation, the waveform cross-correlation coefficient CC, or rather its decorrelation D = 1 - CC, performs more robustly as a misfit criterion than ℓp norms, more commonly used as sample-by-sample measures of misfit based on distances between individual time samples. From a set of over 900 user-supervised, deterministic earthquake source solutions treated as a quality-controlled reference, we derive the noise distribution on signal decorrelation D = 1 - CC of the broadband seismogram fits between observed and modelled waveforms. The noise on D is found to approximately follow a log-normal distribution, a fortunate fact that readily accommodates the formulation of an empirical likelihood function for D for our multivariate problem. The first and second moments of this multivariate distribution are shown to depend mostly on the signal-to-noise ratio (SNR) of the CC measurements and on the back-azimuthal distances of seismic stations. By identifying and quantifying this likelihood function, we make D and thus waveform cross-correlation measurements usable for fully probabilistic sampling strategies, in source inversion and related applications such as seismic tomography.

Bayesian classification for the selection of in vitro human embryos using morphological and clinical data.

PubMed

Morales, Dinora Araceli; Bengoetxea, Endika; Larrañaga, Pedro; García, Miguel; Franco, Yosu; Fresnada, Mónica; Merino, Marisa

2008-05-01

In vitro fertilization (IVF) is a medically assisted reproduction technique that enables infertile couples to achieve successful pregnancy. Given the uncertainty of the treatment, we propose an intelligent decision support system based on supervised classification by Bayesian classifiers to aid to the selection of the most promising embryos that will form the batch to be transferred to the woman's uterus. The aim of the supervised classification system is to improve overall success rate of each IVF treatment in which a batch of embryos is transferred each time, where the success is achieved when implantation (i.e. pregnancy) is obtained. Due to ethical reasons, different legislative restrictions apply in every country on this technique. In Spain, legislation allows a maximum of three embryos to form each transfer batch. As a result, clinicians prefer to select the embryos by non-invasive embryo examination based on simple methods and observation focused on morphology and dynamics of embryo development after fertilization. This paper proposes the application of Bayesian classifiers to this embryo selection problem in order to provide a decision support system that allows a more accurate selection than with the actual procedures which fully rely on the expertise and experience of embryologists. For this, we propose to take into consideration a reduced subset of feature variables related to embryo morphology and clinical data of patients, and from this data to induce Bayesian classification models. Results obtained applying a filter technique to choose the subset of variables, and the performance of Bayesian classifiers using them, are presented.

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: methodology, model constraints and joint inversion with electrical resistivity data

NASA Astrophysics Data System (ADS)

Rosas-Carbajal, Marina; Linde, Niklas; Kalscheuer, Thomas; Vrugt, Jasper A.

2014-03-01

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

A mesostate-space model for EEG and MEG.

PubMed

Daunizeau, Jean; Friston, Karl J

2007-10-15

We present a multi-scale generative model for EEG, that entails a minimum number of assumptions about evoked brain responses, namely: (1) bioelectric activity is generated by a set of distributed sources, (2) the dynamics of these sources can be modelled as random fluctuations about a small number of mesostates, (3) mesostates evolve in a temporal structured way and are functionally connected (i.e. influence each other), and (4) the number of mesostates engaged by a cognitive task is small (e.g. between one and a few). A Variational Bayesian learning scheme is described that furnishes the posterior density on the models parameters and its evidence. Since the number of meso-sources specifies the model, the model evidence can be used to compare models and find the optimum number of meso-sources. In addition to estimating the dynamics at each cortical dipole, the mesostate-space model and its inversion provide a description of brain activity at the level of the mesostates (i.e. in terms of the dynamics of meso-sources that are distributed over dipoles). The inclusion of a mesostate level allows one to compute posterior probability maps of each dipole being active (i.e. belonging to an active mesostate). Critically, this model accommodates constraints on the number of meso-sources, while retaining the flexibility of distributed source models in explaining data. In short, it bridges the gap between standard distributed and equivalent current dipole models. Furthermore, because it is explicitly spatiotemporal, the model can embed any stochastic dynamical causal model (e.g. a neural mass model) as a Markov process prior on the mesostate dynamics. The approach is evaluated and compared to standard inverse EEG techniques, using synthetic data and real data. The results demonstrate the added-value of the mesostate-space model and its variational inversion.

Bayesian analyses of time-interval data for environmental radiation monitoring.

PubMed

Luo, Peng; Sharp, Julia L; DeVol, Timothy A

2013-01-01

Time-interval (time difference between two consecutive pulses) analysis based on the principles of Bayesian inference was investigated for online radiation monitoring. Using experimental and simulated data, Bayesian analysis of time-interval data [Bayesian (ti)] was compared with Bayesian and a conventional frequentist analysis of counts in a fixed count time [Bayesian (cnt) and single interval test (SIT), respectively]. The performances of the three methods were compared in terms of average run length (ARL) and detection probability for several simulated detection scenarios. Experimental data were acquired with a DGF-4C system in list mode. Simulated data were obtained using Monte Carlo techniques to obtain a random sampling of the Poisson distribution. All statistical algorithms were developed using the R Project for statistical computing. Bayesian analysis of time-interval information provided a similar detection probability as Bayesian analysis of count information, but the authors were able to make a decision with fewer pulses at relatively higher radiation levels. In addition, for the cases with very short presence of the source (< count time), time-interval information is more sensitive to detect a change than count information since the source data is averaged by the background data over the entire count time. The relationships of the source time, change points, and modifications to the Bayesian approach for increasing detection probability are presented.

Comparing inversion techniques for constraining CO2 fluxes in the Brazilian Amazon Basin with aircraft observations

NASA Astrophysics Data System (ADS)

Chow, V. Y.; Gerbig, C.; Longo, M.; Koch, F.; Nehrkorn, T.; Eluszkiewicz, J.; Ceballos, J. C.; Longo, K.; Wofsy, S. C.

2012-12-01

The Balanço Atmosférico Regional de Carbono na Amazônia (BARCA) aircraft program spanned the dry to wet and wet to dry transition seasons in November 2008 & May 2009 respectively. It resulted in ~150 vertical profiles covering the Brazilian Amazon Basin (BAB). With the data we attempt to estimate a carbon budget for the BAB, to determine if regional aircraft experiments can provide strong constraints for a budget, and to compare inversion frameworks when optimizing flux estimates. We use a LPDM to integrate satellite-, aircraft-, & surface-data with mesoscale meteorological fields to link bottom-up and top-down models to provide constraints and error bounds for regional fluxes. The Stochastic Time-Inverted Lagrangian Transport (STILT) model driven by meteorological fields from BRAMS, ECMWF, and WRF are coupled to a biosphere model, the Vegetation Photosynthesis Respiration Model (VPRM), to determine regional CO2 fluxes for the BAB. The VPRM is a prognostic biosphere model driven by MODIS 8-day EVI and LSWI indices along with shortwave radiation and temperature from tower measurements and mesoscale meteorological data. VPRM parameters are tuned using eddy flux tower data from the Large-Scale Biosphere Atmosphere experiment. VPRM computes hourly CO2 fluxes by calculating Gross Ecosystem Exchange (GEE) and Respiration (R) for 8 different vegetation types. The VPRM fluxes are scaled up to the BAB by using time-averaged drivers (shortwave radiation & temperature) from high-temporal resolution runs of BRAMS, ECMWF, and WRF and vegetation maps from SYNMAP and IGBP2007. Shortwave radiation from each mesoscale model is validated using surface data and output from GL 1.2, a global radiation model based on GOES 8 visible imagery. The vegetation maps are updated to 2008 and 2009 using landuse scenarios modeled by Sim Amazonia 2 and Sim Brazil. A priori fluxes modeled by STILT-VPRM are optimized using data from BARCA, eddy covariance sites, and flask measurements. The aircraft mixing ratios are applied as a top down constraint in Maximum Likelihood Estimation (MLE) and Bayesian inversion frameworks that solves for parameters controlling the flux. Posterior parameter estimates are used to estimate the carbon budget of the BAB. Preliminary results show that the STILT-VPRM model simulates the net emission of CO2 during both transition periods reasonably well. There is significant enhancement from biomass burning during the November 2008 profiles and some from fossil fuel combustion during the May 2009 flights. ΔCO/ΔCO2 emission ratios are used in combination with continuous observations of CO to remove the CO2 contributions from biomass burning and fossil fuel combustion from the observed CO2 measurements resulting in better agreement of observed and modeled aircraft data. Comparing column calculations for each of the vertical profiles shows our model represents the variability in the diurnal cycle. The high altitude CO2 values from above 3500m are similar to the lateral boundary conditions from CarbonTracker 2010 and GEOS-Chem indicating little influence from surface fluxes at these levels. The MLE inversion provides scaling factors for GEE and R for each of the 8 vegetation types and a Bayesian inversion is being conducted. Our initial inversion results suggest the BAB represents a small net source of CO2 during both of the BARCA intensives.

A Bayesian alternative for multi-objective ecohydrological model specification

NASA Astrophysics Data System (ADS)

Tang, Yating; Marshall, Lucy; Sharma, Ashish; Ajami, Hoori

2018-01-01

Recent studies have identified the importance of vegetation processes in terrestrial hydrologic systems. Process-based ecohydrological models combine hydrological, physical, biochemical and ecological processes of the catchments, and as such are generally more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov chain Monte Carlo (MCMC) techniques. The Bayesian approach offers an appealing alternative to traditional multi-objective hydrologic model calibrations by defining proper prior distributions that can be considered analogous to the ad-hoc weighting often prescribed in multi-objective calibration. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological modeling framework based on a traditional Pareto-based model calibration technique. In our study, a Pareto-based multi-objective optimization and a formal Bayesian framework are implemented in a conceptual ecohydrological model that combines a hydrological model (HYMOD) and a modified Bucket Grassland Model (BGM). Simulations focused on one objective (streamflow/LAI) and multiple objectives (streamflow and LAI) with different emphasis defined via the prior distribution of the model error parameters. Results show more reliable outputs for both predicted streamflow and LAI using Bayesian multi-objective calibration with specified prior distributions for error parameters based on results from the Pareto front in the ecohydrological modeling. The methodology implemented here provides insight into the usefulness of multiobjective Bayesian calibration for ecohydrologic systems and the importance of appropriate prior distributions in such approaches.

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.

PubMed

Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.

BISIP I: A program for Bayesian inference of spectral induced polarization parameters, and application to mineral exploration at the Canadian Malartic gold deposit, Québec, CA

NASA Astrophysics Data System (ADS)

Lafrenière-Bérubé, Charles; Chouteau, Michel; Shamsipour, Pejman; Olivo, Gema R.

2016-04-01

Spectral induced polarization (SIP) parameters can be extracted from field or laboratory complex resistivity measurements, and even airborne or ground frequency domain electromagnetic data. With the growing interest in application of complex resistivity measurements to environmental and mineral exploration problems, there is a need for accurate and easy-to-use inversion tools to estimate SIP parameters. These parameters, which often include chargeability and relaxation time may then be studied and related to other rock attributes such as porosity or metallic grain content, in the case of mineral exploration. We present an open source program, available both as a standalone application or Python module, to estimate SIP parameters using Markov-chain Monte Carlo (MCMC) sampling. The Python language is a high level, open source language that is now widely used in scientific computing. Our program allows the user to choose between the more common Cole-Cole (Pelton), Dias, or Debye decomposition models. Simple circuits composed of resistances and constant phase elements may also be used to represent SIP data. Initial guesses are required when using more classic inversion techniques such as the least-squares formulation, and wrong estimates are often the cause of bad curve fitting. In stochastic optimization using MCMC, the effect of the starting values disappears as the simulation proceeds. Our program is then optimized to do batch inversion over large data sets with as little user-interaction as possible. Additionally, the Bayesian formulation allows the user to do quality control by fully propagating the measurement errors in the inversion process, providing an estimation of the SIP parameters uncertainty. This information is valuable when trying to relate chargeability or relaxation time to other physical properties. We test the inversion program on complex resistivity measurements of 12 core samples from the world-class gold deposit of Canadian Malartic. Results show that the Cole-Cole and Debye decomposition models converge quickly to a solution and often provide the best fit with experimental data. The Dias model requires the least amount of iterations to fully converge, but we note a small discrepancy between experimental data and mathematical model for most samples. Using petrographic analysis we test possible relationships between porosity, sulfur content and grain size with parameters obtained from the different models, and note that sulfur content influences both the chargeability and frequency dependence of the Cole-Cole model. Finally, we use our program to compare the different definitions of chargeability and relaxation time given by the three models. We note that these parameters tend to be correlated from one model to another. However, they have different electrochemical definitions and a single sample may possess different chargeability or relaxation time values depending on the model used. In the near future, the program will be used on a more extensive collection of samples from the Canadian Malartic gold deposit, the Highland Valley copper deposit, and the Millennium-McArthur uranium deposits. CMIC-NSERC Exploration Footprints Network Contribution 082

iSEDfit: Bayesian spectral energy distribution modeling of galaxies

NASA Astrophysics Data System (ADS)

Moustakas, John

2017-08-01

iSEDfit uses Bayesian inference to extract the physical properties of galaxies from their observed broadband photometric spectral energy distribution (SED). In its default mode, the inputs to iSEDfit are the measured photometry (fluxes and corresponding inverse variances) and a measurement of the galaxy redshift. Alternatively, iSEDfit can be used to estimate photometric redshifts from the input photometry alone. After the priors have been specified, iSEDfit calculates the marginalized posterior probability distributions for the physical parameters of interest, including the stellar mass, star-formation rate, dust content, star formation history, and stellar metallicity. iSEDfit also optionally computes K-corrections and produces multiple "quality assurance" (QA) plots at each stage of the modeling procedure to aid in the interpretation of the prior parameter choices and subsequent fitting results. The software is distributed as part of the impro IDL suite.

Kinematic source inversions of teleseismic data based on the QUESO library for uncertainty quantification and prediction

NASA Astrophysics Data System (ADS)

Zielke, O.; McDougall, D.; Mai, P. M.; Babuska, I.

2014-12-01

One fundamental aspect of seismic hazard mitigation is gaining a better understanding of the rupture process. Because direct observation of the relevant parameters and properties is not possible, other means such as kinematic source inversions are used instead. By constraining the spatial and temporal evolution of fault slip during an earthquake, those inversion approaches may enable valuable insights in the physics of the rupture process. However, due to the underdetermined nature of this inversion problem (i.e., inverting a kinematic source model for an extended fault based on seismic data), the provided solutions are generally non-unique. Here we present a statistical (Bayesian) inversion approach based on an open-source library for uncertainty quantification (UQ) called QUESO that was developed at ICES (UT Austin). The approach has advantages with respect to deterministic inversion approaches as it provides not only a single (non-unique) solution but also provides uncertainty bounds with it. Those uncertainty bounds help to qualitatively and quantitatively judge how well constrained an inversion solution is and how much rupture complexity the data reliably resolve. The presented inversion scheme uses only tele-seismically recorded body waves but future developments may lead us towards joint inversion schemes. After giving an insight in the inversion scheme ifself (based on delayed rejection adaptive metropolis, DRAM) we explore the method's resolution potential. For that, we synthetically generate tele-seismic data, add for example different levels of noise and/or change fault plane parameterization and then apply our inversion scheme in the attempt to extract the (known) kinematic rupture model. We conclude with exemplary inverting real tele-seismic data of a recent large earthquake and compare those results with deterministically derived kinematic source models provided by other research groups.

Learning classification trees

NASA Technical Reports Server (NTRS)

Buntine, Wray

1991-01-01

Algorithms for learning classification trees have had successes in artificial intelligence and statistics over many years. How a tree learning algorithm can be derived from Bayesian decision theory is outlined. This introduces Bayesian techniques for splitting, smoothing, and tree averaging. The splitting rule turns out to be similar to Quinlan's information gain splitting rule, while smoothing and averaging replace pruning. Comparative experiments with reimplementations of a minimum encoding approach, Quinlan's C4 and Breiman et al. Cart show the full Bayesian algorithm is consistently as good, or more accurate than these other approaches though at a computational price.

The inverse problem of brain energetics: ketone bodies as alternative substrates

NASA Astrophysics Data System (ADS)

Calvetti, D.; Occhipinti, R.; Somersalo, E.

2008-07-01

Little is known about brain energy metabolism under ketosis, although there is evidence that ketone bodies have a neuroprotective role in several neurological disorders. We investigate the inverse problem of estimating reaction fluxes and transport rates in the different cellular compartments of the brain, when the data amounts to a few measured arterial venous concentration differences. By using a recently developed methodology to perform Bayesian Flux Balance Analysis and a new five compartment model of the astrocyte-glutamatergic neuron cellular complex, we are able to identify the preferred biochemical pathways during shortage of glucose and in the presence of ketone bodies in the arterial blood. The analysis is performed in a minimally biased way, therefore revealing the potential of this methodology for hypothesis testing.

A physiologically motivated sparse, compact, and smooth (SCS) approach to EEG source localization.

PubMed

Cao, Cheng; Akalin Acar, Zeynep; Kreutz-Delgado, Kenneth; Makeig, Scott

2012-01-01

Here, we introduce a novel approach to the EEG inverse problem based on the assumption that principal cortical sources of multi-channel EEG recordings may be assumed to be spatially sparse, compact, and smooth (SCS). To enforce these characteristics of solutions to the EEG inverse problem, we propose a correlation-variance model which factors a cortical source space covariance matrix into the multiplication of a pre-given correlation coefficient matrix and the square root of the diagonal variance matrix learned from the data under a Bayesian learning framework. We tested the SCS method using simulated EEG data with various SNR and applied it to a real ECOG data set. We compare the results of SCS to those of an established SBL algorithm.

Finite-fault inversion of the Mw 5.9 2012 Emilia-Romagna earthquake (Northern Italy) using aftershocks as near-field Green's function approximations

NASA Astrophysics Data System (ADS)

Causse, Mathieu; Cultrera, Giovanna; Herrero, André; Courboulex, Françoise; Schiappapietra, Erika; Moreau, Ludovic

2017-04-01

On May 29, 2012 occurred a Mw 5.9 earthquake in the Emilia-Romagna region (Po Plain) on a thrust fault system. This shock, as well as hundreds of aftershocks, were recorded by 10 strong motion stations located less than 10 km away from the rupture plane, with 4 stations located within the surface rupture projection. The Po Plain is a very large EW trending syntectonic alluvial basin, delimited by the Alps and Apennines chains to the North and South. The Plio-Quaternary sedimentary sequence filling the Po Plain is characterized by an uneven thickness, ranging from several thousands of meters to a few tens of meters. This particular context results especially in a resonance basin below 1 Hz and strong surface waves, which makes it particularly difficult to model wave propagation and hence to obtain robust images of the rupture propagation. This study proposes to take advantage of the large set of recorded aftershocks, considered as point sources, to model wave propagation. Due to the heterogeneous distribution of the aftershocks on the fault plane, an interpolation technique is proposed to compute an approximation of the Green's function between each fault point and each strong motion station in the frequency range [0.2-1Hz]. We then use a Bayesian inversion technique (Monte Carlo Markov Chain algorithm) to obtain images of the rupture propagation from the strong motion data. We propose to retrieve the slip distribution by inverting the final slip value at some control points, which are allowed to move on the fault plane, and by interpolating the slip value between these points. We show that the use of 5 control points to describe the slip, coupled with the hypothesis of spatially constant rupture velocity and rise-time (that is 18 free source parameters), results in a good level of fit with the data. This indicates that despite their complexity, the strong motion data can be properly modeled up to 1 Hz using a relatively simple rupture. The inversion results also reveal that the rupture propagated slowly, at a speed of about 45% of the shear wave velocity.

Bayesian inversion of surface-wave data for radial and azimuthal shear-wave anisotropy, with applications to central Mongolia and west-central Italy

NASA Astrophysics Data System (ADS)

Ravenna, Matteo; Lebedev, Sergei

2018-04-01

Seismic anisotropy provides important information on the deformation history of the Earth's interior. Rayleigh and Love surface-waves are sensitive to and can be used to determine both radial and azimuthal shear-wave anisotropies at depth, but parameter trade-offs give rise to substantial model non-uniqueness. Here, we explore the trade-offs between isotropic and anisotropic structure parameters and present a suite of methods for the inversion of surface-wave, phase-velocity curves for radial and azimuthal anisotropies. One Markov chain Monte Carlo (McMC) implementation inverts Rayleigh and Love dispersion curves for a radially anisotropic shear velocity profile of the crust and upper mantle. Another McMC implementation inverts Rayleigh phase velocities and their azimuthal anisotropy for profiles of vertically polarized shear velocity and its depth-dependent azimuthal anisotropy. The azimuthal anisotropy inversion is fully non-linear, with the forward problem solved numerically at different azimuths for every model realization, which ensures that any linearization biases are avoided. The computations are performed in parallel, in order to reduce the computing time. The often challenging issue of data noise estimation is addressed by means of a Hierarchical Bayesian approach, with the variance of the noise treated as an unknown during the radial anisotropy inversion. In addition to the McMC inversions, we also present faster, non-linear gradient-search inversions for the same anisotropic structure. The results of the two approaches are mutually consistent; the advantage of the McMC inversions is that they provide a measure of uncertainty of the models. Applying the method to broad-band data from the Baikal-central Mongolia region, we determine radial anisotropy from the crust down to the transition-zone depths. Robust negative anisotropy (Vsh < Vsv) in the asthenosphere, at 100-300 km depths, presents strong new evidence for a vertical component of asthenospheric flow. This is consistent with an upward flow from below the thick lithosphere of the Siberian Craton to below the thinner lithosphere of central Mongolia, likely to give rise to decompression melting and the scattered, sporadic volcanism observed in the Baikal Rift area, as proposed previously. Inversion of phase-velocity data from west-central Italy for azimuthal anisotropy reveals a clear change in the shear-wave fast-propagation direction at 70-100 km depths, near the lithosphere-asthenosphere boundary. The orientation of the fabric in the lithosphere is roughly E-W, parallel to the direction of stretching over the last 10 m.y. The orientation of the fabric in the asthenosphere is NW-SE, matching the fast directions inferred from shear-wave splitting and probably indicating the direction of the asthenospheric flow.

