Bayesian ensemble refinement by replica simulations and reweighting

NASA Astrophysics Data System (ADS)

Hummer, Gerhard; Köfinger, Jürgen

2015-12-01

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

Nested Sampling for Bayesian Model Comparison in the Context of Salmonella Disease Dynamics

PubMed Central

Dybowski, Richard; McKinley, Trevelyan J.; Mastroeni, Pietro; Restif, Olivier

2013-01-01

Understanding the mechanisms underlying the observed dynamics of complex biological systems requires the statistical assessment and comparison of multiple alternative models. Although this has traditionally been done using maximum likelihood-based methods such as Akaike's Information Criterion (AIC), Bayesian methods have gained in popularity because they provide more informative output in the form of posterior probability distributions. However, comparison between multiple models in a Bayesian framework is made difficult by the computational cost of numerical integration over large parameter spaces. A new, efficient method for the computation of posterior probabilities has recently been proposed and applied to complex problems from the physical sciences. Here we demonstrate how nested sampling can be used for inference and model comparison in biological sciences. We present a reanalysis of data from experimental infection of mice with Salmonella enterica showing the distribution of bacteria in liver cells. In addition to confirming the main finding of the original analysis, which relied on AIC, our approach provides: (a) integration across the parameter space, (b) estimation of the posterior parameter distributions (with visualisations of parameter correlations), and (c) estimation of the posterior predictive distributions for goodness-of-fit assessments of the models. The goodness-of-fit results suggest that alternative mechanistic models and a relaxation of the quasi-stationary assumption should be considered. PMID:24376528

Mean Field Variational Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Vrettas, M.; Cornford, D.; Opper, M.

2012-04-01

Current data assimilation schemes propose a range of approximate solutions to the classical data assimilation problem, particularly state estimation. Broadly there are three main active research areas: ensemble Kalman filter methods which rely on statistical linearization of the model evolution equations, particle filters which provide a discrete point representation of the posterior filtering or smoothing distribution and 4DVAR methods which seek the most likely posterior smoothing solution. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the most probably posterior distribution over the states, within the family of non-stationary Gaussian processes. Our original work on variational Bayesian approaches to data assimilation sought the best approximating time varying Gaussian process to the posterior smoothing distribution for stochastic dynamical systems. This approach was based on minimising the Kullback-Leibler divergence between the true posterior over paths, and our Gaussian process approximation. So long as the observation density was sufficiently high to bring the posterior smoothing density close to Gaussian the algorithm proved very effective, on lower dimensional systems. However for higher dimensional systems, the algorithm was computationally very demanding. We have been developing a mean field version of the algorithm which treats the state variables at a given time as being independent in the posterior approximation, but still accounts for their relationships between each other in the mean solution arising from the original dynamical system. In this work we present the new mean field variational Bayesian approach, illustrating its performance on a range of classical data assimilation problems. We discuss the potential and limitations of the new approach. We emphasise that the variational Bayesian approach we adopt, in contrast to other variational approaches, provides a bound on the marginal likelihood of the observations given parameters in the model which also allows inference of parameters such as observation errors, and parameters in the model and model error representation, particularly if this is written as a deterministic form with small additive noise. We stress that our approach can address very long time window and weak constraint settings. However like traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem. We finish with a sketch of the future directions for our approach.

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.

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…

Efficient implementation of the Metropolis-Hastings algorithm, with application to the Cormack?Jolly?Seber model

USGS Publications Warehouse

Link, W.A.; Barker, R.J.

2008-01-01

Judicious choice of candidate generating distributions improves efficiency of the Metropolis-Hastings algorithm. In Bayesian applications, it is sometimes possible to identify an approximation to the target posterior distribution; this approximate posterior distribution is a good choice for candidate generation. These observations are applied to analysis of the Cormack?Jolly?Seber model and its extensions.