Constraining the Magmatic System at Mount St. Helens (2004-2008) Using Bayesian Inversion With Physics-Based Models Including Gas Escape and Crystallization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Ying -Qi; Segall, Paul; Bradley, Andrew

Physics-based models of volcanic eruptions track conduit processes as functions of depth and time. When used in inversions, these models permit integration of diverse geological and geophysical data sets to constrain important parameters of magmatic systems. We develop a 1-D steady state conduit model for effusive eruptions including equilibrium crystallization and gas transport through the conduit and compare with the quasi-steady dome growth phase of Mount St. Helens in 2005. Viscosity increase resulting from pressure-dependent crystallization leads to a natural transition from viscous flow to frictional sliding on the conduit margin. Erupted mass flux depends strongly on wall rock andmore » magma permeabilities due to their impact on magma density. Including both lateral and vertical gas transport reveals competing effects that produce nonmonotonic behavior in the mass flux when increasing magma permeability. Using this physics-based model in a Bayesian inversion, we link data sets from Mount St. Helens such as extrusion flux and earthquake depths with petrological data to estimate unknown model parameters, including magma chamber pressure and water content, magma permeability constants, conduit radius, and friction along the conduit walls. Even with this relatively simple model and limited data, we obtain improved constraints on important model parameters. We find that the magma chamber had low (<5 wt %) total volatiles and that the magma permeability scale is well constrained at ~10 –11.4m 2 to reproduce observed dome rock porosities. Here, compared with previous results, higher magma overpressure and lower wall friction are required to compensate for increased viscous resistance while keeping extrusion rate at the observed value.« less

Methane emissions in East Asia for 2000-2011 estimated using an atmospheric Bayesian inversion

NASA Astrophysics Data System (ADS)

Thompson, R. L.; Stohl, A.; Zhou, L. X.; Dlugokencky, E.; Fukuyama, Y.; Tohjima, Y.; Kim, S.-Y.; Lee, H.; Nisbet, E. G.; Fisher, R. E.; Lowry, D.; Weiss, R. F.; Prinn, R. G.; O'Doherty, S.; Young, D.; White, J. W. C.

2015-05-01

We present methane (CH4) emissions for East Asia from a Bayesian inversion of CH4 mole fraction and stable isotope (δ13C-CH4) measurements. Emissions were estimated at monthly resolution from 2000 to 2011. A posteriori, the total emission for East Asia increased from 43 ± 4 to 59 ± 4 Tg yr-1 between 2000 and 2011, owing largely to the increase in emissions from China, from 39 ± 4 to 54 ± 4 Tg yr-1, while emissions in other East Asian countries remained relatively stable. For China, South Korea, and Japan, the total emissions were smaller than the prior estimates (i.e., Emission Database for Global Atmospheric Research 4.2 FT2010 for anthropogenic emissions) by an average of 29%, 20%, and 23%, respectively. For Mongolia, Taiwan, and North Korea, the total emission was less than 2 Tg yr-1 and was not significantly different from the prior. The largest reductions in emissions, compared to the prior, occurred in summer in regions important for rice agriculture suggesting that this source is overestimated in the prior. Furthermore, an analysis of the isotope data suggests that the prior underestimates emissions from landfills and ruminant animals for winter 2010 to spring 2011 (no data available for other times). The inversion also found a lower average emission trend for China, 1.2 Tg yr-1 compared to 2.8 Tg yr-1 in the prior. This trend was not constant, however, and increased significantly after 2005, up to 2.0 Tg yr-1. Overall, the changes in emissions from China explain up to 40% of the increase in global emissions in the 2000s.

Constraining the Magmatic System at Mount St. Helens (2004-2008) Using Bayesian Inversion With Physics-Based Models Including Gas Escape and Crystallization

NASA Astrophysics Data System (ADS)

Wong, Ying-Qi; Segall, Paul; Bradley, Andrew; Anderson, Kyle

2017-10-01

Physics-based models of volcanic eruptions track conduit processes as functions of depth and time. When used in inversions, these models permit integration of diverse geological and geophysical data sets to constrain important parameters of magmatic systems. We develop a 1-D steady state conduit model for effusive eruptions including equilibrium crystallization and gas transport through the conduit and compare with the quasi-steady dome growth phase of Mount St. Helens in 2005. Viscosity increase resulting from pressure-dependent crystallization leads to a natural transition from viscous flow to frictional sliding on the conduit margin. Erupted mass flux depends strongly on wall rock and magma permeabilities due to their impact on magma density. Including both lateral and vertical gas transport reveals competing effects that produce nonmonotonic behavior in the mass flux when increasing magma permeability. Using this physics-based model in a Bayesian inversion, we link data sets from Mount St. Helens such as extrusion flux and earthquake depths with petrological data to estimate unknown model parameters, including magma chamber pressure and water content, magma permeability constants, conduit radius, and friction along the conduit walls. Even with this relatively simple model and limited data, we obtain improved constraints on important model parameters. We find that the magma chamber had low (<5 wt %) total volatiles and that the magma permeability scale is well constrained at ˜10-11.4m2 to reproduce observed dome rock porosities. Compared with previous results, higher magma overpressure and lower wall friction are required to compensate for increased viscous resistance while keeping extrusion rate at the observed value.

Constraining the Magmatic System at Mount St. Helens (2004-2008) Using Bayesian Inversion With Physics-Based Models Including Gas Escape and Crystallization

DOE PAGES

Wong, Ying -Qi; Segall, Paul; Bradley, Andrew; ...

2017-10-04

Physics-based models of volcanic eruptions track conduit processes as functions of depth and time. When used in inversions, these models permit integration of diverse geological and geophysical data sets to constrain important parameters of magmatic systems. We develop a 1-D steady state conduit model for effusive eruptions including equilibrium crystallization and gas transport through the conduit and compare with the quasi-steady dome growth phase of Mount St. Helens in 2005. Viscosity increase resulting from pressure-dependent crystallization leads to a natural transition from viscous flow to frictional sliding on the conduit margin. Erupted mass flux depends strongly on wall rock andmore » magma permeabilities due to their impact on magma density. Including both lateral and vertical gas transport reveals competing effects that produce nonmonotonic behavior in the mass flux when increasing magma permeability. Using this physics-based model in a Bayesian inversion, we link data sets from Mount St. Helens such as extrusion flux and earthquake depths with petrological data to estimate unknown model parameters, including magma chamber pressure and water content, magma permeability constants, conduit radius, and friction along the conduit walls. Even with this relatively simple model and limited data, we obtain improved constraints on important model parameters. We find that the magma chamber had low (<5 wt %) total volatiles and that the magma permeability scale is well constrained at ~10 –11.4m 2 to reproduce observed dome rock porosities. Here, compared with previous results, higher magma overpressure and lower wall friction are required to compensate for increased viscous resistance while keeping extrusion rate at the observed value.« less

Constraining the magmatic system at Mount St. Helens (2004–2008) using Bayesian inversion with physics-based models including gas escape and crystallization

USGS Publications Warehouse

Wong, Ying-Qi; Segall, Paul; Bradley, Andrew; Anderson, Kyle R.

2017-01-01

Physics-based models of volcanic eruptions track conduit processes as functions of depth and time. When used in inversions, these models permit integration of diverse geological and geophysical data sets to constrain important parameters of magmatic systems. We develop a 1-D steady state conduit model for effusive eruptions including equilibrium crystallization and gas transport through the conduit and compare with the quasi-steady dome growth phase of Mount St. Helens in 2005. Viscosity increase resulting from pressure-dependent crystallization leads to a natural transition from viscous flow to frictional sliding on the conduit margin. Erupted mass flux depends strongly on wall rock and magma permeabilities due to their impact on magma density. Including both lateral and vertical gas transport reveals competing effects that produce nonmonotonic behavior in the mass flux when increasing magma permeability. Using this physics-based model in a Bayesian inversion, we link data sets from Mount St. Helens such as extrusion flux and earthquake depths with petrological data to estimate unknown model parameters, including magma chamber pressure and water content, magma permeability constants, conduit radius, and friction along the conduit walls. Even with this relatively simple model and limited data, we obtain improved constraints on important model parameters. We find that the magma chamber had low (<5wt%) total volatiles and that the magma permeability scale is well constrained at ~10-11.4 m2 to reproduce observed dome rock porosities. Compared with previous results, higher magma overpressure and lower wall friction are required to compensate for increased viscous resistance while keeping extrusion rate at the observed value.

Are Student Evaluations of Teaching Effectiveness Valid for Measuring Student Learning Outcomes in Business Related Classes? A Neural Network and Bayesian Analyses

ERIC Educational Resources Information Center

Galbraith, Craig S.; Merrill, Gregory B.; Kline, Doug M.

2012-01-01

In this study we investigate the underlying relational structure between student evaluations of teaching effectiveness (SETEs) and achievement of student learning outcomes in 116 business related courses. Utilizing traditional statistical techniques, a neural network analysis and a Bayesian data reduction and classification algorithm, we find…

Bayesian methods in reliability

NASA Astrophysics Data System (ADS)

Sander, P.; Badoux, R.

1991-11-01

The present proceedings from a course on Bayesian methods in reliability encompasses Bayesian statistical methods and their computational implementation, models for analyzing censored data from nonrepairable systems, the traits of repairable systems and growth models, the use of expert judgment, and a review of the problem of forecasting software reliability. Specific issues addressed include the use of Bayesian methods to estimate the leak rate of a gas pipeline, approximate analyses under great prior uncertainty, reliability estimation techniques, and a nonhomogeneous Poisson process. Also addressed are the calibration sets and seed variables of expert judgment systems for risk assessment, experimental illustrations of the use of expert judgment for reliability testing, and analyses of the predictive quality of software-reliability growth models such as the Weibull order statistics.

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

PubMed

Chen, Bo; Chen, Minhua; Paisley, John; Zaas, Aimee; Woods, Christopher; Ginsburg, Geoffrey S; Hero, Alfred; Lucas, Joseph; Dunson, David; Carin, Lawrence

2010-11-09

Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

Embedding the results of focussed Bayesian fusion into a global context

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael

2014-05-01

Bayesian statistics offers a well-founded and powerful fusion methodology also for the fusion of heterogeneous information sources. However, except in special cases, the needed posterior distribution is not analytically derivable. As consequence, Bayesian fusion may cause unacceptably high computational and storage costs in practice. Local Bayesian fusion approaches aim at reducing the complexity of the Bayesian fusion methodology significantly. This is done by concentrating the actual Bayesian fusion on the potentially most task relevant parts of the domain of the Properties of Interest. Our research on these approaches is motivated by an analogy to criminal investigations where criminalists pursue clues also only locally. This publication follows previous publications on a special local Bayesian fusion technique called focussed Bayesian fusion. Here, the actual calculation of the posterior distribution gets completely restricted to a suitably chosen local context. By this, the global posterior distribution is not completely determined. Strategies for using the results of a focussed Bayesian analysis appropriately are needed. In this publication, we primarily contrast different ways of embedding the results of focussed Bayesian fusion explicitly into a global context. To obtain a unique global posterior distribution, we analyze the application of the Maximum Entropy Principle that has been shown to be successfully applicable in metrology and in different other areas. To address the special need for making further decisions subsequently to the actual fusion task, we further analyze criteria for decision making under partial information.

Quantifying uncertainty in soot volume fraction estimates using Bayesian inference of auto-correlated laser-induced incandescence measurements

NASA Astrophysics Data System (ADS)

Hadwin, Paul J.; Sipkens, T. A.; Thomson, K. A.; Liu, F.; Daun, K. J.

2016-01-01

Auto-correlated laser-induced incandescence (AC-LII) infers the soot volume fraction (SVF) of soot particles by comparing the spectral incandescence from laser-energized particles to the pyrometrically inferred peak soot temperature. This calculation requires detailed knowledge of model parameters such as the absorption function of soot, which may vary with combustion chemistry, soot age, and the internal structure of the soot. This work presents a Bayesian methodology to quantify such uncertainties. This technique treats the additional "nuisance" model parameters, including the soot absorption function, as stochastic variables and incorporates the current state of knowledge of these parameters into the inference process through maximum entropy priors. While standard AC-LII analysis provides a point estimate of the SVF, Bayesian techniques infer the posterior probability density, which will allow scientists and engineers to better assess the reliability of AC-LII inferred SVFs in the context of environmental regulations and competing diagnostics.

Bayesian sparse channel estimation

NASA Astrophysics Data System (ADS)

Chen, Chulong; Zoltowski, Michael D.

2012-05-01

In Orthogonal Frequency Division Multiplexing (OFDM) systems, the technique used to estimate and track the time-varying multipath channel is critical to ensure reliable, high data rate communications. It is recognized that wireless channels often exhibit a sparse structure, especially for wideband and ultra-wideband systems. In order to exploit this sparse structure to reduce the number of pilot tones and increase the channel estimation quality, the application of compressed sensing to channel estimation is proposed. In this article, to make the compressed channel estimation more feasible for practical applications, it is investigated from a perspective of Bayesian learning. Under the Bayesian learning framework, the large-scale compressed sensing problem, as well as large time delay for the estimation of the doubly selective channel over multiple consecutive OFDM symbols, can be avoided. Simulation studies show a significant improvement in channel estimation MSE and less computing time compared to the conventional compressed channel estimation techniques.

Joint Bayesian inference for near-surface explosion yield

NASA Astrophysics Data System (ADS)

Bulaevskaya, V.; Ford, S. R.; Ramirez, A. L.; Rodgers, A. J.

2016-12-01

A near-surface explosion generates seismo-acoustic motion that is related to its yield. However, the recorded motion is affected by near-source effects such as depth-of-burial, and propagation-path effects such as variable geology. We incorporate these effects in a forward model relating yield to seismo-acoustic motion, and use Bayesian inference to estimate yield given recordings of the seismo-acoustic wavefield. The Bayesian approach to this inverse problem allows us to obtain the probability distribution of plausible yield values and thus quantify the uncertainty in the yield estimate. Moreover, the sensitivity of the acoustic signal falls as a function of the depth-of-burial, while the opposite relationship holds for the seismic signal. Therefore, using both the acoustic and seismic wavefield data allows us to avoid the trade-offs associated with using only one of these signals alone. In addition, our inference framework allows for correlated features of the same data type (seismic or acoustic) to be incorporated in the estimation of yield in order to make use of as much information from the same waveform as possible. We demonstrate our approach with a historical dataset and a contemporary field experiment.

A Flexible Hierarchical Bayesian Modeling Technique for Risk Analysis of Major Accidents.

PubMed

Yu, Hongyang; Khan, Faisal; Veitch, Brian

2017-09-01

Safety analysis of rare events with potentially catastrophic consequences is challenged by data scarcity and uncertainty. Traditional causation-based approaches, such as fault tree and event tree (used to model rare event), suffer from a number of weaknesses. These include the static structure of the event causation, lack of event occurrence data, and need for reliable prior information. In this study, a new hierarchical Bayesian modeling based technique is proposed to overcome these drawbacks. The proposed technique can be used as a flexible technique for risk analysis of major accidents. It enables both forward and backward analysis in quantitative reasoning and the treatment of interdependence among the model parameters. Source-to-source variability in data sources is also taken into account through a robust probabilistic safety analysis. The applicability of the proposed technique has been demonstrated through a case study in marine and offshore industry. © 2017 Society for Risk Analysis.

An inverse method to estimate the flow through a levee breach

NASA Astrophysics Data System (ADS)

D'Oria, Marco; Mignosa, Paolo; Tanda, Maria Giovanna

2015-08-01

We propose a procedure to estimate the flow through a levee breach based on water levels recorded in river stations downstream and/or upstream of the failure site. The inverse problem is solved using a Bayesian approach and requires the execution of several forward unsteady flow simulations. For this purpose, we have used the well-known 1-D HEC-RAS model, but any unsteady flow model could be adopted in the same way. The procedure has been tested using four synthetic examples. Levee breaches with different characteristics (free flow, flow with tailwater effects, etc.) have been simulated to collect the synthetic level data used at a later stage in the inverse procedure. The method was able to accurately reproduce the flow through the breach in all cases. The practicability of the procedure was then confirmed applying it to the inundation of the Polesine Region (Northern Italy) which occurred in 1951 and was caused by three contiguous and almost simultaneous breaches on the left embankment of the Po River.

Improved source inversion from joint measurements of translational and rotational ground motions

NASA Astrophysics Data System (ADS)

Donner, S.; Bernauer, M.; Reinwald, M.; Hadziioannou, C.; Igel, H.

2017-12-01

Waveform inversion for seismic point (moment tensor) and kinematic sources is a standard procedure. However, especially in the local and regional distances a lack of appropriate velocity models, the sparsity of station networks, or a low signal-to-noise ratio combined with more complex waveforms hamper the successful retrieval of reliable source solutions. We assess the potential of rotational ground motion recordings to increase the resolution power and reduce non-uniquenesses for point and kinematic source solutions. Based on synthetic waveform data, we perform a Bayesian (i.e. probabilistic) inversion. Thus, we avoid the subjective selection of the most reliable solution according the lowest misfit or other constructed criterion. In addition, we obtain unbiased measures of resolution and possible trade-offs. Testing different earthquake mechanisms and scenarios, we can show that the resolution of the source solutions can be improved significantly. Especially depth dependent components show significant improvement. Next to synthetic data of station networks, we also tested sparse-network and single station cases.

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

Karabatsos, George

2017-02-01

Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected functionals and values of covariates. The software is illustrated through the BNP regression analysis of real data.

Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme

NASA Astrophysics Data System (ADS)

Bakoban, Rana A.

2017-08-01

The coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.

Climatic Models Ensemble-based Mid-21st Century Runoff Projections: A Bayesian Framework

NASA Astrophysics Data System (ADS)

Achieng, K. O.; Zhu, J.

2017-12-01

There are a number of North American Regional Climate Change Assessment Program (NARCCAP) climatic models that have been used to project surface runoff in the mid-21st century. Statistical model selection techniques are often used to select the model that best fits data. However, model selection techniques often lead to different conclusions. In this study, ten models are averaged in Bayesian paradigm to project runoff. Bayesian Model Averaging (BMA) is used to project and identify effect of model uncertainty on future runoff projections. Baseflow separation - a two-digital filter which is also called Eckhardt filter - is used to separate USGS streamflow (total runoff) into two components: baseflow and surface runoff. We use this surface runoff as the a priori runoff when conducting BMA of runoff simulated from the ten RCM models. The primary objective of this study is to evaluate how well RCM multi-model ensembles simulate surface runoff, in a Bayesian framework. Specifically, we investigate and discuss the following questions: How well do ten RCM models ensemble jointly simulate surface runoff by averaging over all the models using BMA, given a priori surface runoff? What are the effects of model uncertainty on surface runoff simulation?

Comparison of Bayesian clustering and edge detection methods for inferring boundaries in landscape genetics

USGS Publications Warehouse

Safner, T.; Miller, M.P.; McRae, B.H.; Fortin, M.-J.; Manel, S.

2011-01-01

Recently, techniques available for identifying clusters of individuals or boundaries between clusters using genetic data from natural populations have expanded rapidly. Consequently, there is a need to evaluate these different techniques. We used spatially-explicit simulation models to compare three spatial Bayesian clustering programs and two edge detection methods. Spatially-structured populations were simulated where a continuous population was subdivided by barriers. We evaluated the ability of each method to correctly identify boundary locations while varying: (i) time after divergence, (ii) strength of isolation by distance, (iii) level of genetic diversity, and (iv) amount of gene flow across barriers. To further evaluate the methods' effectiveness to detect genetic clusters in natural populations, we used previously published data on North American pumas and a European shrub. Our results show that with simulated and empirical data, the Bayesian spatial clustering algorithms outperformed direct edge detection methods. All methods incorrectly detected boundaries in the presence of strong patterns of isolation by distance. Based on this finding, we support the application of Bayesian spatial clustering algorithms for boundary detection in empirical datasets, with necessary tests for the influence of isolation by distance. ?? 2011 by the authors; licensee MDPI, Basel, Switzerland.

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors

PubMed Central

Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world’s deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014. PMID:28257437

The effects of time-varying observation errors on semi-empirical sea-level projections

DOE PAGES

Ruckert, Kelsey L.; Guan, Yawen; Bakker, Alexander M. R.; ...

2016-11-30

Sea-level rise is a key driver of projected flooding risks. The design of strategies to manage these risks often hinges on projections that inform decision-makers about the surrounding uncertainties. Producing semi-empirical sea-level projections is difficult, for example, due to the complexity of the error structure of the observations, such as time-varying (heteroskedastic) observation errors and autocorrelation of the data-model residuals. This raises the question of how neglecting the error structure impacts hindcasts and projections. Here, we quantify this effect on sea-level projections and parameter distributions by using a simple semi-empirical sea-level model. Specifically, we compare three model-fitting methods: a frequentistmore » bootstrap as well as a Bayesian inversion with and without considering heteroskedastic residuals. All methods produce comparable hindcasts, but the parametric distributions and projections differ considerably based on methodological choices. In conclusion, our results show that the differences based on the methodological choices are enhanced in the upper tail projections. For example, the Bayesian inversion accounting for heteroskedasticity increases the sea-level anomaly with a 1% probability of being equaled or exceeded in the year 2050 by about 34% and about 40% in the year 2100 compared to a frequentist bootstrap. These results indicate that neglecting known properties of the observation errors and the data-model residuals can lead to low-biased sea-level projections.« less

The effects of time-varying observation errors on semi-empirical sea-level projections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruckert, Kelsey L.; Guan, Yawen; Bakker, Alexander M. R.

Sea-level rise is a key driver of projected flooding risks. The design of strategies to manage these risks often hinges on projections that inform decision-makers about the surrounding uncertainties. Producing semi-empirical sea-level projections is difficult, for example, due to the complexity of the error structure of the observations, such as time-varying (heteroskedastic) observation errors and autocorrelation of the data-model residuals. This raises the question of how neglecting the error structure impacts hindcasts and projections. Here, we quantify this effect on sea-level projections and parameter distributions by using a simple semi-empirical sea-level model. Specifically, we compare three model-fitting methods: a frequentistmore » bootstrap as well as a Bayesian inversion with and without considering heteroskedastic residuals. All methods produce comparable hindcasts, but the parametric distributions and projections differ considerably based on methodological choices. In conclusion, our results show that the differences based on the methodological choices are enhanced in the upper tail projections. For example, the Bayesian inversion accounting for heteroskedasticity increases the sea-level anomaly with a 1% probability of being equaled or exceeded in the year 2050 by about 34% and about 40% in the year 2100 compared to a frequentist bootstrap. These results indicate that neglecting known properties of the observation errors and the data-model residuals can lead to low-biased sea-level projections.« less

Reconstruction of the water table from self-potential data: a bayesian approach.

PubMed

Jardani, A; Revil, A; Barrash, W; Crespy, A; Rizzo, E; Straface, S; Cardiff, M; Malama, B; Miller, C; Johnson, T

2009-01-01

Ground water flow associated with pumping and injection tests generates self-potential signals that can be measured at the ground surface and used to estimate the pattern of ground water flow at depth. We propose an inversion of the self-potential signals that accounts for the heterogeneous nature of the aquifer and a relationship between the electrical resistivity and the streaming current coupling coefficient. We recast the inversion of the self-potential data into a Bayesian framework. Synthetic tests are performed showing the advantage in using self-potential signals in addition to in situ measurements of the potentiometric levels to reconstruct the shape of the water table. This methodology is applied to a new data set from a series of coordinated hydraulic tomography, self-potential, and electrical resistivity tomography experiments performed at the Boise Hydrogeophysical Research Site, Idaho. In particular, we examine one of the dipole hydraulic tests and its reciprocal to show the sensitivity of the self-potential signals to variations of the potentiometric levels under steady-state conditions. However, because of the high pumping rate, the response was also influenced by the Reynolds number, especially near the pumping well for a given test. Ground water flow in the inertial laminar flow regime is responsible for nonlinearity that is not yet accounted for in self-potential tomography. Numerical modeling addresses the sensitivity of the self-potential response to this problem.

Source Partitioning of Methane Emissions and its Seasonality in the U.S. Midwest

NASA Astrophysics Data System (ADS)

Chen, Zichong; Griffis, Timothy J.; Baker, John M.; Millet, Dylan B.; Wood, Jeffrey D.; Dlugokencky, Edward J.; Andrews, Arlyn E.; Sweeney, Colm; Hu, Cheng; Kolka, Randall K.

2018-02-01

The methane (CH4) budget and its source partitioning are poorly constrained in the Midwestern United States. We used tall tower (185 m) aerodynamic flux measurements and atmospheric scale factor Bayesian inversions to constrain the monthly budget and to partition the total budget into natural (e.g., wetlands) and anthropogenic (e.g., livestock, waste, and natural gas) sources for the period June 2016 to September 2017. Aerodynamic flux observations indicated that the landscape was a CH4 source with a mean annual CH4 flux of +13.7 ± 0.34 nmol m-2 s-1 and was rarely a net sink. The scale factor Bayesian inversion analyses revealed a mean annual source of +12.3 ± 2.1 nmol m-2 s-1. Flux partitioning revealed that the anthropogenic source (7.8 ± 1.6 Tg CH4 yr-1) was 1.5 times greater than the bottom-up gridded United States Environmental Protection Agency inventory, in which livestock and oil/gas sources were underestimated by 1.8-fold and 1.3-fold, respectively. Wetland emissions (4.0 ± 1.2 Tg CH4 yr-1) were the second largest source, accounting for 34% of the total budget. The temporal variability of total CH4 emissions was dominated by wetlands with peak emissions occurring in August. In contrast, emissions from oil/gas and other anthropogenic sources showed relatively weak seasonality.

Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model.

PubMed

Merlé, Y; Mentré, F

1995-02-01

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the pre-posterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and the Emax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for the Emax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for the Emax model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.

Adaptively Reevaluated Bayesian Localization (ARBL). A Novel Technique for Radiological Source Localization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miller, Erin A.; Robinson, Sean M.; Anderson, Kevin K.

2015-01-19

Here we present a novel technique for the localization of radiological sources in urban or rural environments from an aerial platform. The technique is based on a Bayesian approach to localization, in which measured count rates in a time series are compared with predicted count rates from a series of pre-calculated test sources to define likelihood. Furthermore, this technique is expanded by using a localized treatment with a limited field of view (FOV), coupled with a likelihood ratio reevaluation, allowing for real-time computation on commodity hardware for arbitrarily complex detector models and terrain. In particular, detectors with inherent asymmetry ofmore » response (such as those employing internal collimation or self-shielding for enhanced directional awareness) are leveraged by this approach to provide improved localization. Our results from the localization technique are shown for simulated flight data using monolithic as well as directionally-aware detector models, and the capability of the methodology to locate radioisotopes is estimated for several test cases. This localization technique is shown to facilitate urban search by allowing quick and adaptive estimates of source location, in many cases from a single flyover near a source. In particular, this method represents a significant advancement from earlier methods like full-field Bayesian likelihood, which is not generally fast enough to allow for broad-field search in real time, and highest-net-counts estimation, which has a localization error that depends strongly on flight path and cannot generally operate without exhaustive search« less

Bayesian networks in overlay recipe optimization

NASA Astrophysics Data System (ADS)

Binns, Lewis A.; Reynolds, Greg; Rigden, Timothy C.; Watkins, Stephen; Soroka, Andrew

2005-05-01

Currently, overlay measurements are characterized by "recipe", which defines both physical parameters such as focus, illumination et cetera, and also the software parameters such as algorithm to be used and regions of interest. Setting up these recipes requires both engineering time and wafer availability on an overlay tool, so reducing these requirements will result in higher tool productivity. One of the significant challenges to automating this process is that the parameters are highly and complexly correlated. At the same time, a high level of traceability and transparency is required in the recipe creation process, so a technique that maintains its decisions in terms of well defined physical parameters is desirable. Running time should be short, given the system (automatic recipe creation) is being implemented to reduce overheads. Finally, a failure of the system to determine acceptable parameters should be obvious, so a certainty metric is also desirable. The complex, nonlinear interactions make solution by an expert system difficult at best, especially in the verification of the resulting decision network. The transparency requirements tend to preclude classical neural networks and similar techniques. Genetic algorithms and other "global minimization" techniques require too much computational power (given system footprint and cost requirements). A Bayesian network, however, provides a solution to these requirements. Such a network, with appropriate priors, can be used during recipe creation / optimization not just to select a good set of parameters, but also to guide the direction of search, by evaluating the network state while only incomplete information is available. As a Bayesian network maintains an estimate of the probability distribution of nodal values, a maximum-entropy approach can be utilized to obtain a working recipe in a minimum or near-minimum number of steps. In this paper we discuss the potential use of a Bayesian network in such a capacity, reducing the amount of engineering intervention. We discuss the benefits of this approach, especially improved repeatability and traceability of the learning process, and quantification of uncertainty in decisions made. We also consider the problems associated with this approach, especially in detailed construction of network topology, validation of the Bayesian network and the recipes it generates, and issues arising from the integration of a Bayesian network with a complex multithreaded application; these primarily relate to maintaining Bayesian network and system architecture integrity.

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

DOE PAGES

Moral, Pierre Del; Jasra, Ajay; Law, Kody J. H.; ...

2017-08-24

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of themore » solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.« less

Non-linear Parameter Estimates from Non-stationary MEG Data

PubMed Central

Martínez-Vargas, Juan D.; López, Jose D.; Baker, Adam; Castellanos-Dominguez, German; Woolrich, Mark W.; Barnes, Gareth

2016-01-01

We demonstrate a method to estimate key electrophysiological parameters from resting state data. In this paper, we focus on the estimation of head-position parameters. The recovery of these parameters is especially challenging as they are non-linearly related to the measured field. In order to do this we use an empirical Bayesian scheme to estimate the cortical current distribution due to a range of laterally shifted head-models. We compare different methods of approaching this problem from the division of M/EEG data into stationary sections and performing separate source inversions, to explaining all of the M/EEG data with a single inversion. We demonstrate this through estimation of head position in both simulated and empirical resting state MEG data collected using a head-cast. PMID:27597815

GUEST EDITORS' INTRODUCTION: Testing inversion algorithms against experimental data: inhomogeneous targets

NASA Astrophysics Data System (ADS)

Belkebir, Kamal; Saillard, Marc

2005-12-01

This special section deals with the reconstruction of scattering objects from experimental data. A few years ago, inspired by the Ipswich database [1 4], we started to build an experimental database in order to validate and test inversion algorithms against experimental data. In the special section entitled 'Testing inversion algorithms against experimental data' [5], preliminary results were reported through 11 contributions from several research teams. (The experimental data are free for scientific use and can be downloaded from the web site.) The success of this previous section has encouraged us to go further and to design new challenges for the inverse scattering community. Taking into account the remarks formulated by several colleagues, the new data sets deal with inhomogeneous cylindrical targets and transverse electric (TE) polarized incident fields have also been used. Among the four inhomogeneous targets, three are purely dielectric, while the last one is a `hybrid' target mixing dielectric and metallic cylinders. Data have been collected in the anechoic chamber of the Centre Commun de Ressources Micro-ondes in Marseille. The experimental setup as well as the layout of the files containing the measurements are presented in the contribution by J-M Geffrin, P Sabouroux and C Eyraud. The antennas did not change from the ones used previously [5], namely wide-band horn antennas. However, improvements have been achieved by refining the mechanical positioning devices. In order to enlarge the scope of applications, both TE and transverse magnetic (TM) polarizations have been carried out for all targets. Special care has been taken not to move the target under test when switching from TE to TM measurements, ensuring that TE and TM data are available for the same configuration. All data correspond to electric field measurements. In TE polarization the measured component is orthogonal to the axis of invariance. Contributions A Abubakar, P M van den Berg and T M Habashy, Application of the multiplicative regularized contrast source inversion method TM- and TE-polarized experimental Fresnel data, present results of profile inversions obtained using the contrast source inversion (CSI) method, in which a multiplicative regularization is plugged in. The authors successfully inverted both TM- and TE-polarized fields. Note that this paper is one of only two contributions which address the inversion of TE-polarized data. A Baussard, Inversion of multi-frequency experimental data using an adaptive multiscale approach, reports results of reconstructions using the modified gradient method (MGM). It suggests that a coarse-to-fine iterative strategy based on spline pyramids. In this iterative technique, the number of degrees of freedom is reduced, which improves robustness. The introduction, during the iterative process, of finer scales inside areas of interest leads to an accurate representation of the object under test. The efficiency of this technique is shown via comparisons between the results obtained with the standard MGM and those from an adaptive approach. L Crocco, M D'Urso and T Isernia, Testing the contrast source extended Born inversion method against real data: the case of TM data, assume that the main contribution in the domain integral formulation comes from the singularity of Green's function, even though the media involved are lossless. A Fourier Bessel analysis of the incident and scattered measured fields is used to derive a model of the incident field and an estimate of the location and size of the target. The iterative procedure lies on a conjugate gradient method associated with Tikhonov regularization, and the multi-frequency data are dealt with using a frequency-hopping approach. In many cases, it is difficult to reconstruct accurately both real and imaginary parts of the permittivity if no prior information is included. M Donelli, D Franceschini, A Massa, M Pastorino and A Zanetti, Multi-resolution iterative inversion of real inhomogeneous targets, adopt a multi-resolution strategy, which, at each step, adaptive discretization of the integral equation is performed over an irregular mesh, with a coarser grid outside the regions of interest and tighter sampling where better resolution is required. Here, this procedure is achieved while keeping the number of unknowns constant. The way such a strategy could be combined with multi-frequency data, edge preserving regularization, or any technique also devoted to improve resolution, remains to be studied. As done by some other contributors, the model of incident field is chosen to fit the Fourier Bessel expansion of the measured one. A Dubois, K Belkebir and M Saillard, Retrieval of inhomogeneous targets from experimental frequency diversity data, present results of the reconstruction of targets using three different non-regularized techniques. It is suggested to minimize a frequency weighted cost function rather than a standard one. The different approaches are compared and discussed. C Estatico, G Bozza, A Massa, M Pastorino and A Randazzo, A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data, use a two nested iterative methods scheme, based on the second-order Born approximation, which is nonlinear in terms of contrast but does not involve the total field. At each step of the outer iteration, the problem is linearized and solved iteratively using the Landweber method. Better reconstructions than with the Born approximation are obtained at low numerical cost. O Feron, B Duchêne and A Mohammad-Djafari, Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data, adopt a Bayesian framework based on a hidden Markov model, built to take into account, as prior knowledge, that the target is composed of a finite number of homogeneous regions. It has been applied to diffraction tomography and to a rigorous formulation of the inverse problem. The latter can be viewed as a Bayesian adaptation of the contrast source method such that prior information about the contrast can be introduced in the prior law distribution, and it results in estimating the posterior mean instead of minimizing a cost functional. The accuracy of the result is thus closely linked to the prior knowledge of the contrast, making this approach well suited for non-destructive testing. J-M Geffrin, P Sabouroux and C Eyraud, Free space experimental scattering database continuation: experimental set-up and measurement precision, describe the experimental set-up used to carry out the data for the inversions. They report the modifications of the experimental system used previously in order to improve the precision of the measurements. Reliability of data is demonstrated through comparisons between measurements and computed scattered field with both fundamental polarizations. In addition, the reader interested in using the database will find the relevant information needed to perform inversions as well as the description of the targets under test. A Litman, Reconstruction by level sets of n-ary scattering obstacles, presents the reconstruction of targets using a level sets representation. It is assumed that the constitutive materials of the obstacles under test are known and the shape is retrieved. Two approaches are reported. In the first one the obstacles of different constitutive materials are represented in a single level set, while in the second approach several level sets are combined. The approaches are applied to the experimental data and compared. U Shahid, M Testorf and M A Fiddy, Minimum-phase-based inverse scattering algorithm applied to Institut Fresnel data, suggest a way of extending the use of minimum phase functions to 2D problems. In the kind of inverse problems we are concerned with, it consists of separating the contributions from the field and from the contrast in the so-called contrast source term, through homomorphic filtering. Images of the targets are obtained by combination with diffraction tomography. Both pre-processing and imaging are thus based on the use of Fourier transforms, making the algorithm very fast compared to classical iterative approaches. It is also pointed out that the design of appropriate filters remains an open topic. C Yu, L-P Song and Q H Liu, Inversion of multi-frequency experimental data for imaging complex objects by a DTA CSI method, use the contrast source inversion (CSI) method for the reconstruction of the targets, in which the initial guess is a solution deduced from another iterative technique based on the diagonal tensor approximation (DTA). In so doing, the authors combine the fast convergence of the DTA method for generating an accurate initial estimate for the CSI method. Note that this paper is one of only two contributions which address the inversion of TE-polarized data. Conclusion In this special section various inverse scattering techniques were used to successfully reconstruct inhomogeneous targets from multi-frequency multi-static measurements. This shows that the database is reliable and can be useful for researchers wanting to test and validate inversion algorithms. From the database, it is also possible to extract subsets to study particular inverse problems, for instance from phaseless data or from `aspect-limited' configurations. Our future efforts will be directed towards extending the database in order to explore inversions from transient fields and the full three-dimensional problem. Acknowledgments The authors would like to thank the Inverse Problems board for opening the journal to us, and offer profound thanks to Elaine Longden-Chapman and Kate Hooper for their help in organizing this special section.

Patterns of genetic variation across inversions: geographic variation in the In(2L)t inversion in populations of Drosophila melanogaster from eastern Australia.

PubMed

Kennington, W Jason; Hoffmann, Ary A

2013-05-20

Chromosomal inversions are increasingly being recognized as important in adaptive shifts and are expected to influence patterns of genetic variation, but few studies have examined genetic patterns in inversion polymorphisms across and within populations. Here, we examine genetic variation at 20 microsatellite loci and the alcohol dehydrogenase gene (Adh) located within and near the In(2L)t inversion of Drosophila melanogaster at three different sites along a latitudinal cline on the east coast of Australia. We found significant genetic differentiation between the standard and inverted chromosomal arrangements at each site as well as significant, but smaller differences among sites in the same arrangement. Genetic differentiation between pairs of sites was higher for inverted chromosomes than standard chromosomes, while inverted chromosomes had lower levels of genetic variation even well away from inversion breakpoints. Bayesian clustering analysis provided evidence of genetic exchange between chromosomal arrangements at each site. The strong differentiation between arrangements and reduced variation in the inverted chromosomes are likely to reflect ongoing selection at multiple loci within the inverted region. They may also reflect lower effective population sizes of In(2L)t chromosomes and colonization of Australia, although there was no consistent evidence of a recent bottleneck and simulations suggest that differences between arrangements would not persist unless rates of gene exchange between them were low. Genetic patterns therefore support the notion of selection and linkage disequilibrium contributing to inversion polymorphisms, although more work is needed to determine whether there are spatially varying targets of selection within this inversion. They also support the idea that the allelic content within an inversion can vary between geographic locations.

Acoustic classification of zooplankton

NASA Astrophysics Data System (ADS)

Martin Traykovski, Linda V.

1998-11-01

Work on the forward problem in zooplankton bioacoustics has resulted in the identification of three categories of acoustic scatterers: elastic-shelled (e.g. pteropods), fluid-like (e.g. euphausiids), and gas-bearing (e.g. siphonophores). The relationship between backscattered energy and animal biomass has been shown to vary by a factor of ~19,000 across these categories, so that to make accurate estimates of zooplankton biomass from acoustic backscatter measurements of the ocean, the acoustic characteristics of the species of interest must be well-understood. This thesis describes the development of both feature based and model based classification techniques to invert broadband acoustic echoes from individual zooplankton for scatterer type, as well as for particular parameters such as animal orientation. The feature based Empirical Orthogonal Function Classifier (EOFC) discriminates scatterer types by identifying characteristic modes of variability in the echo spectra, exploiting only the inherent characteristic structure of the acoustic signatures. The model based Model Parameterisation Classifier (MPC) classifies based on correlation of observed echo spectra with simplified parameterisations of theoretical scattering models for the three classes. The Covariance Mean Variance Classifiers (CMVC) are a set of advanced model based techniques which exploit the full complexity of the theoretical models by searching the entire physical model parameter space without employing simplifying parameterisations. Three different CMVC algorithms were developed: the Integrated Score Classifier (ISC), the Pairwise Score Classifier (PSC) and the Bayesian Probability Classifier (BPC); these classifiers assign observations to a class based on similarities in covariance, mean, and variance, while accounting for model ambiguity and validity. These feature based and model based inversion techniques were successfully applied to several thousand echoes acquired from broadband (~350 kHz-750 kHz) insonifications of live zooplankton collected on Georges Bank and the Gulf of Maine to determine scatterer class. CMVC techniques were also applied to echoes from fluid-like zooplankton (Antarctic krill) to invert for angle of orientation using generic and animal-specific theoretical and empirical models. Application of these inversion techniques in situ will allow correct apportionment of backscattered energy to animal biomass, significantly improving estimates of zooplankton biomass based on acoustic surveys. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Ultra-low velocity zones beneath the Philippine and Tasman Seas revealed by a trans-dimensional Bayesian waveform inversion

NASA Astrophysics Data System (ADS)

Pachhai, Surya; Dettmer, Jan; Tkalčić, Hrvoje

2015-11-01

Ultra-low velocity zones (ULVZs) are small-scale structures in the Earth's lowermost mantle inferred from the analysis of seismological observations. These structures exhibit a strong decrease in compressional (P)-wave velocity, shear (S)-wave velocity, and an increase in density. Quantifying the elastic properties of ULVZs is crucial for understanding their physical origin, which has been hypothesized either as partial melting, iron enrichment, or a combination of the two. Possible disambiguation of these hypotheses can lead to a better understanding of the dynamic processes of the lowermost mantle, such as, percolation, stirring and thermochemical convection. To date, ULVZs have been predominantly studied by forward waveform modelling of seismic waves that sample the core-mantle boundary region. However, ULVZ parameters (i.e. velocity, density, and vertical and lateral extent) obtained through forward modelling are poorly constrained because inferring Earth structure from seismic observations is a non-linear inverse problem with inherent non-uniqueness. To address these issues, we developed a trans-dimensional hierarchical Bayesian inversion that enables rigorous estimation of ULVZ parameter values and their uncertainties, including the effects of model selection. The model selection includes treating the number of layers and the vertical extent of the ULVZ as unknowns. The posterior probability density (solution to the inverse problem) of the ULVZ parameters is estimated by reversible jump Markov chain Monte Carlo sampling that employs parallel tempering to improve efficiency/convergence. First, we apply our method to study the resolution of complex ULVZ structure (including gradually varying structure) by probabilistically inverting simulated noisy waveforms. Then, two data sets sampling the CMB beneath the Philippine and Tasman Seas are considered in the inversion. Our results indicate that both ULVZs are more complex than previously suggested. For the Philippine Sea data, we find a strong decrease in S-wave velocity, which indicates the presence of iron-rich material, albeit this result is accompanied with larger parameter uncertainties than in a previous study. For the Tasman Sea data, our analysis yields a well-constrained S-wave velocity that gradually decreases with depth. We conclude that this ULVZ represents a partial melt of iron-enriched material with higher melt content near its bottom.

Real Variable Inversion of Laplace Transforms: An Application in Plasma Physics.

ERIC Educational Resources Information Center

Bohn, C. L.; Flynn, R. W.

1978-01-01

Discusses the nature of Laplace transform techniques and explains an alternative to them: the Widder's real inversion. To illustrate the power of this new technique, it is applied to a difficult inversion: the problem of Landau damping. (GA)

Isotropic probability measures in infinite dimensional spaces: Inverse problems/prior information/stochastic inversion

NASA Technical Reports Server (NTRS)

Backus, George

1987-01-01

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub n :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity)(P sub n to the -1(B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

Nowcasting Cloud Fields for U.S. Air Force Special Operations

DTIC Science & Technology

2017-03-01

application of Bayes’ Rule offers many advantages over Kernel Density Estimation (KDE) and other commonly used statistical post-processing methods...reflectance and probability of cloud. A statistical post-processing technique is applied using Bayesian estimation to train the system from a set of past...nowcasting, low cloud forecasting, cloud reflectance, ISR, Bayesian estimation, statistical post-processing, machine learning 15. NUMBER OF PAGES

Reducing uncertainty in Climate Response Time Scale by Bayesian Analysis of the 8.2 ka event

NASA Astrophysics Data System (ADS)

Lorenz, A.; Held, H.; Bauer, E.; Schneider von Deimling, T.

2009-04-01

We analyze the possibility of uncertainty reduction in Climate Response Time Scale by utilizing Greenland ice-core data that contain the 8.2 ka event within a Bayesian model-data intercomparison with the Earth system model of intermediate complexity, CLIMBER-2.3. Within a stochastic version of the model it has been possible to mimic the 8.2 ka event within a plausible experimental setting and with relatively good accuracy considering the timing of the event in comparison to other modeling exercises [1]. The simulation of the centennial cold event is effectively determined by the oceanic cooling rate which depends largely on the ocean diffusivity described by diffusion coefficients of relatively wide uncertainty ranges. The idea now is to discriminate between the different values of diffusivities according to their likelihood to rightly represent the duration of the 8.2 ka event and thus to exploit the paleo data to constrain uncertainty in model parameters in analogue to [2]. Implementing this inverse Bayesian Analysis with this model the technical difficulty arises to establish the related likelihood numerically in addition to the uncertain model parameters: While mainstream uncertainty analyses can assume a quasi-Gaussian shape of likelihood, with weather fluctuating around a long term mean, the 8.2 ka event as a highly nonlinear effect precludes such an a priori assumption. As a result of this study [3] the Bayesian Analysis showed a reduction of uncertainty in vertical ocean diffusivity parameters of factor 2 compared to prior knowledge. This learning effect on the model parameters is propagated to other model outputs of interest; e.g. the inverse ocean heat capacity, which is important for the dominant time scale of climate response to anthropogenic forcing which, in combination with climate sensitivity, strongly influences the climate systems reaction for the near- and medium-term future. 1 References [1] E. Bauer, A. Ganopolski, M. Montoya: Simulation of the cold climate event 8200 years ago by meltwater outburst from lake Agassiz. Paleoceanography 19:PA3014, (2004) [2] T. Schneider von Deimling, H. Held, A. Ganopolski, S. Rahmstorf, Climate sensitivity estimated from ensemble simulations of glacial climates, Climate Dynamics 27, 149-163, DOI 10.1007/s00382-006-0126-8 (2006). [3] A. Lorenz, Diploma Thesis, U Potsdam (2007).