Selecting Summary Statistics in Approximate Bayesian Computation for Calibrating Stochastic Models

PubMed Central

Burr, Tom

2013-01-01

Approximate Bayesian computation (ABC) is an approach for using measurement data to calibrate stochastic computer models, which are common in biology applications. ABC is becoming the “go-to” option when the data and/or parameter dimension is large because it relies on user-chosen summary statistics rather than the full data and is therefore computationally feasible. One technical challenge with ABC is that the quality of the approximation to the posterior distribution of model parameters depends on the user-chosen summary statistics. In this paper, the user requirement to choose effective summary statistics in order to accurately estimate the posterior distribution of model parameters is investigated and illustrated by example, using a model and corresponding real data of mitochondrial DNA population dynamics. We show that for some choices of summary statistics, the posterior distribution of model parameters is closely approximated and for other choices of summary statistics, the posterior distribution is not closely approximated. A strategy to choose effective summary statistics is suggested in cases where the stochastic computer model can be run at many trial parameter settings, as in the example. PMID:24288668

Selecting summary statistics in approximate Bayesian computation for calibrating stochastic models.

PubMed

Burr, Tom; Skurikhin, Alexei

2013-01-01

Approximate Bayesian computation (ABC) is an approach for using measurement data to calibrate stochastic computer models, which are common in biology applications. ABC is becoming the "go-to" option when the data and/or parameter dimension is large because it relies on user-chosen summary statistics rather than the full data and is therefore computationally feasible. One technical challenge with ABC is that the quality of the approximation to the posterior distribution of model parameters depends on the user-chosen summary statistics. In this paper, the user requirement to choose effective summary statistics in order to accurately estimate the posterior distribution of model parameters is investigated and illustrated by example, using a model and corresponding real data of mitochondrial DNA population dynamics. We show that for some choices of summary statistics, the posterior distribution of model parameters is closely approximated and for other choices of summary statistics, the posterior distribution is not closely approximated. A strategy to choose effective summary statistics is suggested in cases where the stochastic computer model can be run at many trial parameter settings, as in the example.

Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2016-12-01

In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posterior distribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, prior construction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In this paper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.

2016-01-01

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

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

Propagation of population pharmacokinetic information using a Bayesian approach: comparison with meta-analysis.

PubMed

Dokoumetzidis, Aristides; Aarons, Leon

2005-08-01

We investigated the propagation of population pharmacokinetic information across clinical studies by applying Bayesian techniques. The aim was to summarize the population pharmacokinetic estimates of a study in appropriate statistical distributions in order to use them as Bayesian priors in consequent population pharmacokinetic analyses. Various data sets of simulated and real clinical data were fitted with WinBUGS, with and without informative priors. The posterior estimates of fittings with non-informative priors were used to build parametric informative priors and the whole procedure was carried on in a consecutive manner. The posterior distributions of the fittings with informative priors where compared to those of the meta-analysis fittings of the respective combinations of data sets. Good agreement was found, for the simulated and experimental datasets when the populations were exchangeable, with the posterior distribution from the fittings with the prior to be nearly identical to the ones estimated with meta-analysis. However, when populations were not exchangeble an alternative parametric form for the prior, the natural conjugate prior, had to be used in order to have consistent results. In conclusion, the results of a population pharmacokinetic analysis may be summarized in Bayesian prior distributions that can be used consecutively with other analyses. The procedure is an alternative to meta-analysis and gives comparable results. It has the advantage that it is faster than the meta-analysis, due to the large datasets used with the latter and can be performed when the data included in the prior are not actually available.

An approach to quantifying the efficiency of a Bayesian filter

USDA-ARS?s Scientific Manuscript database

Data assimilation is defined as the Bayesian conditioning of uncertain model simulations on observations for the purpose of reducing uncertainty about model states. Practical data assimilation applications require that simplifying assumptions be made about the prior and posterior state distributions...

Dynamic Bayesian wavelet transform: New methodology for extraction of repetitive transients

NASA Astrophysics Data System (ADS)

Wang, Dong; Tsui, Kwok-Leung

2017-05-01

Thanks to some recent research works, dynamic Bayesian wavelet transform as new methodology for extraction of repetitive transients is proposed in this short communication to reveal fault signatures hidden in rotating machine. The main idea of the dynamic Bayesian wavelet transform is to iteratively estimate posterior parameters of wavelet transform via artificial observations and dynamic Bayesian inference. First, a prior wavelet parameter distribution can be established by one of many fast detection algorithms, such as the fast kurtogram, the improved kurtogram, the enhanced kurtogram, the sparsogram, the infogram, continuous wavelet transform, discrete wavelet transform, wavelet packets, multiwavelets, empirical wavelet transform, empirical mode decomposition, local mean decomposition, etc.. Second, artificial observations can be constructed based on one of many metrics, such as kurtosis, the sparsity measurement, entropy, approximate entropy, the smoothness index, a synthesized criterion, etc., which are able to quantify repetitive transients. Finally, given artificial observations, the prior wavelet parameter distribution can be posteriorly updated over iterations by using dynamic Bayesian inference. More importantly, the proposed new methodology can be extended to establish the optimal parameters required by many other signal processing methods for extraction of repetitive transients.

Bayesian approach to estimate AUC, partition coefficient and drug targeting index for studies with serial sacrifice design.

PubMed

Wang, Tianli; Baron, Kyle; Zhong, Wei; Brundage, Richard; Elmquist, William

2014-03-01

The current study presents a Bayesian approach to non-compartmental analysis (NCA), which provides the accurate and precise estimate of AUC 0 (∞) and any AUC 0 (∞) -based NCA parameter or derivation. In order to assess the performance of the proposed method, 1,000 simulated datasets were generated in different scenarios. A Bayesian method was used to estimate the tissue and plasma AUC 0 (∞) s and the tissue-to-plasma AUC 0 (∞) ratio. The posterior medians and the coverage of 95% credible intervals for the true parameter values were examined. The method was applied to laboratory data from a mice brain distribution study with serial sacrifice design for illustration. Bayesian NCA approach is accurate and precise in point estimation of the AUC 0 (∞) and the partition coefficient under a serial sacrifice design. It also provides a consistently good variance estimate, even considering the variability of the data and the physiological structure of the pharmacokinetic model. The application in the case study obtained a physiologically reasonable posterior distribution of AUC, with a posterior median close to the value estimated by classic Bailer-type methods. This Bayesian NCA approach for sparse data analysis provides statistical inference on the variability of AUC 0 (∞) -based parameters such as partition coefficient and drug targeting index, so that the comparison of these parameters following destructive sampling becomes statistically feasible.

Using Bayesian neural networks to classify forest scenes

NASA Astrophysics Data System (ADS)

Vehtari, Aki; Heikkonen, Jukka; Lampinen, Jouko; Juujarvi, Jouni

1998-10-01

We present results that compare the performance of Bayesian learning methods for neural networks on the task of classifying forest scenes into trees and background. Classification task is demanding due to the texture richness of the trees, occlusions of the forest scene objects and diverse lighting conditions under operation. This makes it difficult to determine which are optimal image features for the classification. A natural way to proceed is to extract many different types of potentially suitable features, and to evaluate their usefulness in later processing stages. One approach to cope with large number of features is to use Bayesian methods to control the model complexity. Bayesian learning uses a prior on model parameters, combines this with evidence from a training data, and the integrates over the resulting posterior to make predictions. With this method, we can use large networks and many features without fear of overfitting. For this classification task we compare two Bayesian learning methods for multi-layer perceptron (MLP) neural networks: (1) The evidence framework of MacKay uses a Gaussian approximation to the posterior weight distribution and maximizes with respect to hyperparameters. (2) In a Markov Chain Monte Carlo (MCMC) method due to Neal, the posterior distribution of the network parameters is numerically integrated using the MCMC method. As baseline classifiers for comparison we use (3) MLP early stop committee, (4) K-nearest-neighbor and (5) Classification And Regression Tree.

Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation

NASA Astrophysics Data System (ADS)

Reis, D. S.; Stedinger, J. R.; Martins, E. S.

2005-10-01

This paper develops a Bayesian approach to analysis of a generalized least squares (GLS) regression model for regional analyses of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model error variance using a quasi-analytic approach. Two regional skew estimation studies illustrate the value of the Bayesian GLS approach for regional statistical analysis of a shape parameter and demonstrate that regional skew models can be relatively precise with effective record lengths in excess of 60 years. With Bayesian GLS the marginal posterior distribution of the model error variance and the corresponding mean and variance of the parameters can be computed directly, thereby providing a simple but important extension of the regional GLS regression procedures popularized by Tasker and Stedinger (1989), which is sensitive to the likely values of the model error variance when it is small relative to the sampling error in the at-site estimator.