Bayesian techniques for analyzing group differences in the Iowa Gambling Task: A case study of intuitive and deliberate decision-makers.

PubMed

Steingroever, Helen; Pachur, Thorsten; Šmíra, Martin; Lee, Michael D

2018-06-01

The Iowa Gambling Task (IGT) is one of the most popular experimental paradigms for comparing complex decision-making across groups. Most commonly, IGT behavior is analyzed using frequentist tests to compare performance across groups, and to compare inferred parameters of cognitive models developed for the IGT. Here, we present a Bayesian alternative based on Bayesian repeated-measures ANOVA for comparing performance, and a suite of three complementary model-based methods for assessing the cognitive processes underlying IGT performance. The three model-based methods involve Bayesian hierarchical parameter estimation, Bayes factor model comparison, and Bayesian latent-mixture modeling. We illustrate these Bayesian methods by applying them to test the extent to which differences in intuitive versus deliberate decision style are associated with differences in IGT performance. The results show that intuitive and deliberate decision-makers behave similarly on the IGT, and the modeling analyses consistently suggest that both groups of decision-makers rely on similar cognitive processes. Our results challenge the notion that individual differences in intuitive and deliberate decision styles have a broad impact on decision-making. They also highlight the advantages of Bayesian methods, especially their ability to quantify evidence in favor of the null hypothesis, and that they allow model-based analyses to incorporate hierarchical and latent-mixture structures.

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

NASA Astrophysics Data System (ADS)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity in the forward problem. We show that using only a limited number of forward solves, the resulting subspaces lead to an efficient method to explore the high-dimensional posterior.

Earth's Outer Core Properties Estimated Using Bayesian Inversion of Normal Mode Eigenfrequencies

NASA Astrophysics Data System (ADS)

Irving, J. C. E.; Cottaar, S.; Lekic, V.

2016-12-01

The outer core is arguably Earth's most dynamic region, and consists of an iron-nickel liquid with an unknown combination of lighter alloying elements. Frequencies of Earth's normal modes provide the strongest constraints on the radial profiles of compressional wavespeed, VΦ, and density, ρ, in the outer core. Recent great earthquakes have yielded new normal mode measurements; however, mineral physics experiments and calculations are often compared to the Preliminary reference Earth model (PREM), which is 35 years old and does not provide uncertainties. Here we investigate the thermo-elastic properties of the outer core using Earth's free oscillations and a Bayesian framework. To estimate radial structure of the outer core and its uncertainties, we choose to exploit recent datasets of normal mode centre frequencies. Under the self-coupling approximation, centre frequencies are unaffected by lateral heterogeneities in the Earth, for example in the mantle. Normal modes are sensitive to both VΦ and ρ in the outer core, with each mode's specific sensitivity depending on its eigenfunctions. We include a priori bounds on outer core models that ensure compatibility with measurements of mass and moment of inertia. We use Bayesian Monte Carlo Markov Chain techniques to explore different choices in parameterizing the outer core, each of which represents different a priori constraints. We test how results vary (1) assuming a smooth polynomial parametrization, (2) allowing for structure close to the outer core's boundaries, (3) assuming an Equation-of-State and adiabaticity and inverting directly for thermo-elastic parameters. In the second approach we recognize that the outer core may have distinct regions close to the core-mantle and inner core boundaries and investigate models which parameterize the well mixed outer core separately from these two layers. In the last approach we seek to map the uncertainties directly into thermo-elastic parameters including the bulk modulus, its pressure derivative, and molar mass and volume, with particular attention paid to the (inherent) trade-offs between the different coefficients. We discuss our results in terms of added uncertainty to the light element composition of the outer core and the potential existence of anomalous structure near the outer core's boundaries.

Calculating shock arrival in expansion tubes and shock tunnels using Bayesian changepoint analysis

NASA Astrophysics Data System (ADS)

James, Christopher M.; Bourke, Emily J.; Gildfind, David E.

2018-06-01

To understand the flow conditions generated in expansion tubes and shock tunnels, shock speeds are generally calculated based on shock arrival times at high-frequency wall-mounted pressure transducers. These calculations require that the shock arrival times are obtained accurately. This can be non-trivial for expansion tubes especially because pressure rises may be small and shock speeds high. Inaccurate shock arrival times can be a significant source of uncertainty. To help address this problem, this paper investigates two separate but complimentary techniques. Principally, it proposes using a Bayesian changepoint detection method to automatically calculate shock arrival, potentially reducing error and simplifying the shock arrival finding process. To compliment this, a technique for filtering the raw data without losing the shock arrival time is also presented and investigated. To test the validity of the proposed techniques, tests are performed using both a theoretical step change with different levels of noise and real experimental data. It was found that with conditions added to ensure that a real shock arrival time was found, the Bayesian changepoint analysis method was able to automatically find the shock arrival time, even for noisy signals.

Bayesian model-emulation of stochastic gravitational-wave spectra for probes of the final-parsec problem with pulsar-timing arrays

NASA Astrophysics Data System (ADS)

Taylor, Stephen R.; Simon, Joseph; Sampson, Laura

2017-01-01

The final parsec of supermassive black-hole binary evolution is subject to the complex interplay of stellar loss-cone scattering, circumbinary disk accretion, and gravitational-wave emission, with binary eccentricity affected by all of these. The strain spectrum of gravitational-waves in the pulsar-timing band thus encodes rich information about the binary population's response to these various environmental mechanisms. Current spectral models have heretofore followed basic analytic prescriptions, and attempt to investigate these final-parsec mechanisms in an indirect fashion. Here we describe a new technique to directly probe the environmental properties of supermassive black-hole binaries through "Bayesian model-emulation". We perform black-hole binary population synthesis simulations at a restricted set of environmental parameter combinations, compute the strain spectra from these, then train a Gaussian process to learn the shape of the spectrum at any point in parameter space. We describe this technique, demonstrate its efficacy with a program of simulated datasets, then illustrate its power by directly constraining final-parsec physics in a Bayesian analysis of the NANOGrav 5-year dataset. The technique is fast, flexible, and robust.

Bayesian model-emulation of stochastic gravitational-wave spectra for probes of the final-parsec problem with pulsar-timing arrays

NASA Astrophysics Data System (ADS)

Taylor, Stephen; Simon, Joseph; Sampson, Laura

2017-01-01

The final parsec of supermassive black-hole binary evolution is subject to the complex interplay of stellar loss-cone scattering, circumbinary disk accretion, and gravitational-wave emission, with binary eccentricity affected by all of these. The strain spectrum of gravitational-waves in the pulsar-timing band thus encodes rich information about the binary population's response to these various environmental mechanisms. Current spectral models have heretofore followed basic analytic prescriptions, and attempt to investigate these final-parsec mechanisms in an indirect fashion. Here we describe a new technique to directly probe the environmental properties of supermassive black-hole binaries through ``Bayesian model-emulation''. We perform black-hole binary population synthesis simulations at a restricted set of environmental parameter combinations, compute the strain spectra from these, then train a Gaussian process to learn the shape of spectrum at any point in parameter space. We describe this technique, demonstrate its efficacy with a program of simulated datasets, then illustrate its power by directly constraining final-parsec physics in a Bayesian analysis of the NANOGrav 5-year dataset. The technique is fast, flexible, and robust.

Flood quantile estimation at ungauged sites by Bayesian networks

NASA Astrophysics Data System (ADS)

Mediero, L.; Santillán, D.; Garrote, L.

2012-04-01

Estimating flood quantiles at a site for which no observed measurements are available is essential for water resources planning and management. Ungauged sites have no observations about the magnitude of floods, but some site and basin characteristics are known. The most common technique used is the multiple regression analysis, which relates physical and climatic basin characteristic to flood quantiles. Regression equations are fitted from flood frequency data and basin characteristics at gauged sites. Regression equations are a rigid technique that assumes linear relationships between variables and cannot take the measurement errors into account. In addition, the prediction intervals are estimated in a very simplistic way from the variance of the residuals in the estimated model. Bayesian networks are a probabilistic computational structure taken from the field of Artificial Intelligence, which have been widely and successfully applied to many scientific fields like medicine and informatics, but application to the field of hydrology is recent. Bayesian networks infer the joint probability distribution of several related variables from observations through nodes, which represent random variables, and links, which represent causal dependencies between them. A Bayesian network is more flexible than regression equations, as they capture non-linear relationships between variables. In addition, the probabilistic nature of Bayesian networks allows taking the different sources of estimation uncertainty into account, as they give a probability distribution as result. A homogeneous region in the Tagus Basin was selected as case study. A regression equation was fitted taking the basin area, the annual maximum 24-hour rainfall for a given recurrence interval and the mean height as explanatory variables. Flood quantiles at ungauged sites were estimated by Bayesian networks. Bayesian networks need to be learnt from a huge enough data set. As observational data are reduced, a stochastic generator of synthetic data was developed. Synthetic basin characteristics were randomised, keeping the statistical properties of observed physical and climatic variables in the homogeneous region. The synthetic flood quantiles were stochastically generated taking the regression equation as basis. The learnt Bayesian network was validated by the reliability diagram, the Brier Score and the ROC diagram, which are common measures used in the validation of probabilistic forecasts. Summarising, the flood quantile estimations through Bayesian networks supply information about the prediction uncertainty as a probability distribution function of discharges is given as result. Therefore, the Bayesian network model has application as a decision support for water resources and planning management.

Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics. Revised

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1999-01-01

A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.

Bayesian Knowledge Fusion in Prognostics and Health Management—A Case Study

NASA Astrophysics Data System (ADS)

Rabiei, Masoud; Modarres, Mohammad; Mohammad-Djafari, Ali

2011-03-01

In the past few years, a research effort has been in progress at University of Maryland to develop a Bayesian framework based on Physics of Failure (PoF) for risk assessment and fleet management of aging airframes. Despite significant achievements in modelling of crack growth behavior using fracture mechanics, it is still of great interest to find practical techniques for monitoring the crack growth instances using nondestructive inspection and to integrate such inspection results with the fracture mechanics models to improve the predictions. The ultimate goal of this effort is to develop an integrated probabilistic framework for utilizing all of the available information to come up with enhanced (less uncertain) predictions for structural health of the aircraft in future missions. Such information includes material level fatigue models and test data, health monitoring measurements and inspection field data. In this paper, a case study of using Bayesian fusion technique for integrating information from multiple sources in a structural health management problem is presented.

Applying a probabilistic seismic-petrophysical inversion and two different rock-physics models for reservoir characterization in offshore Nile Delta

NASA Astrophysics Data System (ADS)

Aleardi, Mattia

2018-01-01

We apply a two-step probabilistic seismic-petrophysical inversion for the characterization of a clastic, gas-saturated, reservoir located in offshore Nile Delta. In particular, we discuss and compare the results obtained when two different rock-physics models (RPMs) are employed in the inversion. The first RPM is an empirical, linear model directly derived from the available well log data by means of an optimization procedure. The second RPM is a theoretical, non-linear model based on the Hertz-Mindlin contact theory. The first step of the inversion procedure is a Bayesian linearized amplitude versus angle (AVA) inversion in which the elastic properties, and the associated uncertainties, are inferred from pre-stack seismic data. The estimated elastic properties constitute the input to the second step that is a probabilistic petrophysical inversion in which we account for the noise contaminating the recorded seismic data and the uncertainties affecting both the derived rock-physics models and the estimated elastic parameters. In particular, a Gaussian mixture a-priori distribution is used to properly take into account the facies-dependent behavior of petrophysical properties, related to the different fluid and rock properties of the different litho-fluid classes. In the synthetic and in the field data tests, the very minor differences between the results obtained by employing the two RPMs, and the good match between the estimated properties and well log information, confirm the applicability of the inversion approach and the suitability of the two different RPMs for reservoir characterization in the investigated area.

Global Monthly CO2 Flux Inversion Based on Results of Terrestrial Ecosystem Modeling

NASA Astrophysics Data System (ADS)

Deng, F.; Chen, J.; Peters, W.; Krol, M.

2008-12-01

Most of our understanding of the sources and sinks of atmospheric CO2 has come from inverse studies of atmospheric CO2 concentration measurements. However, the number of currently available observation stations and our ability to simulate the diurnal planetary boundary layer evolution over continental regions essentially limit the number of regions that can be reliably inverted globally, especially over continental areas. In order to overcome these restrictions, a nested inverse modeling system was developed based on the Bayesian principle for estimating carbon fluxes of 30 regions in North America and 20 regions for the rest of the globe. Inverse modeling was conducted in monthly steps using CO2 concentration measurements of 5 years (2000 - 2005) with the following two models: (a) An atmospheric transport model (TM5) is used to generate the transport matrix where the diurnal variation n of atmospheric CO2 concentration is considered to enhance the use of the afternoon-hour average CO2 concentration measurements over the continental sites. (b) A process-based terrestrial ecosystem model (BEPS) is used to produce hourly step carbon fluxes, which could minimize the limitation due to our inability to solve the inverse problem in a high resolution, as the background of our inversion. We will present our recent results achieved through a combination of the bottom-up modeling with BEPS and the top-down modeling based on TM5 driven by offline meteorological fields generated by the European Centre for Medium Range Weather Forecast (ECMFW).

Nested Global Inversion for the Carbon Flux Distribution in Canada and USA from 1994 to 2003

NASA Astrophysics Data System (ADS)

Chen, J. M.; Deng, F.; Ishizawa, M.; Ju, W.; Mo, G.; Chan, D.; Higuchi, K.; Maksyutov, S.

2007-12-01

Based on TransCom inverse modeling for 22 global regions, we developed a nested global inversion system for estimating carbon fluxes of 30 regions in North America (2 of the 22 regions are divided into 30). Irregular boundaries of these 30 regions are delineated based on ecosystem types and provincial/state borders. Synthesis Bayesian inversion is conducted in monthly steps using CO2 concentration measurements at 88 coastal and continental stations of the globe for the 1994-2003 period (NOAA GlobalView database). Responses of these stations to carbon fluxes from the 50 regions are simulated using the transport model of National Institute for Environmental Studies of Japan and reanalysis wind fields of the National Centers for Environmental Prediction (NCEP). Terrestrial carbon flux fields modeled using BEPS and Biome-BGC driven by NCEP reanalysis meteorological data are used as two different a priori to constrain the inversion. The inversion (top- down) results are compared with remote sensing-based ecosystem modeling (bottom-up) results in Canada's forests and wetlands. There is a broad consistency in the spatial pattern of the carbon source and sink distributions obtained using these two independent methods. Both sets of results also indicate that Canada's forests and wetlands are carbon sinks in 1994-2003, but the top-down method produces consistently larger sinks than the bottom-up results. Reasons for this discrepancy may lie in both methods, and several issues are identified for further investigation.

Atmospheric observations and inverse modelling for quantifying emissions of point-source synthetic greenhouse gases in East Asia

NASA Astrophysics Data System (ADS)

Arnold, Tim; Manning, Alistair; Li, Shanlan; Kim, Jooil; Park, Sunyoung; Muhle, Jens; Weiss, Ray

2017-04-01

The fluorinated species carbon tetrafluoride (CF4; PFC-14), nitrogen trifluoride (NF3) and trifluoromethane (CHF3; HFC-23) are potent greenhouse gases with 100-year global warming potentials of 6,630, 16,100 and 12,400, respectively. Unlike the majority of CFC-replacements that are emitted from fugitive and mobile emission sources, these gases are mostly emitted from large single point sources - semiconductor manufacturing facilities (all three), aluminium smelting plants (CF4) and chlorodifluoromethane (HCFC-22) factories (HFC-23). In this work we show that atmospheric measurements can serve as a basis to calculate emissions of these gases and to highlight emission 'hotspots'. We use measurements from one Advanced Global Atmospheric Gases Experiment (AGAGE) long term monitoring sites at Gosan on Jeju Island in the Republic of Korea. This site measures CF4, NF3 and HFC-23 alongside a suite of greenhouse and stratospheric ozone depleting gases every two hours using automated in situ gas-chromatography mass-spectrometry instrumentation. We couple each measurement to an analysis of air history using the regional atmospheric transport model NAME (Numerical Atmospheric dispersion Modelling Environment) driven by 3D meteorology from the Met Office's Unified Model, and use a Bayesian inverse method (InTEM - Inversion Technique for Emission Modelling) to calculate yearly emission changes over seven years between 2008 and 2015. We show that our 'top-down' emission estimates for NF3 and CF4 are significantly larger than 'bottom-up' estimates in the EDGAR emissions inventory (edgar.jrc.ec.europa.eu). For example we calculate South Korean emissions of CF4 in 2010 to be 0.29±0.04 Gg/yr, which is significantly larger than the Edgar prior emissions of 0.07 Gg/yr. Further, inversions for several separate years indicate that emission hotspots can be found without prior spatial information. At present these gases make a small contribution to global radiative forcing, however, given that the impact of these long-lived gases could rise significantly and that point sources of such gases can be mitigated, atmospheric monitoring could be an important tool for aiding emissions reduction policy.

Imaging the Earth's anisotropic structure with Bayesian Inversion of fundamental and higher mode surface-wave dispersion data

NASA Astrophysics Data System (ADS)

Ravenna, Matteo; Lebedev, Sergei; Celli, Nicolas

2017-04-01

We develop a Markov Chain Monte Carlo inversion of fundamental and higher mode phase-velocity curves for radially and azimuthally anisotropic structure of the crust and upper mantle. In the inversions of Rayleigh- and Love-wave dispersion curves for radially anisotropic structure, we obtain probabilistic 1D radially anisotropic shear-velocity profiles of the isotropic average Vs and anisotropy (or Vsv and Vsh) as functions of depth. In the inversions for azimuthal anisotropy, Rayleigh-wave dispersion curves at different azimuths are inverted for the vertically polarized shear-velocity structure (Vsv) and the 2-phi component of azimuthal anisotropy. The strength and originality of the method is in its fully non-linear approach. Each model realization is computed using exact forward calculations. The uncertainty of the models is a part of the output. In the inversions for azimuthal anisotropy, in particular, the computation of the forward problem is performed separately at different azimuths, with no linear approximations on the relation of the Earth's elastic parameters to surface wave phase velocities. The computations are performed in parallel in order reduce the computing time. We compare inversions of the fundamental mode phase-velocity curves alone with inversions that also include overtones. The addition of higher modes enhances the resolving power of the anisotropic structure of the deep upper mantle. We apply the inversion method to phase-velocity curves in a few regions, including the Hangai dome region in Mongolia. Our models provide constraints on the Moho depth, the Lithosphere-Asthenosphere Boundary, and the alignment of the anisotropic fabric and the direction of current and past flow, from the crust down to the deep asthenosphere.

Joint Inversion of 1-Hz GPS Data and Strong Motion Records for the Rupture Process of the 2008 Iwate-Miyagi Nairiku Earthquake: Objectively Determining Relative Weighting

NASA Astrophysics Data System (ADS)

Wang, Z.; Kato, T.; Wang, Y.

2015-12-01

The spatiotemporal fault slip history of the 2008 Iwate-Miyagi Nairiku earthquake, Japan, is obtained by the joint inversion of 1-Hz GPS waveforms and near-field strong motion records. 1-Hz GPS data from GEONET is processed by GAMIT/GLOBK and then a low-pass filter of 0.05 Hz is applied. The ground surface strong motion records from stations of K-NET and Kik-Net are band-pass filtered for the range of 0.05 ~ 0.3 Hz and integrated once to obtain velocity. The joint inversion exploits a broader frequency band for near-field ground motions, which provides excellent constraints for both the detailed slip history and slip distribution. A fully Bayesian inversion method is performed to simultaneously and objectively determine the rupture model, the unknown relative weighting of multiple data sets and the unknown smoothing hyperparameters. The preferred rupture model is stable for different choices of velocity structure model and station distribution, with maximum slip of ~ 8.0 m and seismic moment of 2.9 × 1019 Nm (Mw 6.9). By comparison with the single inversion of strong motion records, the cumulative slip distribution of joint inversion shows sparser slip distribution with two slip asperities. One common slip asperity extends from the hypocenter southeastward to the ground surface of breakage; another slip asperity, which is unique for joint inversion contributed by 1-Hz GPS waveforms, appears in the deep part of fault where very few aftershocks are occurring. The differential moment rate function of joint and single inversions obviously indicates that rich high frequency waves are radiated in the first three seconds but few low frequency waves.

Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background

NASA Astrophysics Data System (ADS)

McEwen, J. D.; Feeney, S. M.; Peiris, H. V.; Wiaux, Y.; Ringeval, C.; Bouchet, F. R.

2017-12-01

Cosmic strings are a well-motivated extension to the standard cosmological model and could induce a subdominant component in the anisotropies of the cosmic microwave background (CMB), in addition to the standard inflationary component. The detection of strings, while observationally challenging, would provide a direct probe of physics at very high-energy scales. We develop a framework for cosmic string inference from observations of the CMB made over the celestial sphere, performing a Bayesian analysis in wavelet space where the string-induced CMB component has distinct statistical properties to the standard inflationary component. Our wavelet-Bayesian framework provides a principled approach to compute the posterior distribution of the string tension Gμ and the Bayesian evidence ratio comparing the string model to the standard inflationary model. Furthermore, we present a technique to recover an estimate of any string-induced CMB map embedded in observational data. Using Planck-like simulations, we demonstrate the application of our framework and evaluate its performance. The method is sensitive to Gμ ∼ 5 × 10-7 for Nambu-Goto string simulations that include an integrated Sachs-Wolfe contribution only and do not include any recombination effects, before any parameters of the analysis are optimized. The sensitivity of the method compares favourably with other techniques applied to the same simulations.

BAYESIAN SEMI-BLIND COMPONENT SEPARATION FOR FOREGROUND REMOVAL IN INTERFEROMETRIC 21 cm OBSERVATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Le; Timbie, Peter T.; Bunn, Emory F.

In this paper, we present a new Bayesian semi-blind approach for foreground removal in observations of the 21 cm signal measured by interferometers. The technique, which we call H i Expectation–Maximization Independent Component Analysis (HIEMICA), is an extension of the Independent Component Analysis technique developed for two-dimensional (2D) cosmic microwave background maps to three-dimensional (3D) 21 cm cosmological signals measured by interferometers. This technique provides a fully Bayesian inference of power spectra and maps and separates the foregrounds from the signal based on the diversity of their power spectra. Relying only on the statistical independence of the components, this approachmore » can jointly estimate the 3D power spectrum of the 21 cm signal, as well as the 2D angular power spectrum and the frequency dependence of each foreground component, without any prior assumptions about the foregrounds. This approach has been tested extensively by applying it to mock data from interferometric 21 cm intensity mapping observations under idealized assumptions of instrumental effects. We also discuss the impact when the noise properties are not known completely. As a first step toward solving the 21 cm power spectrum analysis problem, we compare the semi-blind HIEMICA technique to the commonly used Principal Component Analysis. Under the same idealized circumstances, the proposed technique provides significantly improved recovery of the power spectrum. This technique can be applied in a straightforward manner to all 21 cm interferometric observations, including epoch of reionization measurements, and can be extended to single-dish observations as well.« less

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies

PubMed Central

2010-01-01

Background Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Results Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Conclusions Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data. PMID:21062443

On the applicability of surrogate-based Markov chain Monte Carlo-Bayesian inversion to the Community Land Model: Case studies at flux tower sites

NASA Astrophysics Data System (ADS)

Huang, Maoyi; Ray, Jaideep; Hou, Zhangshuan; Ren, Huiying; Liu, Ying; Swiler, Laura

2016-07-01

The Community Land Model (CLM) has been widely used in climate and Earth system modeling. Accurate estimation of model parameters is needed for reliable model simulations and predictions under current and future conditions, respectively. In our previous work, a subset of hydrological parameters has been identified to have significant impact on surface energy fluxes at selected flux tower sites based on parameter screening and sensitivity analysis, which indicate that the parameters could potentially be estimated from surface flux observations at the towers. To date, such estimates do not exist. In this paper, we assess the feasibility of applying a Bayesian model calibration technique to estimate CLM parameters at selected flux tower sites under various site conditions. The parameters are estimated as a joint probability density function (PDF) that provides estimates of uncertainty of the parameters being inverted, conditional on climatologically average latent heat fluxes derived from observations. We find that the simulated mean latent heat fluxes from CLM using the calibrated parameters are generally improved at all sites when compared to those obtained with CLM simulations using default parameter sets. Further, our calibration method also results in credibility bounds around the simulated mean fluxes which bracket the measured data. The modes (or maximum a posteriori values) and 95% credibility intervals of the site-specific posterior PDFs are tabulated as suggested parameter values for each site. Analysis of relationships between the posterior PDFs and site conditions suggests that the parameter values are likely correlated with the plant functional type, which needs to be confirmed in future studies by extending the approach to more sites.

Advances in Applications of Hierarchical Bayesian Methods with Hydrological Models

NASA Astrophysics Data System (ADS)

Alexander, R. B.; Schwarz, G. E.; Boyer, E. W.

2017-12-01

Mechanistic and empirical watershed models are increasingly used to inform water resource decisions. Growing access to historical stream measurements and data from in-situ sensor technologies has increased the need for improved techniques for coupling models with hydrological measurements. Techniques that account for the intrinsic uncertainties of both models and measurements are especially needed. Hierarchical Bayesian methods provide an efficient modeling tool for quantifying model and prediction uncertainties, including those associated with measurements. Hierarchical methods can also be used to explore spatial and temporal variations in model parameters and uncertainties that are informed by hydrological measurements. We used hierarchical Bayesian methods to develop a hybrid (statistical-mechanistic) SPARROW (SPAtially Referenced Regression On Watershed attributes) model of long-term mean annual streamflow across diverse environmental and climatic drainages in 18 U.S. hydrological regions. Our application illustrates the use of a new generation of Bayesian methods that offer more advanced computational efficiencies than the prior generation. Evaluations of the effects of hierarchical (regional) variations in model coefficients and uncertainties on model accuracy indicates improved prediction accuracies (median of 10-50%) but primarily in humid eastern regions, where model uncertainties are one-third of those in arid western regions. Generally moderate regional variability is observed for most hierarchical coefficients. Accounting for measurement and structural uncertainties, using hierarchical state-space techniques, revealed the effects of spatially-heterogeneous, latent hydrological processes in the "localized" drainages between calibration sites; this improved model precision, with only minor changes in regional coefficients. Our study can inform advances in the use of hierarchical methods with hydrological models to improve their integration with stream measurements.

Hierarchical Bayesian modeling of spatio-temporal patterns of lung cancer incidence risk in Georgia, USA: 2000-2007

NASA Astrophysics Data System (ADS)

Yin, Ping; Mu, Lan; Madden, Marguerite; Vena, John E.

2014-10-01

Lung cancer is the second most commonly diagnosed cancer in both men and women in Georgia, USA. However, the spatio-temporal patterns of lung cancer risk in Georgia have not been fully studied. Hierarchical Bayesian models are used here to explore the spatio-temporal patterns of lung cancer incidence risk by race and gender in Georgia for the period of 2000-2007. With the census tract level as the spatial scale and the 2-year period aggregation as the temporal scale, we compare a total of seven Bayesian spatio-temporal models including two under a separate modeling framework and five under a joint modeling framework. One joint model outperforms others based on the deviance information criterion. Results show that the northwest region of Georgia has consistently high lung cancer incidence risk for all population groups during the study period. In addition, there are inverse relationships between the socioeconomic status and the lung cancer incidence risk among all Georgian population groups, and the relationships in males are stronger than those in females. By mapping more reliable variations in lung cancer incidence risk at a relatively fine spatio-temporal scale for different Georgian population groups, our study aims to better support healthcare performance assessment, etiological hypothesis generation, and health policy making.

Pollen-Based Inverse Modelling versus Data Assimilation, two Different Ways to Consider Priors in Paleoclimate Reconstruction: Application to the Mediterranean Holocene

NASA Astrophysics Data System (ADS)

Guiot, J.

2017-12-01

In the last decades, climate reconstruction has much evolved. A important step has been passed with inverse modelling approach proposed by Guiot et al (2000). It is based on appropriate algorithms in the frame of the Bayesian statistical theory to estimate the inputs of a vegetation model when the outputs are known. The inputs are the climate variables that we want to reconstruct and the outputs are vegetation characteristics, which can be compared to pollen data. The Bayesian framework consists in defining prior distribution of the wanted climate variables and in using data and a model to estimate posterior probability distribution. The main interest of the method is the possibility to set different values of exogenous variables as the atmospheric CO2 concentration. The fact that the CO2 concentration has an influence on the photosynthesis and that its level is different between the calibration period (the 20th century) and the past, there is an important risk of biases on the reconstructions. After that initial paper, numerous papers have been published showing the interested of the method. In that approach, the prior distribution is fixed by educated guess of by using complementary information on the expected climate (other proxies or other records). In the data assimilation approach, the prior distribution is provided by a climate model. The use of a vegetation model together with proxy data, enable to calculate posterior distributions. Data assimilation consists in constraining climate model to reproduce estimates relatively close to the data, taking into account the respective errors of the data and of the climate model (Dubinkina et al, 2011). We compare both approaches using pollen data for the Holocene from the Mediterranean. Pollen data have been extracted from the European Pollen Database. The earth system model, LOVECLIM, is run to simulate Holocene climate with appropriate boundary conditions and realistic forcing. Simulated climate variables (temperature, precipitation and sunshine) are used as the forcing parameters to a vegetation model, BIOME4, that calculates the equilibrium distribution of vegetation types and associated phenological, hydrological and biogeochemical properties. BIOME4 output, constrained with the pollen observations, are off-line coupled using a particle filter technique.

Bayesian least squares deconvolution

NASA Astrophysics Data System (ADS)

Asensio Ramos, A.; Petit, P.

2015-11-01

Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.

Magnetic resonance separation imaging using a divided inversion recovery technique (DIRT).

PubMed

Goldfarb, James W

2010-04-01

The divided inversion recovery technique is an MRI separation method based on tissue T(1) relaxation differences. When tissue T(1) relaxation times are longer than the time between inversion pulses in a segmented inversion recovery pulse sequence, longitudinal magnetization does not pass through the null point. Prior to additional inversion pulses, longitudinal magnetization may have an opposite polarity. Spatial displacement of tissues in inversion recovery balanced steady-state free-precession imaging has been shown to be due to this magnetization phase change resulting from incomplete magnetization recovery. In this paper, it is shown how this phase change can be used to provide image separation. A pulse sequence parameter, the time between inversion pulses (T180), can be adjusted to provide water-fat or fluid separation. Example water-fat and fluid separation images of the head, heart, and abdomen are presented. The water-fat separation performance was investigated by comparing image intensities in short-axis divided inversion recovery technique images of the heart. Fat, blood, and fluid signal was suppressed to the background noise level. Additionally, the separation performance was not affected by main magnetic field inhomogeneities.

Efficient fuzzy Bayesian inference algorithms for incorporating expert knowledge in parameter estimation

NASA Astrophysics Data System (ADS)

Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad

2016-05-01

Bayesian inference has traditionally been conceived as the proper framework for the formal incorporation of expert knowledge in parameter estimation of groundwater models. However, conventional Bayesian inference is incapable of taking into account the imprecision essentially embedded in expert provided information. In order to solve this problem, a number of extensions to conventional Bayesian inference have been introduced in recent years. One of these extensions is 'fuzzy Bayesian inference' which is the result of integrating fuzzy techniques into Bayesian statistics. Fuzzy Bayesian inference has a number of desirable features which makes it an attractive approach for incorporating expert knowledge in the parameter estimation process of groundwater models: (1) it is well adapted to the nature of expert provided information, (2) it allows to distinguishably model both uncertainty and imprecision, and (3) it presents a framework for fusing expert provided information regarding the various inputs of the Bayesian inference algorithm. However an important obstacle in employing fuzzy Bayesian inference in groundwater numerical modeling applications is the computational burden, as the required number of numerical model simulations often becomes extremely exhaustive and often computationally infeasible. In this paper, a novel approach of accelerating the fuzzy Bayesian inference algorithm is proposed which is based on using approximate posterior distributions derived from surrogate modeling, as a screening tool in the computations. The proposed approach is first applied to a synthetic test case of seawater intrusion (SWI) in a coastal aquifer. It is shown that for this synthetic test case, the proposed approach decreases the number of required numerical simulations by an order of magnitude. Then the proposed approach is applied to a real-world test case involving three-dimensional numerical modeling of SWI in Kish Island, located in the Persian Gulf. An expert elicitation methodology is developed and applied to the real-world test case in order to provide a road map for the use of fuzzy Bayesian inference in groundwater modeling applications.

ANUBIS: artificial neuromodulation using a Bayesian inference system.

PubMed

Smith, Benjamin J H; Saaj, Chakravarthini M; Allouis, Elie

2013-01-01

Gain tuning is a crucial part of controller design and depends not only on an accurate understanding of the system in question, but also on the designer's ability to predict what disturbances and other perturbations the system will encounter throughout its operation. This letter presents ANUBIS (artificial neuromodulation using a Bayesian inference system), a novel biologically inspired technique for automatically tuning controller parameters in real time. ANUBIS is based on the Bayesian brain concept and modifies it by incorporating a model of the neuromodulatory system comprising four artificial neuromodulators. It has been applied to the controller of EchinoBot, a prototype walking rover for Martian exploration. ANUBIS has been implemented at three levels of the controller; gait generation, foot trajectory planning using Bézier curves, and foot trajectory tracking using a terminal sliding mode controller. We compare the results to a similar system that has been tuned using a multilayer perceptron. The use of Bayesian inference means that the system retains mathematical interpretability, unlike other intelligent tuning techniques, which use neural networks, fuzzy logic, or evolutionary algorithms. The simulation results show that ANUBIS provides significant improvements in efficiency and adaptability of the three controller components; it allows the robot to react to obstacles and uncertainties faster than the system tuned with the MLP, while maintaining stability and accuracy. As well as advancing rover autonomy, ANUBIS could also be applied to other situations where operating conditions are likely to change or cannot be accurately modeled in advance, such as process control. In addition, it demonstrates one way in which neuromodulation could fit into the Bayesian brain framework.

A comparison of two worlds: How does Bayes hold up to the status quo for the analysis of clinical trials?

PubMed

Pressman, Alice R; Avins, Andrew L; Hubbard, Alan; Satariano, William A

2011-07-01

There is a paucity of literature comparing Bayesian analytic techniques with traditional approaches for analyzing clinical trials using real trial data. We compared Bayesian and frequentist group sequential methods using data from two published clinical trials. We chose two widely accepted frequentist rules, O'Brien-Fleming and Lan-DeMets, and conjugate Bayesian priors. Using the nonparametric bootstrap, we estimated a sampling distribution of stopping times for each method. Because current practice dictates the preservation of an experiment-wise false positive rate (Type I error), we approximated these error rates for our Bayesian and frequentist analyses with the posterior probability of detecting an effect in a simulated null sample. Thus for the data-generated distribution represented by these trials, we were able to compare the relative performance of these techniques. No final outcomes differed from those of the original trials. However, the timing of trial termination differed substantially by method and varied by trial. For one trial, group sequential designs of either type dictated early stopping of the study. In the other, stopping times were dependent upon the choice of spending function and prior distribution. Results indicate that trialists ought to consider Bayesian methods in addition to traditional approaches for analysis of clinical trials. Though findings from this small sample did not demonstrate either method to consistently outperform the other, they did suggest the need to replicate these comparisons using data from varied clinical trials in order to determine the conditions under which the different methods would be most efficient. Copyright © 2011 Elsevier Inc. All rights reserved.

A comparison of two worlds: How does Bayes hold up to the status quo for the analysis of clinical trials?

PubMed Central

Pressman, Alice R.; Avins, Andrew L.; Hubbard, Alan; Satariano, William A.

2014-01-01

Background There is a paucity of literature comparing Bayesian analytic techniques with traditional approaches for analyzing clinical trials using real trial data. Methods We compared Bayesian and frequentist group sequential methods using data from two published clinical trials. We chose two widely accepted frequentist rules, O'Brien–Fleming and Lan–DeMets, and conjugate Bayesian priors. Using the nonparametric bootstrap, we estimated a sampling distribution of stopping times for each method. Because current practice dictates the preservation of an experiment-wise false positive rate (Type I error), we approximated these error rates for our Bayesian and frequentist analyses with the posterior probability of detecting an effect in a simulated null sample. Thus for the data-generated distribution represented by these trials, we were able to compare the relative performance of these techniques. Results No final outcomes differed from those of the original trials. However, the timing of trial termination differed substantially by method and varied by trial. For one trial, group sequential designs of either type dictated early stopping of the study. In the other, stopping times were dependent upon the choice of spending function and prior distribution. Conclusions Results indicate that trialists ought to consider Bayesian methods in addition to traditional approaches for analysis of clinical trials. Though findings from this small sample did not demonstrate either method to consistently outperform the other, they did suggest the need to replicate these comparisons using data from varied clinical trials in order to determine the conditions under which the different methods would be most efficient. PMID:21453792

Comparing models for quantitative risk assessment: an application to the European Registry of foreign body injuries in children.

PubMed

Berchialla, Paola; Scarinzi, Cecilia; Snidero, Silvia; Gregori, Dario

2016-08-01

Risk Assessment is the systematic study of decisions subject to uncertain consequences. An increasing interest has been focused on modeling techniques like Bayesian Networks since their capability of (1) combining in the probabilistic framework different type of evidence including both expert judgments and objective data; (2) overturning previous beliefs in the light of the new information being received and (3) making predictions even with incomplete data. In this work, we proposed a comparison among Bayesian Networks and other classical Quantitative Risk Assessment techniques such as Neural Networks, Classification Trees, Random Forests and Logistic Regression models. Hybrid approaches, combining both Classification Trees and Bayesian Networks, were also considered. Among Bayesian Networks, a clear distinction between purely data-driven approach and combination of expert knowledge with objective data is made. The aim of this paper consists in evaluating among this models which best can be applied, in the framework of Quantitative Risk Assessment, to assess the safety of children who are exposed to the risk of inhalation/insertion/aspiration of consumer products. The issue of preventing injuries in children is of paramount importance, in particular where product design is involved: quantifying the risk associated to product characteristics can be of great usefulness in addressing the product safety design regulation. Data of the European Registry of Foreign Bodies Injuries formed the starting evidence for risk assessment. Results showed that Bayesian Networks appeared to have both the ease of interpretability and accuracy in making prediction, even if simpler models like logistic regression still performed well. © The Author(s) 2013.

A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Jin; Yu, Yaming; Van Dyk, David A.

2014-10-20

Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use amore » principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.« less

Towards quantifying uncertainty in Greenland's contribution to 21st century sea-level rise

NASA Astrophysics Data System (ADS)

Perego, M.; Tezaur, I.; Price, S. F.; Jakeman, J.; Eldred, M.; Salinger, A.; Hoffman, M. J.

2015-12-01

We present recent work towards developing a methodology for quantifying uncertainty in Greenland's 21st century contribution to sea-level rise. While we focus on uncertainties associated with the optimization and calibration of the basal sliding parameter field, the methodology is largely generic and could be applied to other (or multiple) sets of uncertain model parameter fields. The first step in the workflow is the solution of a large-scale, deterministic inverse problem, which minimizes the mismatch between observed and computed surface velocities by optimizing the two-dimensional coefficient field in a linear-friction sliding law. We then expand the deviation in this coefficient field from its estimated "mean" state using a reduced basis of Karhunen-Loeve Expansion (KLE) vectors. A Bayesian calibration is used to determine the optimal coefficient values for this expansion. The prior for the Bayesian calibration can be computed using the Hessian of the deterministic inversion or using an exponential covariance kernel. The posterior distribution is then obtained using Markov Chain Monte Carlo run on an emulator of the forward model. Finally, the uncertainty in the modeled sea-level rise is obtained by performing an ensemble of forward propagation runs. We present and discuss preliminary results obtained using a moderate-resolution model of the Greenland Ice sheet. As demonstrated in previous work, the primary difficulty in applying the complete workflow to realistic, high-resolution problems is that the effective dimension of the parameter space is very large.

Imaging Anisotropic Layering with Bayesian Inversion of Multiple Data Types

NASA Astrophysics Data System (ADS)

Bodin, T.; Leiva, J.; Romanowicz, B. A.; Maupin, V.; Yuan, H.

2015-12-01

Anisotropic images of the upper-mantle are usually obtained by analyzing different types of seismic observables, such as surface wave dispersion curves or waveforms, SKS splitting data, or receiver functions. These different data types sample different volumes of the earth, they are sensitive to separate length-scales, and hence are associated with various levels of uncertainties. They are traditionally interpreted separately, and often result in incompatible models. We present a Bayesian inversion approach to jointly invert these different data types. Seismograms for SKS and P phases are directly inverted, thus avoiding intermediate processing steps such as numerical deconvolution or computation of splitting parameters. Probabilistic 1D profiles are obtained with a transdimensional Markov chain Monte Carlo scheme, in which the number of layers, as well as the presence or absence of anisotropy in each layer, are treated as unknown parameters. In this way, seismic anisotropy is only introduced if required by the data. The algorithm is used to resolve both isotropic and anisotropic layering down to a depth of 350 km beneath two seismic stations in North America in two different tectonic settings: the stable Canadian shield (station FFC), and the tectonically active southern Basin and Range Province (station TA-214A). In both cases, the lithosphere-asthenosphere boundary is clearly visible, and marked by a change in direction of the fast axis of anisotropy. Our study confirms that azimuthal anisotropy is a powerful tool for detecting layering in the upper mantle.

Multilevel Sequential2 Monte Carlo for Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Latz, Jonas; Papaioannou, Iason; Ullmann, Elisabeth

2018-09-01

The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior information to estimate the posterior distribution of a parameter. Specifically, we are interested in the distribution of a diffusion coefficient of an elliptic PDE. In this setting, the sample space is high-dimensional, and each sample of the PDE solution is expensive. To address these issues we propose and analyse a novel Sequential Monte Carlo (SMC) sampler for the approximation of the posterior distribution. Classical, single-level SMC constructs a sequence of measures, starting with the prior distribution, and finishing with the posterior distribution. The intermediate measures arise from a tempering of the likelihood, or, equivalently, a rescaling of the noise. The resolution of the PDE discretisation is fixed. In contrast, our estimator employs a hierarchy of PDE discretisations to decrease the computational cost. We construct a sequence of intermediate measures by decreasing the temperature or by increasing the discretisation level at the same time. This idea builds on and generalises the multi-resolution sampler proposed in P.S. Koutsourelakis (2009) [33] where a bridging scheme is used to transfer samples from coarse to fine discretisation levels. Importantly, our choice between tempering and bridging is fully adaptive. We present numerical experiments in 2D space, comparing our estimator to single-level SMC and the multi-resolution sampler.

Landslide caracteristics determination using bayesian inversion and seismic recording

NASA Astrophysics Data System (ADS)

Mangeney, A.; Moretti, L.; Capdeville, Y.; Stutzmann, E.; Bodin, T.; Bouchut, F.

2014-12-01

Gravitational instabilities, such as landslides, avalanches, or debris flows, play a key role in erosional processes and represent one of the major natural hazards in mountainous, coastal, and volcanic regions. Despite the great amount of field, experimental and numerical work devoted to this problem, the understanding of the physical processes at work in gravitational flows is still an open issue, in particular due to the lack of observations relevant to their dynamics. In this context, the seismic signal generated by gravitational flows is a unique opportunity to obtain information on their dynamics and characteristics. Here we present the study of the 1997 Boxing Day landslide that occurred in Montserrat. We accessed the force applied by the landslide to the ground surface responsible of the seismic waves by inverting the seismic waveform recorded (force-time function). This force was then used as a constraint in a bayesian inversion problem where the forward problem is the force-time function calculation obtained by simulating the landslide with the SHALTOP model (mangeney et al., 2007). With this method, we are able to give an estimate of the rheology (friction coefficient) and the initial shape of the collapsing mass. The volume retrieved is very similar to that obtained by field observations. The friction coefficient determined is also similar to that constrained by former studies or to that predicted by empirical laws (Lucas et al., 2014). Furthermore the method permits to give an estimate of the error made on these parameters.

Joint analysis of input and parametric uncertainties in watershed water quality modeling: A formal Bayesian approach

NASA Astrophysics Data System (ADS)

Han, Feng; Zheng, Yi

2018-06-01

Significant Input uncertainty is a major source of error in watershed water quality (WWQ) modeling. It remains challenging to address the input uncertainty in a rigorous Bayesian framework. This study develops the Bayesian Analysis of Input and Parametric Uncertainties (BAIPU), an approach for the joint analysis of input and parametric uncertainties through a tight coupling of Markov Chain Monte Carlo (MCMC) analysis and Bayesian Model Averaging (BMA). The formal likelihood function for this approach is derived considering a lag-1 autocorrelated, heteroscedastic, and Skew Exponential Power (SEP) distributed error model. A series of numerical experiments were performed based on a synthetic nitrate pollution case and on a real study case in the Newport Bay Watershed, California. The Soil and Water Assessment Tool (SWAT) and Differential Evolution Adaptive Metropolis (DREAM(ZS)) were used as the representative WWQ model and MCMC algorithm, respectively. The major findings include the following: (1) the BAIPU can be implemented and used to appropriately identify the uncertain parameters and characterize the predictive uncertainty; (2) the compensation effect between the input and parametric uncertainties can seriously mislead the modeling based management decisions, if the input uncertainty is not explicitly accounted for; (3) the BAIPU accounts for the interaction between the input and parametric uncertainties and therefore provides more accurate calibration and uncertainty results than a sequential analysis of the uncertainties; and (4) the BAIPU quantifies the credibility of different input assumptions on a statistical basis and can be implemented as an effective inverse modeling approach to the joint inference of parameters and inputs.