Bayesian prediction of future ice sheet volume using local approximation Markov chain Monte Carlo methods

NASA Astrophysics Data System (ADS)

Davis, A. D.; Heimbach, P.; Marzouk, Y.

2017-12-01

We develop a Bayesian inverse modeling framework for predicting future ice sheet volume with associated formal uncertainty estimates. Marine ice sheets are drained by fast-flowing ice streams, which we simulate using a flowline model. Flowline models depend on geometric parameters (e.g., basal topography), parameterized physical processes (e.g., calving laws and basal sliding), and climate parameters (e.g., surface mass balance), most of which are unknown or uncertain. Given observations of ice surface velocity and thickness, we define a Bayesian posterior distribution over static parameters, such as basal topography. We also define a parameterized distribution over variable parameters, such as future surface mass balance, which we assume are not informed by the data. Hyperparameters are used to represent climate change scenarios, and sampling their distributions mimics internal variation. For example, a warming climate corresponds to increasing mean surface mass balance but an individual sample may have periods of increasing or decreasing surface mass balance. We characterize the predictive distribution of ice volume by evaluating the flowline model given samples from the posterior distribution and the distribution over variable parameters. Finally, we determine the effect of climate change on future ice sheet volume by investigating how changing the hyperparameters affects the predictive distribution. We use state-of-the-art Bayesian computation to address computational feasibility. Characterizing the posterior distribution (using Markov chain Monte Carlo), sampling the full range of variable parameters and evaluating the predictive model is prohibitively expensive. Furthermore, the required resolution of the inferred basal topography may be very high, which is often challenging for sampling methods. Instead, we leverage regularity in the predictive distribution to build a computationally cheaper surrogate over the low dimensional quantity of interest (future ice sheet volume). Continual surrogate refinement guarantees asymptotic sampling from the predictive distribution. Directly characterizing the predictive distribution in this way allows us to assess the ice sheet's sensitivity to climate variability and change.

Robust Bayesian Factor Analysis

ERIC Educational Resources Information Center

Hayashi, Kentaro; Yuan, Ke-Hai

2003-01-01

Bayesian factor analysis (BFA) assumes the normal distribution of the current sample conditional on the parameters. Practical data in social and behavioral sciences typically have significant skewness and kurtosis. If the normality assumption is not attainable, the posterior analysis will be inaccurate, although the BFA depends less on the current…

Bayesian Semiparametric Structural Equation Models with Latent Variables

ERIC Educational Resources Information Center

Yang, Mingan; Dunson, David B.

2010-01-01

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In…

Bayesian Inference for Generalized Linear Models for Spiking Neurons

PubMed Central

Gerwinn, Sebastian; Macke, Jakob H.; Bethge, Matthias

2010-01-01

Generalized Linear Models (GLMs) are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate. PMID:20577627

Bayesian posterior distributions without Markov chains.

PubMed

Cole, Stephen R; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B

2012-03-01

Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.

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.

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 Estimation of the DINA Model with Gibbs Sampling

ERIC Educational Resources Information Center

Culpepper, Steven Andrew

2015-01-01

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

A Bayesian Framework of Uncertainties Integration in 3D Geological Model

NASA Astrophysics Data System (ADS)

Liang, D.; Liu, X.

2017-12-01

3D geological model can describe complicated geological phenomena in an intuitive way while its application may be limited by uncertain factors. Great progress has been made over the years, lots of studies decompose the uncertainties of geological model to analyze separately, while ignored the comprehensive impacts of multi-source uncertainties. Great progress has been made over the years, while lots of studies ignored the comprehensive impacts of multi-source uncertainties when analyzed them item by item from each source. To evaluate the synthetical uncertainty, we choose probability distribution to quantify uncertainty, and propose a bayesian framework of uncertainties integration. With this framework, we integrated data errors, spatial randomness, and cognitive information into posterior distribution to evaluate synthetical uncertainty of geological model. Uncertainties propagate and cumulate in modeling process, the gradual integration of multi-source uncertainty is a kind of simulation of the uncertainty propagation. Bayesian inference accomplishes uncertainty updating in modeling process. Maximum entropy principle makes a good effect on estimating prior probability distribution, which ensures the prior probability distribution subjecting to constraints supplied by the given information with minimum prejudice. In the end, we obtained a posterior distribution to evaluate synthetical uncertainty of geological model. This posterior distribution represents the synthetical impact of all the uncertain factors on the spatial structure of geological model. The framework provides a solution to evaluate synthetical impact on geological model of multi-source uncertainties and a thought to study uncertainty propagation mechanism in geological modeling.