Integration of Geophysical Data into Structural Geological Modelling through Bayesian Networks

NASA Astrophysics Data System (ADS)

de la Varga, Miguel; Wellmann, Florian; Murdie, Ruth

2016-04-01

Structural geological models are widely used to represent the spatial distribution of relevant geological features. Several techniques exist to construct these models on the basis of different assumptions and different types of geological observations (e.g. Jessell et al., 2014). However, two problems are prevalent when constructing models: (i) observations and assumptions, and therefore also the constructed model, are subject to uncertainties, and (ii) additional information, such as geophysical data, is often available, but cannot be considered directly in the geological modelling step. In our work, we propose the integration of all available data into a Bayesian network including the generation of the implicit geological method by means of interpolation functions (Mallet, 1992; Lajaunie et al., 1997; Mallet, 2004; Carr et al., 2001; Hillier et al., 2014). As a result, we are able to increase the certainty of the resultant models as well as potentially learn features of our regional geology through data mining and information theory techniques. MCMC methods are used in order to optimize computational time and assure the validity of the results. Here, we apply the aforementioned concepts in a 3-D model of the Sandstone Greenstone Belt in the Archean Yilgarn Craton in Western Australia. The example given, defines the uncertainty in the thickness of greenstone as limited by Bouguer anomaly and the internal structure of the greenstone as limited by the magnetic signature of a banded iron formation. The incorporation of the additional data and specially the gravity provides an important reduction of the possible outcomes and therefore the overall uncertainty. References Carr, C. J., K. R. Beatson, B. J. Cherrie, J. T. Mitchell, R. W. Fright, C. B. McCallum, and R. T. Evans, 2001, Reconstruction and representation of 3D objects with radial basis functions: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, 67-76. Jessell, M., Aillères, L., de Kemp, E., Lindsay, M., Wellmann, F., Hillier, M., ... & Martin, R. (2014). Next Generation Three-Dimensional Geologic Modeling and Inversion. Lajaunie, C., G. Courrioux, and L. Manuel, 1997, Foliation fields and 3D cartography in geology: Principles of a method based on potential interpolation: Mathematical Geology, 29, 571-584. Mallet, J.-L., 1992, Discrete smooth interpolation in geometric modelling: Computer-Aided Design, 24, 178-191 Mallet, L. J., 2004, Space-time mathematical framework for sedimentary geology: Mathematical Geology, 36, 1-32.

Parallelization of a spatial random field characterization process using the Method of Anchored Distributions and the HTCondor high throughput computing system

NASA Astrophysics Data System (ADS)

Osorio-Murillo, C. A.; Over, M. W.; Frystacky, H.; Ames, D. P.; Rubin, Y.

2013-12-01

A new software application called MAD# has been coupled with the HTCondor high throughput computing system to aid scientists and educators with the characterization of spatial random fields and enable understanding the spatial distribution of parameters used in hydrogeologic and related modeling. MAD# is an open source desktop software application used to characterize spatial random fields using direct and indirect information through Bayesian inverse modeling technique called the Method of Anchored Distributions (MAD). MAD relates indirect information with a target spatial random field via a forward simulation model. MAD# executes inverse process running the forward model multiple times to transfer information from indirect information to the target variable. MAD# uses two parallelization profiles according to computational resources available: one computer with multiple cores and multiple computers - multiple cores through HTCondor. HTCondor is a system that manages a cluster of desktop computers for submits serial or parallel jobs using scheduling policies, resources monitoring, job queuing mechanism. This poster will show how MAD# reduces the time execution of the characterization of random fields using these two parallel approaches in different case studies. A test of the approach was conducted using 1D problem with 400 cells to characterize saturated conductivity, residual water content, and shape parameters of the Mualem-van Genuchten model in four materials via the HYDRUS model. The number of simulations evaluated in the inversion was 10 million. Using the one computer approach (eight cores) were evaluated 100,000 simulations in 12 hours (10 million - 1200 hours approximately). In the evaluation on HTCondor, 32 desktop computers (132 cores) were used, with a processing time of 60 hours non-continuous in five days. HTCondor reduced the processing time for uncertainty characterization by a factor of 20 (1200 hours reduced to 60 hours.)

Probabilistic estimation of splitting coefficients of normal modes of the Earth, and their uncertainties, using an autoregressive technique

NASA Astrophysics Data System (ADS)

Pachhai, S.; Masters, G.; Laske, G.

2017-12-01

Earth's normal-mode spectra are crucial to studying the long wavelength structure of the Earth. Such observations have been used extensively to estimate "splitting coefficients" which, in turn, can be used to determine the three-dimensional velocity and density structure. Most past studies apply a non-linear iterative inversion to estimate the splitting coefficients which requires that the earthquake source is known. However, it is challenging to know the source details, particularly for big events as used in normal-mode analyses. Additionally, the final solution of the non-linear inversion can depend on the choice of damping parameter and starting model. To circumvent the need to know the source, a two-step linear inversion has been developed and successfully applied to many mantle and core sensitive modes. The first step takes combinations of the data from a single event to produce spectra known as "receiver strips". The autoregressive nature of the receiver strips can then be used to estimate the structure coefficients without the need to know the source. Based on this approach, we recently employed a neighborhood algorithm to measure the splitting coefficients for an isolated inner-core sensitive mode (13S2). This approach explores the parameter space efficiently without any need of regularization and finds the structure coefficients which best fit the observed strips. Here, we implement a Bayesian approach to data collected for earthquakes from early 2000 and more recent. This approach combines the data (through likelihood) and prior information to provide rigorous parameter values and their uncertainties for both isolated and coupled modes. The likelihood function is derived from the inferred errors of the receiver strips which allows us to retrieve proper uncertainties. Finally, we apply model selection criteria that balance the trade-offs between fit (likelihood) and model complexity to investigate the degree and type of structure (elastic and anelastic) required to explain the data.

Dealing with non-unique and non-monotonic response in particle sizing instruments

NASA Astrophysics Data System (ADS)

Rosenberg, Phil

2017-04-01

A number of instruments used as de-facto standards for measuring particle size distributions are actually incapable of uniquely determining the size of an individual particle. This is due to non-unique or non-monotonic response functions. Optical particle counters have non monotonic response due to oscillations in the Mie response curves, especially for large aerosol and small cloud droplets. Scanning mobility particle sizers respond identically to two particles where the ratio of particle size to particle charge is approximately the same. Images of two differently sized cloud or precipitation particles taken by an optical array probe can have similar dimensions or shadowed area depending upon where they are in the imaging plane. A number of methods exist to deal with these issues, including assuming that positive and negative errors cancel, smoothing response curves, integrating regions in measurement space before conversion to size space and matrix inversion. Matrix inversion (also called kernel inversion) has the advantage that it determines the size distribution which best matches the observations, given specific information about the instrument (a matrix which specifies the probability that a particle of a given size will be measured in a given instrument size bin). In this way it maximises use of the information in the measurements. However this technique can be confused by poor counting statistics which can cause erroneous results and negative concentrations. Also an effective method for propagating uncertainties is yet to be published or routinely implemented. Her we present a new alternative which overcomes these issues. We use Bayesian methods to determine the probability that a given size distribution is correct given a set of instrument data and then we use Markov Chain Monte Carlo methods to sample this many dimensional probability distribution function to determine the expectation and (co)variances - hence providing a best guess and an uncertainty for the size distribution which includes contributions from the non-unique response curve, counting statistics and can propagate calibration uncertainties.

Three-dimensional mapping of the local interstellar medium with composite data

NASA Astrophysics Data System (ADS)

Capitanio, L.; Lallement, R.; Vergely, J. L.; Elyajouri, M.; Monreal-Ibero, A.

2017-10-01

Context. Three-dimensional maps of the Galactic interstellar medium are general astrophysical tools. Reddening maps may be based on the inversion of color excess measurements for individual target stars or on statistical methods using stellar surveys. Three-dimensional maps based on diffuse interstellar bands (DIBs) have also been produced. All methods benefit from the advent of massive surveys and may benefit from Gaia data. Aims: All of the various methods and databases have their own advantages and limitations. Here we present a first attempt to combine different datasets and methods to improve the local maps. Methods: We first updated our previous local dust maps based on a regularized Bayesian inversion of individual color excess data by replacing Hipparcos or photometric distances with Gaia Data Release 1 values when available. Secondly, we complemented this database with a series of ≃5000 color excess values estimated from the strength of the λ15273 DIB toward stars possessing a Gaia parallax. The DIB strengths were extracted from SDSS/APOGEE spectra. Third, we computed a low-resolution map based on a grid of Pan-STARRS reddening measurements by means of a new hierarchical technique and used this map as the prior distribution during the inversion of the two other datasets. Results: The use of Gaia parallaxes introduces significant changes in some areas and globally increases the compactness of the structures. Additional DIB-based data make it possible to assign distances to clouds located behind closer opaque structures and do not introduce contradictory information for the close structures. A more realistic prior distribution instead of a plane-parallel homogeneous distribution helps better define the structures. We validated the results through comparisons with other maps and with soft X-ray data. Conclusions: Our study demonstrates that the combination of various tracers is a potential tool for more accurate maps. An online tool makes it possible to retrieve maps and reddening estimations. Our online tool is available at http://stilism.obspm.fr

Direct Estimation of Optical Parameters From Photoacoustic Time Series in Quantitative Photoacoustic Tomography.

PubMed

Pulkkinen, Aki; Cox, Ben T; Arridge, Simon R; Goh, Hwan; Kaipio, Jari P; Tarvainen, Tanja

2016-11-01

Estimation of optical absorption and scattering of a target is an inverse problem associated with quantitative photoacoustic tomography. Conventionally, the problem is expressed as two folded. First, images of initial pressure distribution created by absorption of a light pulse are formed based on acoustic boundary measurements. Then, the optical properties are determined based on these photoacoustic images. The optical stage of the inverse problem can thus suffer from, for example, artefacts caused by the acoustic stage. These could be caused by imperfections in the acoustic measurement setting, of which an example is a limited view acoustic measurement geometry. In this work, the forward model of quantitative photoacoustic tomography is treated as a coupled acoustic and optical model and the inverse problem is solved by using a Bayesian approach. Spatial distribution of the optical properties of the imaged target are estimated directly from the photoacoustic time series in varying acoustic detection and optical illumination configurations. It is numerically demonstrated, that estimation of optical properties of the imaged target is feasible in limited view acoustic detection setting.

Bayesian prestack seismic inversion with a self-adaptive Huber-Markov random-field edge protection scheme

NASA Astrophysics Data System (ADS)

Tian, Yu-Kun; Zhou, Hui; Chen, Han-Ming; Zou, Ya-Ming; Guan, Shou-Jun

2013-12-01

Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., the Tikhonov regularization are usually applied. The Tikhonov method can maintain a global smooth solution, but cause a fuzzy structure edge. In this paper we use Huber-Markov random-field edge protection method in the procedure of inverting three parameters, P-velocity, S-velocity and density. The method can avoid blurring the structure edge and resist noise. For the parameter to be inverted, the Huber-Markov random-field constructs a neighborhood system, which further acts as the vertical and lateral constraints. We use a quadratic Huber edge penalty function within the layer to suppress noise and a linear one on the edges to avoid a fuzzy result. The effectiveness of our method is proved by inverting the synthetic data without and with noises. The relationship between the adopted constraints and the inversion results is analyzed as well.

Bayesian techniques for surface fuel loading estimation

Treesearch

Kathy Gray; Robert Keane; Ryan Karpisz; Alyssa Pedersen; Rick Brown; Taylor Russell

2016-01-01

A study by Keane and Gray (2013) compared three sampling techniques for estimating surface fine woody fuels. Known amounts of fine woody fuel were distributed on a parking lot, and researchers estimated the loadings using different sampling techniques. An important result was that precise estimates of biomass required intensive sampling for both the planar intercept...

BaTMAn: Bayesian Technique for Multi-image Analysis

NASA Astrophysics Data System (ADS)

Casado, J.; Ascasibar, Y.; García-Benito, R.; Guidi, G.; Choudhury, O. S.; Bellocchi, E.; Sánchez, S. F.; Díaz, A. I.

2016-12-01

Bayesian Technique for Multi-image Analysis (BaTMAn) characterizes any astronomical dataset containing spatial information and performs a tessellation based on the measurements and errors provided as input. The algorithm iteratively merges spatial elements as long as they are statistically consistent with carrying the same information (i.e. identical signal within the errors). The output segmentations successfully adapt to the underlying spatial structure, regardless of its morphology and/or the statistical properties of the noise. BaTMAn identifies (and keeps) all the statistically-significant information contained in the input multi-image (e.g. an IFS datacube). The main aim of the algorithm is to characterize spatially-resolved data prior to their analysis.

Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data.

PubMed

Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

2017-01-01

Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

PRIFIRA: General regularization using prior-conditioning for fast radio interferometric imaging†

NASA Astrophysics Data System (ADS)

Naghibzadeh, Shahrzad; van der Veen, Alle-Jan

2018-06-01

Image formation in radio astronomy is a large-scale inverse problem that is inherently ill-posed. We present a general algorithmic framework based on a Bayesian-inspired regularized maximum likelihood formulation of the radio astronomical imaging problem with a focus on diffuse emission recovery from limited noisy correlation data. The algorithm is dubbed PRIor-conditioned Fast Iterative Radio Astronomy (PRIFIRA) and is based on a direct embodiment of the regularization operator into the system by right preconditioning. The resulting system is then solved using an iterative method based on projections onto Krylov subspaces. We motivate the use of a beamformed image (which includes the classical "dirty image") as an efficient prior-conditioner. Iterative reweighting schemes generalize the algorithmic framework and can account for different regularization operators that encourage sparsity of the solution. The performance of the proposed method is evaluated based on simulated one- and two-dimensional array arrangements as well as actual data from the core stations of the Low Frequency Array radio telescope antenna configuration, and compared to state-of-the-art imaging techniques. We show the generality of the proposed method in terms of regularization schemes while maintaining a competitive reconstruction quality with the current reconstruction techniques. Furthermore, we show that exploiting Krylov subspace methods together with the proper noise-based stopping criteria results in a great improvement in imaging efficiency.

Diagnostic accuracy of a bayesian latent group analysis for the detection of malingering-related poor effort.

PubMed

Ortega, Alonso; Labrenz, Stephan; Markowitsch, Hans J; Piefke, Martina

2013-01-01

In the last decade, different statistical techniques have been introduced to improve assessment of malingering-related poor effort. In this context, we have recently shown preliminary evidence that a Bayesian latent group model may help to optimize classification accuracy using a simulation research design. In the present study, we conducted two analyses. Firstly, we evaluated how accurately this Bayesian approach can distinguish between participants answering in an honest way (honest response group) and participants feigning cognitive impairment (experimental malingering group). Secondly, we tested the accuracy of our model in the differentiation between patients who had real cognitive deficits (cognitively impaired group) and participants who belonged to the experimental malingering group. All Bayesian analyses were conducted using the raw scores of a visual recognition forced-choice task (2AFC), the Test of Memory Malingering (TOMM, Trial 2), and the Word Memory Test (WMT, primary effort subtests). The first analysis showed 100% accuracy for the Bayesian model in distinguishing participants of both groups with all effort measures. The second analysis showed outstanding overall accuracy of the Bayesian model when estimates were obtained from the 2AFC and the TOMM raw scores. Diagnostic accuracy of the Bayesian model diminished when using the WMT total raw scores. Despite, overall diagnostic accuracy can still be considered excellent. The most plausible explanation for this decrement is the low performance in verbal recognition and fluency tasks of some patients of the cognitively impaired group. Additionally, the Bayesian model provides individual estimates, p(zi |D), of examinees' effort levels. In conclusion, both high classification accuracy levels and Bayesian individual estimates of effort may be very useful for clinicians when assessing for effort in medico-legal settings.

Electrical source imaging of interictal spikes using multiple sparse volumetric priors for presurgical epileptogenic focus localization

PubMed Central

Strobbe, Gregor; Carrette, Evelien; López, José David; Montes Restrepo, Victoria; Van Roost, Dirk; Meurs, Alfred; Vonck, Kristl; Boon, Paul; Vandenberghe, Stefaan; van Mierlo, Pieter

2016-01-01

Electrical source imaging of interictal spikes observed in EEG recordings of patients with refractory epilepsy provides useful information to localize the epileptogenic focus during the presurgical evaluation. However, the selection of the time points or time epochs of the spikes in order to estimate the origin of the activity remains a challenge. In this study, we consider a Bayesian EEG source imaging technique for distributed sources, i.e. the multiple volumetric sparse priors (MSVP) approach. The approach allows to estimate the time courses of the intensity of the sources corresponding with a specific time epoch of the spike. Based on presurgical averaged interictal spikes in six patients who were successfully treated with surgery, we estimated the time courses of the source intensities for three different time epochs: (i) an epoch starting 50 ms before the spike peak and ending at 50% of the spike peak during the rising phase of the spike, (ii) an epoch starting 50 ms before the spike peak and ending at the spike peak and (iii) an epoch containing the full spike time period starting 50 ms before the spike peak and ending 230 ms after the spike peak. To identify the primary source of the spike activity, the source with the maximum energy from 50 ms before the spike peak till 50% of the spike peak was subsequently selected for each of the time windows. For comparison, the activity at the spike peaks and at 50% of the peaks was localized using the LORETA inversion technique and an ECD approach. Both patient-specific spherical forward models and patient-specific 5-layered finite difference models were considered to evaluate the influence of the forward model. Based on the resected zones in each of the patients, extracted from post-operative MR images, we compared the distances to the resection border of the estimated activity. Using the spherical models, the distances to the resection border for the MSVP approach and each of the different time epochs were in the same range as the LORETA and ECD techniques. We found distances smaller than 23 mm, with robust results for all the patients. For the finite difference models, we found that the distances to the resection border for the MSVP inversions of the full spike time epochs were generally smaller compared to the MSVP inversions of the time epochs before the spike peak. The results also suggest that the inversions using the finite difference models resulted in slightly smaller distances to the resection border compared to the spherical models. The results we obtained are promising because the MSVP approach allows to study the network of the estimated source-intensities and allows to characterize the spatial extent of the underlying sources. PMID:26958464

Improving estimates of N2O emissions for western and central Europe using a Bayesian inversion approach

NASA Astrophysics Data System (ADS)

Thompson, R. L.; Gerbig, C.; Roedenbeck, C.; Heimann, M.

2009-04-01

The nitrous oxide (N2O) mixing ratio has been increasing in the atmosphere since the industrial revolution, from 270 ppb in 1750 to 320 ppb in 2007 with a steady growth rate of around 0.26% since the early 1980's. The increase in N2O is worrisome for two main reasons. First, it is a greenhouse gas; this means that its atmospheric increase translates to an enhancement in radiative forcing of 0.16 ± 0.02 Wm-2 making it currently the fourth most important long-lived greenhouse gas and is predicted to soon overtake CFC's to become the third most important. Second, it plays an important role in stratospheric ozone chemistry. Human activities are the primary cause of the atmospheric N2O increase. The largest anthropogenic source of N2O is from the use of N-fertilizers in agriculture but fossil fuel combustion and industrial processes, such as adipic and nitric acid production, are also important. We present a Bayesian inversion approach for estimating N2O fluxes over central and western Europe using high frequency in-situ concentration data from the Ochsenkopf tall tower (50 °01′N, 11 °48′, 1022 masl). For the inversion, we employ a Lagrangian-type transport model, STILT, which provides source-receptor relationships at 10 km using ECMWF meteorological data. The a priori flux estimates used were from IER, for anthropogenic, and GEIA, for natural fluxes. N2O fluxes were retrieved monthly at 2 x 2 degree spatial resolution for 2007. The retrieved N2O fluxes showed significantly more spatial heterogeneity than in the a priori field and considerable seasonal variability. The timing of peak emissions was different for different regions but in general the months with the strongest emissions were May and August. Overall, the retrieved flux (anthropogenic and natural) was lower than in the a priori field.

North American Crust and Upper Mantle Structure Imaged Using an Adaptive Bayesian Inversion

NASA Astrophysics Data System (ADS)

Eilon, Z.; Fischer, K. M.; Dalton, C. A.

2017-12-01

We present a methodology for imaging upper mantle structure using a Bayesian approach that incorporates a novel combination of seismic data types and an adaptive parameterization based on piecewise discontinuous splines. Our inversion algorithm lays the groundwork for improved seismic velocity models of the lithosphere and asthenosphere by harnessing increased computing power alongside sophisticated data analysis, with the flexibility to include multiple datatypes with complementary resolution. Our new method has been designed to simultaneously fit P-s and S-p converted phases and Rayleigh wave phase velocities measured from ambient noise (periods 6-40 s) and earthquake sources (periods 30-170s). Careful processing of the body wave data isolates the signals from velocity gradients between the mid-crust and 250 km depth. We jointly invert the body and surface wave data to obtain detailed 1-D velocity models that include robustly imaged mantle discontinuities. Synthetic tests demonstrate that S-p phases are particularly important for resolving mantle structure, while surface waves capture absolute velocities with resolution better than 0.1 km/s. By treating data noise as an unknown parameter, and by generating posterior parameter distributions, model trade offs and uncertainties are fully captured by the inversion. We apply the method to stations across the northwest and north-central United States, finding that the imaged structure improves upon existing models by sharpening the vertical resolution of absolute velocity profiles and offering robust uncertainty estimates. In the tectonically active northwestern US, a strong velocity drop immediately beneath the Moho connotes thin (<70 km) lithosphere and a sharp lithosphere-asthenosphere transition; the asthenospheric velocity profile here matches observations at mid-ocean ridges. Within the Wyoming and Superior cratons, our models reveal mid-lithospheric velocity gradients indicative of thermochemical cratonic layering, but the lithosphere-asthenosphere boundary is relatively gradual. This flexible method holds promise for increasingly detailed understanding of the lithosphere-asthenosphere system.

Multiscale Bayesian neural networks for soil water content estimation

NASA Astrophysics Data System (ADS)

Jana, Raghavendra B.; Mohanty, Binayak P.; Springer, Everett P.

2008-08-01

Artificial neural networks (ANN) have been used for some time now to estimate soil hydraulic parameters from other available or more easily measurable soil properties. However, most such uses of ANNs as pedotransfer functions (PTFs) have been at matching spatial scales (1:1) of inputs and outputs. This approach assumes that the outputs are only required at the same scale as the input data. Unfortunately, this is rarely true. Different hydrologic, hydroclimatic, and contaminant transport models require soil hydraulic parameter data at different spatial scales, depending upon their grid sizes. While conventional (deterministic) ANNs have been traditionally used in these studies, the use of Bayesian training of ANNs is a more recent development. In this paper, we develop a Bayesian framework to derive soil water retention function including its uncertainty at the point or local scale using PTFs trained with coarser-scale Soil Survey Geographic (SSURGO)-based soil data. The approach includes an ANN trained with Bayesian techniques as a PTF tool with training and validation data collected across spatial extents (scales) in two different regions in the United States. The two study areas include the Las Cruces Trench site in the Rio Grande basin of New Mexico, and the Southern Great Plains 1997 (SGP97) hydrology experimental region in Oklahoma. Each region-specific Bayesian ANN is trained using soil texture and bulk density data from the SSURGO database (scale 1:24,000), and predictions of the soil water contents at different pressure heads with point scale data (1:1) inputs are made. The resulting outputs are corrected for bias using both linear and nonlinear correction techniques. The results show good agreement between the soil water content values measured at the point scale and those predicted by the Bayesian ANN-based PTFs for both the study sites. Overall, Bayesian ANNs coupled with nonlinear bias correction are found to be very suitable tools for deriving soil hydraulic parameters at the local/fine scale from soil physical properties at coarser-scale and across different spatial extents. This approach could potentially be used for soil hydraulic properties estimation and downscaling.

Uncertainty in training image-based inversion of hydraulic head data constrained to ERT data: Workflow and case study

NASA Astrophysics Data System (ADS)

Hermans, Thomas; Nguyen, Frédéric; Caers, Jef

2015-07-01

In inverse problems, investigating uncertainty in the posterior distribution of model parameters is as important as matching data. In recent years, most efforts have focused on techniques to sample the posterior distribution with reasonable computational costs. Within a Bayesian context, this posterior depends on the prior distribution. However, most of the studies ignore modeling the prior with realistic geological uncertainty. In this paper, we propose a workflow inspired by a Popper-Bayes philosophy that data should first be used to falsify models, then only be considered for matching. We propose a workflow consisting of three steps: (1) in defining the prior, we interpret multiple alternative geological scenarios from literature (architecture of facies) and site-specific data (proportions of facies). Prior spatial uncertainty is modeled using multiple-point geostatistics, where each scenario is defined using a training image. (2) We validate these prior geological scenarios by simulating electrical resistivity tomography (ERT) data on realizations of each scenario and comparing them to field ERT in a lower dimensional space. In this second step, the idea is to probabilistically falsify scenarios with ERT, meaning that scenarios which are incompatible receive an updated probability of zero while compatible scenarios receive a nonzero updated belief. (3) We constrain the hydrogeological model with hydraulic head and ERT using a stochastic search method. The workflow is applied to a synthetic and a field case studies in an alluvial aquifer. This study highlights the importance of considering and estimating prior uncertainty (without data) through a process of probabilistic falsification.

Water Table Uncertainties due to Uncertainties in Structure and Properties of an Unconfined Aquifer.

PubMed

Hauser, Juerg; Wellmann, Florian; Trefry, Mike

2018-03-01

We consider two sources of geology-related uncertainty in making predictions of the steady-state water table elevation for an unconfined aquifer. That is the uncertainty in the depth to base of the aquifer and in the hydraulic conductivity distribution within the aquifer. Stochastic approaches to hydrological modeling commonly use geostatistical techniques to account for hydraulic conductivity uncertainty within the aquifer. In the absence of well data allowing derivation of a relationship between geophysical and hydrological parameters, the use of geophysical data is often limited to constraining the structural boundaries. If we recover the base of an unconfined aquifer from an analysis of geophysical data, then the associated uncertainties are a consequence of the geophysical inversion process. In this study, we illustrate this by quantifying water table uncertainties for the unconfined aquifer formed by the paleochannel network around the Kintyre Uranium deposit in Western Australia. The focus of the Bayesian parametric bootstrap approach employed for the inversion of the available airborne electromagnetic data is the recovery of the base of the paleochannel network and the associated uncertainties. This allows us to then quantify the associated influences on the water table in a conceptualized groundwater usage scenario and compare the resulting uncertainties with uncertainties due to an uncertain hydraulic conductivity distribution within the aquifer. Our modeling shows that neither uncertainties in the depth to the base of the aquifer nor hydraulic conductivity uncertainties alone can capture the patterns of uncertainty in the water table that emerge when the two are combined. © 2017, National Ground Water Association.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

NASA Technical Reports Server (NTRS)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

An ionospheric occultation inversion technique based on epoch difference

NASA Astrophysics Data System (ADS)

Lin, Jian; Xiong, Jing; Zhu, Fuying; Yang, Jian; Qiao, Xuejun

2013-09-01

Of the ionospheric radio occultation (IRO) electron density profile (EDP) retrievals, the Abel based calibrated TEC inversion (CTI) is the most widely used technique. In order to eliminate the contribution from the altitude above the RO satellite, it is necessary to utilize the calibrated TEC to retrieve the EDP, which introduces the error due to the coplanar assumption. In this paper, a new technique based on the epoch difference inversion (EDI) is firstly proposed to eliminate this error. The comparisons between CTI and EDI have been done, taking advantage of the simulated and real COSMIC data. The following conclusions can be drawn: the EDI technique can successfully retrieve the EDPs without non-occultation side measurements and shows better performance than the CTI method, especially for lower orbit mission; no matter which technique is used, the inversion results at the higher altitudes are better than those at the lower altitudes, which could be explained theoretically.

High-resolution moisture profiles from full-waveform probabilistic inversion of TDR signals

NASA Astrophysics Data System (ADS)

Laloy, Eric; Huisman, Johan Alexander; Jacques, Diederik

2014-11-01

This study presents an novel Bayesian inversion scheme for high-dimensional undetermined TDR waveform inversion. The methodology quantifies uncertainty in the moisture content distribution, using a Gaussian Markov random field (GMRF) prior as regularization operator. A spatial resolution of 1 cm along a 70-cm long TDR probe is considered for the inferred moisture content. Numerical testing shows that the proposed inversion approach works very well in case of a perfect model and Gaussian measurement errors. Real-world application results are generally satisfying. For a series of TDR measurements made during imbibition and evaporation from a laboratory soil column, the average root-mean-square error (RMSE) between maximum a posteriori (MAP) moisture distribution and reference TDR measurements is 0.04 cm3 cm-3. This RMSE value reduces to less than 0.02 cm3 cm-3 for a field application in a podzol soil. The observed model-data discrepancies are primarily due to model inadequacy, such as our simplified modeling of the bulk soil electrical conductivity profile. Among the important issues that should be addressed in future work are the explicit inference of the soil electrical conductivity profile along with the other sampled variables, the modeling of the temperature-dependence of the coaxial cable properties and the definition of an appropriate statistical model of the residual errors.

Inversion technique for IR heterodyne sounding of stratospheric constituents from space platforms

NASA Technical Reports Server (NTRS)

Abbas, M. M.; Shapiro, G. L.; Alvarez, J. M.

1981-01-01

The techniques which have been employed for inversion of IR heterodyne measurements for remote sounding of stratospheric trace constituents usually rely on either geometric effects based on limb-scan observations (i.e., onion peel techniques) or spectral effects by using weighting functions corresponding to different frequencies of an IR spectral line. An experimental approach and inversion technique are discussed which optimize the retrieval of concentration profiles by combining the geometric and the spectral effects in an IR heterodyne receiver. The results of inversions of some synthetic CIO spectral lines corresponding to solar occultation limb scans of the stratosphere are presented, indicating considerable improvement in the accuracy of the retrieved profiles. The effects of noise on the accuracy of retrievals are discussed for realistic situations.

Inversion technique for IR heterodyne sounding of stratospheric constituents from space platforms.

PubMed

Abbas, M M; Shapiro, G L; Alvarez, J M

1981-11-01

The techniques which have been employed for inversion of IR heterodyne measurements for remote sounding of stratospheric trace constituents usually rely on either geometric effects based on limb-scan observations (i.e., onion peel techniques) or spectral effects by using weighting functions corresponding to different frequencies of an IR spectral line. An experimental approach and inversion technique are discussed which optimize the retrieval of concentration profiles by combining the geometric and the spectral effects in an IR heterodyne receiver. The results of inversions of some synthetic ClO spectral lines corresponding to solar occultation limb scans of the stratosphere are presented, indicating considerable improvement in the accuracy of the retrieved profiles. The effects of noise on the accuracy of retrievals are discussed for realistic situations.

Bayesian characterization of micro-perforated panels and multi-layer absorbers

NASA Astrophysics Data System (ADS)

Schmitt, Andrew Alexander Joseph

First described by the late acoustician Dah-You Maa, micro-perforated panel (MPP) absorbers produce extremely high acoustic absorption coefficients. This is done without the use of conventional fibrous or porous materials that are often used in acoustic treatments, meaning MPP absorbers are capable of being implemented and withstanding critical situations where traditional absorbers do not suffice. The absorption function of a micro-perforated panel yields high yet relatively narrow results at certain frequencies, although wide-band absorption can be designed by stacking multiple MPP absorbers comprised of different characteristic parameters. Using Bayesian analysis, the physical properties of panel thickness, pore diameter, perforation ratio, and air depth are estimated inversely from experimental data of acoustic absorption, based on theoretical models for design of micro-perforated panels. Furthermore, this analysis helps to understand the interdependence and uncertainties of the parameters and how each affects the performance of the panel. Various micro-perforated panels are manufactured and tested in single- and double-layer absorber constructions.

A Bayesian rupture model of the 2007 Mw 8.1 Solomon Islands earthquake in Southwest Pacific with coral reef displacement measurements

NASA Astrophysics Data System (ADS)

Chen, Ting; Luo, Haipeng; Furlong, Kevin P.

2017-05-01

On 1st April 2007 a Mw 8.1 megathrust earthquake occurred in the western Solomon Islands of the Southwest Pacific and generated a regional tsunami with run-up heights of up to 12 m. A Bayesian inversion model is constructed to derive fault dip angle and cumulative co-seismic and early post-seismic slip using coral reef displacement measurements, in which both data misfit and moment magnitude are used as constraints. Results show three shallow, high-slip patches concentrated along the trench from west of Ranongga Island to Rendova Island on a fault plane dipping 20°, and a maximum dip slip of 11.6 m beneath Ranongga Island. Considerable subsidence on Simbo Island outboard of the trench on the subducting plate is not well explained with this model, but may be related to the effects of afterslip and/or Simbo Island's location near the triple junction among the Australia, Woodlark and Pacific plates.

Optical characterization limits of nanoparticle aggregates at different wavelengths using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Eriçok, Ozan Burak; Ertürk, Hakan

2018-07-01

Optical characterization of nanoparticle aggregates is a complex inverse problem that can be solved by deterministic or statistical methods. Previous studies showed that there exists a different lower size limit of reliable characterization, corresponding to the wavelength of light source used. In this study, these characterization limits are determined considering a light source wavelength range changing from ultraviolet to near infrared (266-1064 nm) relying on numerical light scattering experiments. Two different measurement ensembles are considered. Collection of well separated aggregates made up of same sized particles and that of having particle size distribution. Filippov's cluster-cluster algorithm is used to generate the aggregates and the light scattering behavior is calculated by discrete dipole approximation. A likelihood-free Approximate Bayesian Computation, relying on Adaptive Population Monte Carlo method, is used for characterization. It is found that when the wavelength range of 266-1064 nm is used, successful characterization limit changes from 21-62 nm effective radius for monodisperse and polydisperse soot aggregates.

Measuring soil moisture with imaging radars

NASA Technical Reports Server (NTRS)

Dubois, Pascale C.; Vanzyl, Jakob; Engman, Ted

1995-01-01

An empirical model was developed to infer soil moisture and surface roughness from radar data. The accuracy of the inversion technique is assessed by comparing soil moisture obtained with the inversion technique to in situ measurements. The effect of vegetation on the inversion is studied and a method to eliminate the areas where vegetation impairs the algorithm is described.

Minimum relative entropy, Bayes and Kapur

NASA Astrophysics Data System (ADS)

Woodbury, Allan D.

2011-04-01

The focus of this paper is to illustrate important philosophies on inversion and the similarly and differences between Bayesian and minimum relative entropy (MRE) methods. The development of each approach is illustrated through the general-discrete linear inverse. MRE differs from both Bayes and classical statistical methods in that knowledge of moments are used as ‘data’ rather than sample values. MRE like Bayes, presumes knowledge of a prior probability distribution and produces the posterior pdf itself. MRE attempts to produce this pdf based on the information provided by new moments. It will use moments of the prior distribution only if new data on these moments is not available. It is important to note that MRE makes a strong statement that the imposed constraints are exact and complete. In this way, MRE is maximally uncommitted with respect to unknown information. In general, since input data are known only to within a certain accuracy, it is important that any inversion method should allow for errors in the measured data. The MRE approach can accommodate such uncertainty and in new work described here, previous results are modified to include a Gaussian prior. A variety of MRE solutions are reproduced under a number of assumed moments and these include second-order central moments. Various solutions of Jacobs & van der Geest were repeated and clarified. Menke's weighted minimum length solution was shown to have a basis in information theory, and the classic least-squares estimate is shown as a solution to MRE under the conditions of more data than unknowns and where we utilize the observed data and their associated noise. An example inverse problem involving a gravity survey over a layered and faulted zone is shown. In all cases the inverse results match quite closely the actual density profile, at least in the upper portions of the profile. The similar results to Bayes presented in are a reflection of the fact that the MRE posterior pdf, and its mean are constrained not by d=Gm but by its first moment E(d=Gm), a weakened form of the constraints. If there is no error in the data then one should expect a complete agreement between Bayes and MRE and this is what is shown. Similar results are shown when second moment data is available (e.g. posterior covariance equal to zero). But dissimilar results are noted when we attempt to derive a Bayesian like result from MRE. In the various examples given in this paper, the problems look similar but are, in the final analysis, not equal. The methods of attack are different and so are the results even though we have used the linear inverse problem as a common template.

High-resolution atmospheric inversion of urban CO2 emissions during the dormant season of the Indianapolis Flux Experiment (INFLUX)

NASA Astrophysics Data System (ADS)

Lauvaux, Thomas; Miles, Natasha L.; Deng, Aijun; Richardson, Scott J.; Cambaliza, Maria O.; Davis, Kenneth J.; Gaudet, Brian; Gurney, Kevin R.; Huang, Jianhua; O'Keefe, Darragh; Song, Yang; Karion, Anna; Oda, Tomohiro; Patarasuk, Risa; Razlivanov, Igor; Sarmiento, Daniel; Shepson, Paul; Sweeney, Colm; Turnbull, Jocelyn; Wu, Kai

2016-05-01

Based on a uniquely dense network of surface towers measuring continuously the atmospheric concentrations of greenhouse gases (GHGs), we developed the first comprehensive monitoring systems of CO2 emissions at high resolution over the city of Indianapolis. The urban inversion evaluated over the 2012-2013 dormant season showed a statistically significant increase of about 20% (from 4.5 to 5.7 MtC ± 0.23 MtC) compared to the Hestia CO2 emission estimate, a state-of-the-art building-level emission product. Spatial structures in prior emission errors, mostly undetermined, appeared to affect the spatial pattern in the inverse solution and the total carbon budget over the entire area by up to 15%, while the inverse solution remains fairly insensitive to the CO2 boundary inflow and to the different prior emissions (i.e., ODIAC). Preceding the surface emission optimization, we improved the atmospheric simulations using a meteorological data assimilation system also informing our Bayesian inversion system through updated observations error variances. Finally, we estimated the uncertainties associated with undetermined parameters using an ensemble of inversions. The total CO2 emissions based on the ensemble mean and quartiles (5.26-5.91 MtC) were statistically different compared to the prior total emissions (4.1 to 4.5 MtC). Considering the relatively small sensitivity to the different parameters, we conclude that atmospheric inversions are potentially able to constrain the carbon budget of the city, assuming sufficient data to measure the inflow of GHG over the city, but additional information on prior emission error structures are required to determine the spatial structures of urban emissions at high resolution.

Seismic source inversion using Green's reciprocity and a 3-D structural model for the Japanese Islands

NASA Astrophysics Data System (ADS)

Simutė, S.; Fichtner, A.

2015-12-01

We present a feasibility study for seismic source inversions using a 3-D velocity model for the Japanese Islands. The approach involves numerically calculating 3-D Green's tensors, which is made efficient by exploiting Green's reciprocity. The rationale for 3-D seismic source inversion has several aspects. For structurally complex regions, such as the Japan area, it is necessary to account for 3-D Earth heterogeneities to prevent unknown structure polluting source solutions. In addition, earthquake source characterisation can serve as a means to delineate existing faults. Source parameters obtained for more realistic Earth models can then facilitate improvements in seismic tomography and early warning systems, which are particularly important for seismically active areas, such as Japan. We have created a database of numerically computed 3-D Green's reciprocals for a 40°× 40°× 600 km size area around the Japanese Archipelago for >150 broadband stations. For this we used a regional 3-D velocity model, recently obtained from full waveform inversion. The model includes attenuation and radial anisotropy and explains seismic waveform data for periods between 10 - 80 s generally well. The aim is to perform source inversions using the database of 3-D Green's tensors. As preliminary steps, we present initial concepts to address issues that are at the basis of our approach. We first investigate to which extent Green's reciprocity works in a discrete domain. Considering substantial amounts of computed Green's tensors we address storage requirements and file formatting. We discuss the importance of the initial source model, as an intelligent choice can substantially reduce the search volume. Possibilities to perform a Bayesian inversion and ways to move to finite source inversion are also explored.

Azimuthal Seismic Amplitude Variation with Offset and Azimuth Inversion in Weakly Anisotropic Media with Orthorhombic Symmetry

NASA Astrophysics Data System (ADS)

Pan, Xinpeng; Zhang, Guangzhi; Yin, Xingyao

2018-01-01

Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen's weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen's WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen's WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen's WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the real data illustrate the inversion stabilities of orthorhombic anisotropy in a fractured reservoir.

Joint Application of Concentrations and Isotopic Signatures to Investigate the Global Atmospheric Carbon Monoxide Budget: Inverse Modeling Approach

NASA Astrophysics Data System (ADS)

Park, K.; Emmons, L. K.; Mak, J. E.

2007-12-01

Carbon monoxide is not only an important component for determining the atmospheric oxidizing capacity but also a key trace gas in the atmospheric chemistry of the Earth's background environment. The global CO cycle and its change are closely related to both the change of CO mixing ratio and the change of source strength. Previously, to estimate the global CO budget, most top-down estimation techniques have been applied the concentrations of CO solely. Since CO from certain sources has a unique isotopic signature, its isotopes provide additional information to constrain its sources. Thus, coupling the concentration and isotope fraction information enables to tightly constrain CO flux by its sources and allows better estimations on the global CO budget. MOZART4 (Model for Ozone And Related chemical Tracers), a 3-D global chemical transport model developed at NCAR, MPI for meteorology and NOAA/GFDL and is used to simulate the global CO concentration and its isotopic signature. Also, a tracer version of MOZART4 which tagged for C16O and C18O from each region and each source was developed to see their contributions to the atmosphere efficiently. Based on the nine-year- simulation results we analyze the influences of each source of CO to the isotopic signature and the concentration. Especially, the evaluations are focused on the oxygen isotope of CO (δ18O), which has not been extensively studied yet. To validate the model performance, CO concentrations and isotopic signatures measured from MPI, NIWA and our lab are compared to the modeled results. The MOZART4 reproduced observational data fairly well; especially in mid to high latitude northern hemisphere. Bayesian inversion techniques have been used to estimate the global CO budget with combining observed and modeled CO concentration. However, previous studies show significant differences in their estimations on CO source strengths. Because, in addition to the CO mixing ratio, isotopic signatures are independent tracers that contain the source information, jointly applying the isotope and the concentration information is expected to provide more precise optimization results in CO budget estimation. Our accumulated long-term CO isotope measurement data contribute to having more confidence of the inversions as well. Besides the benefit of adding isotope data on the inverse modeling, a trait of each isotope of CO (oxygen and carbon isotope) contains another advantageous use in the top-down estimation of the CO budget. δ18O and δ13C has a distinctive isotopic signature on a specific source; combustion sources such as a fossil fuel use show clearly different values from other natural sources in the δ18O signatures and the methane source can be easily separated by using δ13C information. Therefore, inversions of the two major sources of CO respond with different sensitivity for the different isotopes. To maximize the strengths of using isotope data in the inverse modeling analysis, various coupling schemes combining [CO], δ18O and δ13C have been investigated to enhance the credibility of the CO budget optimization.

Joint Application of Concentrations and Isotopic Signatures to Investigate the Global Atmospheric Carbon Monoxide Budget: Inverse Modeling Approach

NASA Astrophysics Data System (ADS)

Park, K.; Mak, J. E.; Emmons, L. K.

2008-12-01

Carbon monoxide is not only an important component for determining the atmospheric oxidizing capacity but also a key trace gas in the atmospheric chemistry of the Earth's background environment. The global CO cycle and its change are closely related to both the change of CO mixing ratio and the change of source strength. Previously, to estimate the global CO budget, most top-down estimation techniques have been applied the concentrations of CO solely. Since CO from certain sources has a unique isotopic signature, its isotopes provide additional information to constrain its sources. Thus, coupling the concentration and isotope fraction information enables to tightly constrain CO flux by its sources and allows better estimations on the global CO budget. MOZART4 (Model for Ozone And Related chemical Tracers), a 3-D global chemical transport model developed at NCAR, MPI for meteorology and NOAA/GFDL and is used to simulate the global CO concentration and its isotopic signature. Also, a tracer version of MOZART4 which tagged for C16O and C18O from each region and each source was developed to see their contributions to the atmosphere efficiently. Based on the nine-year-simulation results we analyze the influences of each source of CO to the isotopic signature and the concentration. Especially, the evaluations are focused on the oxygen isotope of CO (δ18O), which has not been extensively studied yet. To validate the model performance, CO concentrations and isotopic signatures measured from MPI, NIWA and our lab are compared to the modeled results. The MOZART4 reproduced observational data fairly well; especially in mid to high latitude northern hemisphere. Bayesian inversion techniques have been used to estimate the global CO budget with combining observed and modeled CO concentration. However, previous studies show significant differences in their estimations on CO source strengths. Because, in addition to the CO mixing ratio, isotopic signatures are independent tracers that contain the source information, jointly applying the isotope and the concentration information is expected to provide more precise optimization results in CO budget estimation. Our accumulated long-term CO isotope measurement data contribute to having more confidence of the inversions as well. Besides the benefit of adding isotope data on the inverse modeling, a trait of each isotope of CO (oxygen and carbon isotope) contains another advantageous use in the top-down estimation of the CO budget. δ18O and δ13C has a distinctive isotopic signature on a specific source; combustion sources such as a fossil fuel use show clearly different values from other natural sources in the δ18O signatures and the methane source can be easily separated by using δ13C information. Therefore, inversions of the two major sources of CO respond with different sensitivity for the different isotopes. To maximize the strengths of using isotope data in the inverse modeling analysis, various coupling schemes combining [CO], δ18O and δ13C have been investigated to enhance the credibility of the CO budget optimization.