A Bayesian test for Hardy–Weinberg equilibrium of biallelic X-chromosomal markers

PubMed Central

Puig, X; Ginebra, J; Graffelman, J

2017-01-01

The X chromosome is a relatively large chromosome, harboring a lot of genetic information. Much of the statistical analysis of X-chromosomal information is complicated by the fact that males only have one copy. Recently, frequentist statistical tests for Hardy–Weinberg equilibrium have been proposed specifically for dealing with markers on the X chromosome. Bayesian test procedures for Hardy–Weinberg equilibrium for the autosomes have been described, but Bayesian work on the X chromosome in this context is lacking. This paper gives the first Bayesian approach for testing Hardy–Weinberg equilibrium with biallelic markers at the X chromosome. Marginal and joint posterior distributions for the inbreeding coefficient in females and the male to female allele frequency ratio are computed, and used for statistical inference. The paper gives a detailed account of the proposed Bayesian test, and illustrates it with data from the 1000 Genomes project. In that implementation, a novel approach to tackle multiple testing from a Bayesian perspective through posterior predictive checks is used. PMID:28900292

A hierarchical Bayesian GEV model for improving local and regional flood quantile estimates

NASA Astrophysics Data System (ADS)

Lima, Carlos H. R.; Lall, Upmanu; Troy, Tara; Devineni, Naresh

2016-10-01

We estimate local and regional Generalized Extreme Value (GEV) distribution parameters for flood frequency analysis in a multilevel, hierarchical Bayesian framework, to explicitly model and reduce uncertainties. As prior information for the model, we assume that the GEV location and scale parameters for each site come from independent log-normal distributions, whose mean parameter scales with the drainage area. From empirical and theoretical arguments, the shape parameter for each site is shrunk towards a common mean. Non-informative prior distributions are assumed for the hyperparameters and the MCMC method is used to sample from the joint posterior distribution. The model is tested using annual maximum series from 20 streamflow gauges located in an 83,000 km2 flood prone basin in Southeast Brazil. The results show a significant reduction of uncertainty estimates of flood quantile estimates over the traditional GEV model, particularly for sites with shorter records. For return periods within the range of the data (around 50 years), the Bayesian credible intervals for the flood quantiles tend to be narrower than the classical confidence limits based on the delta method. As the return period increases beyond the range of the data, the confidence limits from the delta method become unreliable and the Bayesian credible intervals provide a way to estimate satisfactory confidence bands for the flood quantiles considering parameter uncertainties and regional information. In order to evaluate the applicability of the proposed hierarchical Bayesian model for regional flood frequency analysis, we estimate flood quantiles for three randomly chosen out-of-sample sites and compare with classical estimates using the index flood method. The posterior distributions of the scaling law coefficients are used to define the predictive distributions of the GEV location and scale parameters for the out-of-sample sites given only their drainage areas and the posterior distribution of the average shape parameter is taken as the regional predictive distribution for this parameter. While the index flood method does not provide a straightforward way to consider the uncertainties in the index flood and in the regional parameters, the results obtained here show that the proposed Bayesian method is able to produce adequate credible intervals for flood quantiles that are in accordance with empirical estimates.

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.

Bayesian Inference and Online Learning in Poisson Neuronal Networks.

PubMed

Huang, Yanping; Rao, Rajesh P N

2016-08-01

Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.

Comparison of sampling techniques for Bayesian parameter estimation

NASA Astrophysics Data System (ADS)

Allison, Rupert; Dunkley, Joanna

2014-02-01

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the posterior probability distribution we have to decide how to explore parameter space. Here we compare three prescriptions for how parameter space is navigated, discussing their relative merits. We consider Metropolis-Hasting sampling, nested sampling and affine-invariant ensemble Markov chain Monte Carlo (MCMC) sampling. We focus on their performance on toy-model Gaussian likelihoods and on a real-world cosmological data set. We outline the sampling algorithms themselves and elaborate on performance diagnostics such as convergence time, scope for parallelization, dimensional scaling, requisite tunings and suitability for non-Gaussian distributions. We find that nested sampling delivers high-fidelity estimates for posterior statistics at low computational cost, and should be adopted in favour of Metropolis-Hastings in many cases. Affine-invariant MCMC is competitive when computing clusters can be utilized for massive parallelization. Affine-invariant MCMC and existing extensions to nested sampling naturally probe multimodal and curving distributions.

Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

NASA Astrophysics Data System (ADS)

Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas

2017-02-01

A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally, locally and un-identifiable model classes, and then to model updating of a two degree-of-freedom nonlinear structure with Duffing nonlinearities in its interstory force-deflection relationship.

Bayesian model selection: Evidence estimation based on DREAM simulation and bridge sampling

NASA Astrophysics Data System (ADS)

Volpi, Elena; Schoups, Gerrit; Firmani, Giovanni; Vrugt, Jasper A.

2017-04-01

Bayesian inference has found widespread application in Earth and Environmental Systems Modeling, providing an effective tool for prediction, data assimilation, parameter estimation, uncertainty analysis and hypothesis testing. Under multiple competing hypotheses, the Bayesian approach also provides an attractive alternative to traditional information criteria (e.g. AIC, BIC) for model selection. The key variable for Bayesian model selection is the evidence (or marginal likelihood) that is the normalizing constant in the denominator of Bayes theorem; while it is fundamental for model selection, the evidence is not required for Bayesian inference. It is computed for each hypothesis (model) by averaging the likelihood function over the prior parameter distribution, rather than maximizing it as by information criteria; the larger a model evidence the more support it receives among a collection of hypothesis as the simulated values assign relatively high probability density to the observed data. Hence, the evidence naturally acts as an Occam's razor, preferring simpler and more constrained models against the selection of over-fitted ones by information criteria that incorporate only the likelihood maximum. Since it is not particularly easy to estimate the evidence in practice, Bayesian model selection via the marginal likelihood has not yet found mainstream use. We illustrate here the properties of a new estimator of the Bayesian model evidence, which provides robust and unbiased estimates of the marginal likelihood; the method is coined Gaussian Mixture Importance Sampling (GMIS). GMIS uses multidimensional numerical integration of the posterior parameter distribution via bridge sampling (a generalization of importance sampling) of a mixture distribution fitted to samples of the posterior distribution derived from the DREAM algorithm (Vrugt et al., 2008; 2009). Some illustrative examples are presented to show the robustness and superiority of the GMIS estimator with respect to other commonly used approaches in the literature.

Bayesian calibration of terrestrial ecosystem models: A study of advanced Markov chain Monte Carlo methods

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

Lu, Dan; Ricciuto, Daniel; Walker, Anthony

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this study, a Differential Evolution Adaptive Metropolis (DREAM) algorithm was used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The DREAM is a multi-chainmore » method and uses differential evolution technique for chain movement, allowing it to be efficiently applied to high-dimensional problems, and can reliably estimate heavy-tailed and multimodal distributions that are difficult for single-chain schemes using a Gaussian proposal distribution. The results were evaluated against the popular Adaptive Metropolis (AM) scheme. DREAM indicated that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identified one mode. The calibration of DREAM resulted in a better model fit and predictive performance compared to the AM. DREAM provides means for a good exploration of the posterior distributions of model parameters. Lastly, it reduces the risk of false convergence to a local optimum and potentially improves the predictive performance of the calibrated model.« less

Bayesian calibration of terrestrial ecosystem models: A study of advanced Markov chain Monte Carlo methods

DOE PAGES

Lu, Dan; Ricciuto, Daniel; Walker, Anthony; ...