Non-recursive augmented Lagrangian algorithms for the forward and inverse dynamics of constrained flexible multibodies

NASA Technical Reports Server (NTRS)

Bayo, Eduardo; Ledesma, Ragnar

1993-01-01

A technique is presented for solving the inverse dynamics of flexible planar multibody systems. This technique yields the non-causal joint efforts (inverse dynamics) as well as the internal states (inverse kinematics) that produce a prescribed nominal trajectory of the end effector. A non-recursive global Lagrangian approach is used in formulating the equations for motion as well as in solving the inverse dynamics equations. Contrary to the recursive method previously presented, the proposed method solves the inverse problem in a systematic and direct manner for both open-chain as well as closed-chain configurations. Numerical simulation shows that the proposed procedure provides an excellent tracking of the desired end effector trajectory.

Slice sampling technique in Bayesian extreme of gold price modelling

NASA Astrophysics Data System (ADS)

Rostami, Mohammad; Adam, Mohd Bakri; Ibrahim, Noor Akma; Yahya, Mohamed Hisham

2013-09-01

In this paper, a simulation study of Bayesian extreme values by using Markov Chain Monte Carlo via slice sampling algorithm is implemented. We compared the accuracy of slice sampling with other methods for a Gumbel model. This study revealed that slice sampling algorithm offers more accurate and closer estimates with less RMSE than other methods . Finally we successfully employed this procedure to estimate the parameters of Malaysia extreme gold price from 2000 to 2011.

Quantifying Carbon Flux Estimation Errors

NASA Astrophysics Data System (ADS)

Wesloh, D.

2017-12-01

Atmospheric Bayesian inversions have been used to estimate surface carbon dioxide (CO2) fluxes from global to sub-continental scales using atmospheric mixing ratio measurements. These inversions use an atmospheric transport model, coupled to a set of fluxes, in order to simulate mixing ratios that can then be compared to the observations. The comparison is then used to update the fluxes to better match the observations in a manner consistent with the uncertainties prescribed for each. However, inversion studies disagree with each other at continental scales, prompting further investigations to examine the causes of these differences. Inter-comparison studies have shown that the errors resulting from atmospheric transport inaccuracies are comparable to those from the errors in the prior fluxes. However, not as much effort has gone into studying the origins of the errors induced by errors in the transport as by errors in the prior distribution. This study uses a mesoscale transport model to evaluate the effects of representation errors in the observations and of incorrect descriptions of the transport. To obtain realizations of these errors, we performed an Observing System Simulation Experiments (OSSEs), with the transport model used for the inversion operating at two resolutions, one typical of a global inversion and the other of a mesoscale, and with various prior flux distributions to. Transport error covariances are inferred from an ensemble of perturbed mesoscale simulations while flux error covariances are computed using prescribed distributions and magnitudes. We examine how these errors can be diagnosed in the inversion process using aircraft, ground-based, and satellite observations of meteorological variables and CO2.

Dynamics of Genome Rearrangement in Bacterial Populations

PubMed Central

Darling, Aaron E.; Miklós, István; Ragan, Mark A.

2008-01-01

Genome structure variation has profound impacts on phenotype in organisms ranging from microbes to humans, yet little is known about how natural selection acts on genome arrangement. Pathogenic bacteria such as Yersinia pestis, which causes bubonic and pneumonic plague, often exhibit a high degree of genomic rearrangement. The recent availability of several Yersinia genomes offers an unprecedented opportunity to study the evolution of genome structure and arrangement. We introduce a set of statistical methods to study patterns of rearrangement in circular chromosomes and apply them to the Yersinia. We constructed a multiple alignment of eight Yersinia genomes using Mauve software to identify 78 conserved segments that are internally free from genome rearrangement. Based on the alignment, we applied Bayesian statistical methods to infer the phylogenetic inversion history of Yersinia. The sampling of genome arrangement reconstructions contains seven parsimonious tree topologies, each having different histories of 79 inversions. Topologies with a greater number of inversions also exist, but were sampled less frequently. The inversion phylogenies agree with results suggested by SNP patterns. We then analyzed reconstructed inversion histories to identify patterns of rearrangement. We confirm an over-representation of “symmetric inversions”—inversions with endpoints that are equally distant from the origin of chromosomal replication. Ancestral genome arrangements demonstrate moderate preference for replichore balance in Yersinia. We found that all inversions are shorter than expected under a neutral model, whereas inversions acting within a single replichore are much shorter than expected. We also found evidence for a canonical configuration of the origin and terminus of replication. Finally, breakpoint reuse analysis reveals that inversions with endpoints proximal to the origin of DNA replication are nearly three times more frequent. Our findings represent the first characterization of genome arrangement evolution in a bacterial population evolving outside laboratory conditions. Insight into the process of genomic rearrangement may further the understanding of pathogen population dynamics and selection on the architecture of circular bacterial chromosomes. PMID:18650965

Inverse modeling of the terrestrial carbon flux in China with flux covariance among inverted regions

NASA Astrophysics Data System (ADS)

Wang, H.; Jiang, F.; Chen, J. M.; Ju, W.; Wang, H.

2011-12-01

Quantitative understanding of the role of ocean and terrestrial biosphere in the global carbon cycle, their response and feedback to climate change is required for the future projection of the global climate. China has the largest amount of anthropogenic CO2 emission, diverse terrestrial ecosystems and an unprecedented rate of urbanization. Thus information on spatial and temporal distributions of the terrestrial carbon flux in China is of great importance in understanding the global carbon cycle. We developed a nested inversion with focus in China. Based on Transcom 22 regions for the globe, we divide China and its neighboring countries into 17 regions, making 39 regions in total for the globe. A Bayesian synthesis inversion is made to estimate the terrestrial carbon flux based on GlobalView CO2 data. In the inversion, GEOS-Chem is used as the transport model to develop the transport matrix. A terrestrial ecosystem model named BEPS is used to produce the prior surface flux to constrain the inversion. However, the sparseness of available observation stations in Asia poses a challenge to the inversion for the 17 small regions. To obtain additional constraint on the inversion, a prior flux covariance matrix is constructed using the BEPS model through analyzing the correlation in the net carbon flux among regions under variable climate conditions. The use of the covariance among different regions in the inversion effectively extends the information content of CO2 observations to more regions. The carbon flux over the 39 land and ocean regions are inverted for the period from 2004 to 2009. In order to investigate the impact of introducing the covariance matrix with non-zero off-diagonal values to the inversion, the inverted terrestrial carbon flux over China is evaluated against ChinaFlux eddy-covariance observations after applying an upscaling methodology.

Bayesian extraction of the parton distribution amplitude from the Bethe-Salpeter wave function

NASA Astrophysics Data System (ADS)

Gao, Fei; Chang, Lei; Liu, Yu-xin

2017-07-01

We propose a new numerical method to compute the parton distribution amplitude (PDA) from the Euclidean Bethe-Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe-Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method (MEM). The Nakanishi weight function as well as the corresponding light-front parton distribution amplitude (PDA) can be well determined. We confirm prior work on PDA computations, which was based on different methods.

Uncertainty quantification for PZT bimorph actuators

NASA Astrophysics Data System (ADS)

Bravo, Nikolas; Smith, Ralph C.; Crews, John

2018-03-01

In this paper, we discuss the development of a high fidelity model for a PZT bimorph actuator used for micro-air vehicles, which includes the Robobee. We developed a high-fidelity model for the actuator using the homogenized energy model (HEM) framework, which quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. We then discussed an inverse problem on the model. We included local and global sensitivity analysis of the parameters in the high-fidelity model. Finally, we will discuss the results of Bayesian inference and uncertainty quantification on the HEM.

Bayesian Inversion of Concentration Data for an Unknown Number of Contaminant Sources

DTIC Science & Technology

2007-06-01

répondre aux urgences et celle de leur gestion rétrospective dirigée contre des incidents ter- roristes comprenant la dissémination secrète d’agent CBR...d’intervention d’urgence avancé pour la prédiction et l’évaluation des risques CBRN en mi- lieu urbain). Cette composante a été incorporée dans le...computationally efficient methodology for de - termination of the likelihood function for the problem, based on an adjoint representation of the source–receptor

DATMAN: A reliability data analysis program using Bayesian updating

DOE Office of Scientific and Technical Information (OSTI.GOV)

Becker, M.; Feltus, M.A.

1996-12-31

Preventive maintenance (PM) techniques focus on the prevention of failures, in particular, system components that are important to plant functions. Reliability-centered maintenance (RCM) improves on the PM techniques by introducing a set of guidelines by which to evaluate the system functions. It also minimizes intrusive maintenance, labor, and equipment downtime without sacrificing system performance when its function is essential for plant safety. Both the PM and RCM approaches require that system reliability data be updated as more component failures and operation time are acquired. Systems reliability and the likelihood of component failures can be calculated by Bayesian statistical methods, whichmore » can update these data. The DATMAN computer code has been developed at Penn State to simplify the Bayesian analysis by performing tedious calculations needed for RCM reliability analysis. DATMAN reads data for updating, fits a distribution that best fits the data, and calculates component reliability. DATMAN provides a user-friendly interface menu that allows the user to choose from several common prior and posterior distributions, insert new failure data, and visually select the distribution that matches the data most accurately.« less

Atmospheric temperature changes over the 20th century at very high elevations in the European Alps from englacial temperatures

NASA Astrophysics Data System (ADS)

Gilbert, A.; Vincent, C.

2013-05-01

the paucity of observations, a great deal of uncertainty remains concerning temperature changes at very high altitudes over the last century. Englacial temperature measurements performed in boreholes provide a very good indicator of atmospheric temperatures for very high elevations although they are not directly related to air temperatures. Temperature profiles from seven deep boreholes drilled at three different sites between 4240 and 4300 m above sea level in the Mont Blanc area (French Alps) have been analyzed using a heat flow model and a Bayesian inverse modeling approach. Atmospheric temperature changes over the last century were estimated by simultaneous inversion of these temperature profiles. A mean warming rate of 0.14°C/decade between 1900 and 2004 was found. This is similar to the observed regional low altitude trend in the northwestern Alps, suggesting that air temperature trends are not altitude dependent.

Improvement of Storm Forecasts Using Gridded Bayesian Linear Regression for Northeast United States

NASA Astrophysics Data System (ADS)

Yang, J.; Astitha, M.; Schwartz, C. S.

2017-12-01

Bayesian linear regression (BLR) is a post-processing technique in which regression coefficients are derived and used to correct raw forecasts based on pairs of observation-model values. This study presents the development and application of a gridded Bayesian linear regression (GBLR) as a new post-processing technique to improve numerical weather prediction (NWP) of rain and wind storm forecasts over northeast United States. Ten controlled variables produced from ten ensemble members of the National Center for Atmospheric Research (NCAR) real-time prediction system are used for a GBLR model. In the GBLR framework, leave-one-storm-out cross-validation is utilized to study the performances of the post-processing technique in a database composed of 92 storms. To estimate the regression coefficients of the GBLR, optimization procedures that minimize the systematic and random error of predicted atmospheric variables (wind speed, precipitation, etc.) are implemented for the modeled-observed pairs of training storms. The regression coefficients calculated for meteorological stations of the National Weather Service are interpolated back to the model domain. An analysis of forecast improvements based on error reductions during the storms will demonstrate the value of GBLR approach. This presentation will also illustrate how the variances are optimized for the training partition in GBLR and discuss the verification strategy for grid points where no observations are available. The new post-processing technique is successful in improving wind speed and precipitation storm forecasts using past event-based data and has the potential to be implemented in real-time.

Inverse boundary-layer theory and comparison with experiment

NASA Technical Reports Server (NTRS)

Carter, J. E.

1978-01-01

Inverse boundary layer computational procedures, which permit nonsingular solutions at separation and reattachment, are presented. In the first technique, which is for incompressible flow, the displacement thickness is prescribed; in the second technique, for compressible flow, a perturbation mass flow is the prescribed condition. The pressure is deduced implicitly along with the solution in each of these techniques. Laminar and turbulent computations, which are typical of separated flow, are presented and comparisons are made with experimental data. In both inverse procedures, finite difference techniques are used along with Newton iteration. The resulting procedure is no more complicated than conventional boundary layer computations. These separated boundary layer techniques appear to be well suited for complete viscous-inviscid interaction computations.

A Modular GIS-Based Software Architecture for Model Parameter Estimation using the Method of Anchored Distributions (MAD)

NASA Astrophysics Data System (ADS)

Ames, D. P.; Osorio-Murillo, C.; Over, M. W.; Rubin, Y.

2012-12-01

The Method of Anchored Distributions (MAD) is an inverse modeling technique that is well-suited for estimation of spatially varying parameter fields using limited observations and Bayesian methods. This presentation will discuss the design, development, and testing of a free software implementation of the MAD technique using the open source DotSpatial geographic information system (GIS) framework, R statistical software, and the MODFLOW groundwater model. This new tool, dubbed MAD-GIS, is built using a modular architecture that supports the integration of external analytical tools and models for key computational processes including a forward model (e.g. MODFLOW, HYDRUS) and geostatistical analysis (e.g. R, GSLIB). The GIS-based graphical user interface provides a relatively simple way for new users of the technique to prepare the spatial domain, to identify observation and anchor points, to perform the MAD analysis using a selected forward model, and to view results. MAD-GIS uses the Managed Extensibility Framework (MEF) provided by the Microsoft .NET programming platform to support integration of different modeling and analytical tools at run-time through a custom "driver." Each driver establishes a connection with external programs through a programming interface, which provides the elements for communicating with core MAD software. This presentation gives an example of adapting the MODFLOW to serve as the external forward model in MAD-GIS for inferring the distribution functions of key MODFLOW parameters. Additional drivers for other models are being developed and it is expected that the open source nature of the project will engender the development of additional model drivers by 3rd party scientists.

A Comparison of FPGA and GPGPU Designs for Bayesian Occupancy Filters.

PubMed

Medina, Luis; Diez-Ochoa, Miguel; Correal, Raul; Cuenca-Asensi, Sergio; Serrano, Alejandro; Godoy, Jorge; Martínez-Álvarez, Antonio; Villagra, Jorge

2017-11-11

Grid-based perception techniques in the automotive sector based on fusing information from different sensors and their robust perceptions of the environment are proliferating in the industry. However, one of the main drawbacks of these techniques is the traditionally prohibitive, high computing performance that is required for embedded automotive systems. In this work, the capabilities of new computing architectures that embed these algorithms are assessed in a real car. The paper compares two ad hoc optimized designs of the Bayesian Occupancy Filter; one for General Purpose Graphics Processing Unit (GPGPU) and the other for Field-Programmable Gate Array (FPGA). The resulting implementations are compared in terms of development effort, accuracy and performance, using datasets from a realistic simulator and from a real automated vehicle.

A BAYESIAN APPROACH TO DERIVING AGES OF INDIVIDUAL FIELD WHITE DWARFS

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Malley, Erin M.; Von Hippel, Ted; Van Dyk, David A., E-mail: ted.vonhippel@erau.edu, E-mail: dvandyke@imperial.ac.uk

2013-09-20

We apply a self-consistent and robust Bayesian statistical approach to determine the ages, distances, and zero-age main sequence (ZAMS) masses of 28 field DA white dwarfs (WDs) with ages of approximately 4-8 Gyr. Our technique requires only quality optical and near-infrared photometry to derive ages with <15% uncertainties, generally with little sensitivity to our choice of modern initial-final mass relation. We find that age, distance, and ZAMS mass are correlated in a manner that is too complex to be captured by traditional error propagation techniques. We further find that the posterior distributions of age are often asymmetric, indicating that themore » standard approach to deriving WD ages can yield misleading results.« less

Large-scale inverse model analyses employing fast randomized data reduction

NASA Astrophysics Data System (ADS)

Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

2017-08-01

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

Quantifying uncertainty in geoacoustic inversion. II. Application to broadband, shallow-water data.

PubMed

Dosso, Stan E; Nielsen, Peter L

2002-01-01

This paper applies the new method of fast Gibbs sampling (FGS) to estimate the uncertainties of seabed geoacoustic parameters in a broadband, shallow-water acoustic survey, with the goal of interpreting the survey results and validating the method for experimental data. FGS applies a Bayesian approach to geoacoustic inversion based on sampling the posterior probability density to estimate marginal probability distributions and parameter covariances. This requires knowledge of the statistical distribution of the data errors, including both measurement and theory errors, which is generally not available. Invoking the simplifying assumption of independent, identically distributed Gaussian errors allows a maximum-likelihood estimate of the data variance and leads to a practical inversion algorithm. However, it is necessary to validate these assumptions, i.e., to verify that the parameter uncertainties obtained represent meaningful estimates. To this end, FGS is applied to a geoacoustic experiment carried out at a site off the west coast of Italy where previous acoustic and geophysical studies have been performed. The parameter uncertainties estimated via FGS are validated by comparison with: (i) the variability in the results of inverting multiple independent data sets collected during the experiment; (ii) the results of FGS inversion of synthetic test cases designed to simulate the experiment and data errors; and (iii) the available geophysical ground truth. Comparisons are carried out for a number of different source bandwidths, ranges, and levels of prior information, and indicate that FGS provides reliable and stable uncertainty estimates for the geoacoustic inverse problem.

Evaluating the inverse reasoning account of object discovery.

PubMed

Carroll, Christopher D; Kemp, Charles

2015-06-01

People routinely make inferences about unobserved objects. A hotel guest with welts on his arms, for example, will often worry about bed bugs. The discovery of unobserved objects almost always involves a backward inference from some observed effects (e.g., welts) to unobserved causes (e.g., bed bugs). The inverse reasoning account, which is typically formalized as Bayesian inference, posits that the strength of a backward inference is closely connected to the strength of the corresponding forward inference from the unobserved causes to the observed effects. We evaluated the inverse reasoning account of object discovery in three experiments where participants were asked to discover the unobserved "attractors" and "repellers" that controlled a "particle" moving within an arena. Experiments 1 and 2 showed that participants often failed to provide the best explanations for various particle motions, even when the best explanations were simple and when participants enthusiastically endorsed these explanations when presented with them. This failure demonstrates that object discovery is critically dependent on the processes that support hypothesis generation-processes that the inverse reasoning account does not explain. Experiment 3 demonstrated that people sometimes generate explanations that are invalid even according to their own forward inferences, suggesting that the psychological processes that support forward and backward inference are less intertwined than the inverse reasoning account suggests. The experimental findings support an alternative account of object discovery in which people rely on heuristics to generate possible explanations. Copyright © 2015 Elsevier B.V. All rights reserved.

Using field inversion to quantify functional errors in turbulence closures

NASA Astrophysics Data System (ADS)

Singh, Anand Pratap; Duraisamy, Karthik

2016-04-01

A data-informed approach is presented with the objective of quantifying errors and uncertainties in the functional forms of turbulence closure models. The approach creates modeling information from higher-fidelity simulations and experimental data. Specifically, a Bayesian formalism is adopted to infer discrepancies in the source terms of transport equations. A key enabling idea is the transformation of the functional inversion procedure (which is inherently infinite-dimensional) into a finite-dimensional problem in which the distribution of the unknown function is estimated at discrete mesh locations in the computational domain. This allows for the use of an efficient adjoint-driven inversion procedure. The output of the inversion is a full-field of discrepancy that provides hitherto inaccessible modeling information. The utility of the approach is demonstrated by applying it to a number of problems including channel flow, shock-boundary layer interactions, and flows with curvature and separation. In all these cases, the posterior model correlates well with the data. Furthermore, it is shown that even if limited data (such as surface pressures) are used, the accuracy of the inferred solution is improved over the entire computational domain. The results suggest that, by directly addressing the connection between physical data and model discrepancies, the field inversion approach materially enhances the value of computational and experimental data for model improvement. The resulting information can be used by the modeler as a guiding tool to design more accurate model forms, or serve as input to machine learning algorithms to directly replace deficient modeling terms.

Comparing Three Estimation Methods for the Three-Parameter Logistic IRT Model

ERIC Educational Resources Information Center

Lamsal, Sunil

2015-01-01

Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each…

A Sparsity-based Framework for Resolution Enhancement in Optical Fault Analysis of Integrated Circuits

DTIC Science & Technology

2015-01-01

for IC fault detection . This section provides background information on inversion methods. Conventional inversion techniques and their shortcomings are...physical techniques, electron beam imaging/analysis, ion beam techniques, scanning probe techniques. Electrical tests are used to detect faults in 13 an...hand, there is also the second harmonic technique through which duty cycle degradation faults are detected by collecting the magnitude and the phase of

Seismic Tomography

NASA Astrophysics Data System (ADS)

Nowack, Robert L.; Li, Cuiping

The inversion of seismic travel-time data for radially varying media was initially investigated by Herglotz, Wiechert, and Bateman (the HWB method) in the early part of the 20th century [1]. Tomographic inversions for laterally varying media began in seismology starting in the 1970’s. This included early work by Aki, Christoffersson, and Husebye who developed an inversion technique for estimating lithospheric structure beneath a seismic array from distant earthquakes (the ACH method) [2]. Also, Alekseev and others in Russia performed early inversions of refraction data for laterally varying upper mantle structure [3]. Aki and Lee [4] developed an inversion technique using travel-time data from local earthquakes.

The multicategory case of the sequential Bayesian pixel selection and estimation procedure

NASA Technical Reports Server (NTRS)

Pore, M. D.; Dennis, T. B. (Principal Investigator)

1980-01-01

A Bayesian technique for stratified proportion estimation and a sampling based on minimizing the mean squared error of this estimator were developed and tested on LANDSAT multispectral scanner data using the beta density function to model the prior distribution in the two-class case. An extention of this procedure to the k-class case is considered. A generalization of the beta function is shown to be a density function for the general case which allows the procedure to be extended.

Immune allied genetic algorithm for Bayesian network structure learning

NASA Astrophysics Data System (ADS)

Song, Qin; Lin, Feng; Sun, Wei; Chang, KC

2012-06-01

Bayesian network (BN) structure learning is a NP-hard problem. In this paper, we present an improved approach to enhance efficiency of BN structure learning. To avoid premature convergence in traditional single-group genetic algorithm (GA), we propose an immune allied genetic algorithm (IAGA) in which the multiple-population and allied strategy are introduced. Moreover, in the algorithm, we apply prior knowledge by injecting immune operator to individuals which can effectively prevent degeneration. To illustrate the effectiveness of the proposed technique, we present some experimental results.