2017-02-22

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this study, a Differential Evolution Adaptive Metropolis (DREAM) algorithm was used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The DREAM is a multi-chainmore » method and uses differential evolution technique for chain movement, allowing it to be efficiently applied to high-dimensional problems, and can reliably estimate heavy-tailed and multimodal distributions that are difficult for single-chain schemes using a Gaussian proposal distribution. The results were evaluated against the popular Adaptive Metropolis (AM) scheme. DREAM indicated that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identified one mode. The calibration of DREAM resulted in a better model fit and predictive performance compared to the AM. DREAM provides means for a good exploration of the posterior distributions of model parameters. Lastly, it reduces the risk of false convergence to a local optimum and potentially improves the predictive performance of the calibrated model.« less

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Bayesian Regression with Network Prior: Optimal Bayesian Filtering Perspective

PubMed Central

Qian, Xiaoning; Dougherty, Edward R.

2017-01-01

The recently introduced intrinsically Bayesian robust filter (IBRF) provides fully optimal filtering relative to a prior distribution over an uncertainty class ofjoint random process models, whereas formerly the theory was limited to model-constrained Bayesian robust filters, for which optimization was limited to the filters that are optimal for models in the uncertainty class. This paper extends the IBRF theory to the situation where there are both a prior on the uncertainty class and sample data. The result is optimal Bayesian filtering (OBF), where optimality is relative to the posterior distribution derived from the prior and the data. The IBRF theories for effective characteristics and canonical expansions extend to the OBF setting. A salient focus of the present work is to demonstrate the advantages of Bayesian regression within the OBF setting over the classical Bayesian approach in the context otlinear Gaussian models. PMID:28824268

Bayesian parameter estimation for chiral effective field theory

NASA Astrophysics Data System (ADS)

Wesolowski, Sarah; Furnstahl, Richard; Phillips, Daniel; Klco, Natalie

2016-09-01

The low-energy constants (LECs) of a chiral effective field theory (EFT) interaction in the two-body sector are fit to observable data using a Bayesian parameter estimation framework. By using Bayesian prior probability distributions (pdfs), we quantify relevant physical expectations such as LEC naturalness and include them in the parameter estimation procedure. The final result is a posterior pdf for the LECs, which can be used to propagate uncertainty resulting from the fit to data to the final observable predictions. The posterior pdf also allows an empirical test of operator redundancy and other features of the potential. We compare results of our framework with other fitting procedures, interpreting the underlying assumptions in Bayesian probabilistic language. We also compare results from fitting all partial waves of the interaction simultaneously to cross section data compared to fitting to extracted phase shifts, appropriately accounting for correlations in the data. Supported in part by the NSF and DOE.

XID+: Next generation XID development

NASA Astrophysics Data System (ADS)

Hurley, Peter

2017-04-01

XID+ is a prior-based source extraction tool which carries out photometry in the Herschel SPIRE (Spectral and Photometric Imaging Receiver) maps at the positions of known sources. It uses a probabilistic Bayesian framework that provides a natural framework in which to include prior information, and uses the Bayesian inference tool Stan to obtain the full posterior probability distribution on flux estimates.

Validation of Bayesian analysis of compartmental kinetic models in medical imaging.

PubMed

Sitek, Arkadiusz; Li, Quanzheng; El Fakhri, Georges; Alpert, Nathaniel M

2016-10-01

Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated. The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach. Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001). The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Validation of the thermal challenge problem using Bayesian Belief Networks.

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

McFarland, John; Swiler, Laura Painton

The thermal challenge problem has been developed at Sandia National Laboratories as a testbed for demonstrating various types of validation approaches and prediction methods. This report discusses one particular methodology to assess the validity of a computational model given experimental data. This methodology is based on Bayesian Belief Networks (BBNs) and can incorporate uncertainty in experimental measurements, in physical quantities, and model uncertainties. The approach uses the prior and posterior distributions of model output to compute a validation metric based on Bayesian hypothesis testing (a Bayes' factor). This report discusses various aspects of the BBN, specifically in the context ofmore » the thermal challenge problem. A BBN is developed for a given set of experimental data in a particular experimental configuration. The development of the BBN and the method for ''solving'' the BBN to develop the posterior distribution of model output through Monte Carlo Markov Chain sampling is discussed in detail. The use of the BBN to compute a Bayes' factor is demonstrated.« less

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

NASA Astrophysics Data System (ADS)

Lu, Dan; Ricciuto, Daniel; Walker, Anthony; Safta, Cosmin; Munger, William

2017-09-01

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.

2D Bayesian automated tilted-ring fitting of disc galaxies in large H I galaxy surveys: 2DBAT

NASA Astrophysics Data System (ADS)

Oh, Se-Heon; Staveley-Smith, Lister; Spekkens, Kristine; Kamphuis, Peter; Koribalski, Bärbel S.

2018-01-01

We present a novel algorithm based on a Bayesian method for 2D tilted-ring analysis of disc galaxy velocity fields. Compared to the conventional algorithms based on a chi-squared minimization procedure, this new Bayesian-based algorithm suffers less from local minima of the model parameters even with highly multimodal posterior distributions. Moreover, the Bayesian analysis, implemented via Markov Chain Monte Carlo sampling, only requires broad ranges of posterior distributions of the parameters, which makes the fitting procedure fully automated. This feature will be essential when performing kinematic analysis on the large number of resolved galaxies expected to be detected in neutral hydrogen (H I) surveys with the Square Kilometre Array and its pathfinders. The so-called 2D Bayesian Automated Tilted-ring fitter (2DBAT) implements Bayesian fits of 2D tilted-ring models in order to derive rotation curves of galaxies. We explore 2DBAT performance on (a) artificial H I data cubes built based on representative rotation curves of intermediate-mass and massive spiral galaxies, and (b) Australia Telescope Compact Array H I data from the Local Volume H I Survey. We find that 2DBAT works best for well-resolved galaxies with intermediate inclinations (20° < i < 70°), complementing 3D techniques better suited to modelling inclined galaxies.

A Bayesian Alternative for Multi-objective Ecohydrological Model Specification

NASA Astrophysics Data System (ADS)

Tang, Y.; Marshall, L. A.; Sharma, A.; Ajami, H.

2015-12-01

Process-based ecohydrological models combine the study of hydrological, physical, biogeochemical and ecological processes of the catchments, which are usually 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. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological framework. In our study, a formal Bayesian approach is implemented in an ecohydrological model which combines a hydrological model (HyMOD) and a dynamic vegetation model (DVM). Simulations focused on one objective likelihood (Streamflow/LAI) and multi-objective likelihoods (Streamflow and LAI) with different weights are compared. Uniform, weakly informative and strongly informative prior distributions are used in different simulations. The Kullback-leibler divergence (KLD) is used to measure the dis(similarity) between different priors and corresponding posterior distributions to examine the parameter sensitivity. Results show that different prior distributions can strongly influence posterior distributions for parameters, especially when the available data is limited or parameters are insensitive to the available data. We demonstrate differences in optimized parameters and uncertainty limits in different cases based on multi-objective likelihoods vs. single objective likelihoods. We also demonstrate the importance of appropriately defining the weights of objectives in multi-objective calibration according to different data types.

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.

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.

A Variational Bayes Genomic-Enabled Prediction Model with Genotype × Environment Interaction

PubMed Central

Montesinos-López, Osval A.; Montesinos-López, Abelardo; Crossa, José; Montesinos-López, José Cricelio; Luna-Vázquez, Francisco Javier; Salinas-Ruiz, Josafhat; Herrera-Morales, José R.; Buenrostro-Mariscal, Raymundo

2017-01-01

There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments. PMID:28391241

A Variational Bayes Genomic-Enabled Prediction Model with Genotype × Environment Interaction.

PubMed

Montesinos-López, Osval A; Montesinos-López, Abelardo; Crossa, José; Montesinos-López, José Cricelio; Luna-Vázquez, Francisco Javier; Salinas-Ruiz, Josafhat; Herrera-Morales, José R; Buenrostro-Mariscal, Raymundo

2017-06-07

There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments. Copyright © 2017 Montesinos-López et al.

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

Accelerating Approximate Bayesian Computation with Quantile Regression: application to cosmological redshift distributions

NASA Astrophysics Data System (ADS)

Kacprzak, T.; Herbel, J.; Amara, A.; Réfrégier, A.

2018-02-01

Approximate Bayesian Computation (ABC) is a method to obtain a posterior distribution without a likelihood function, using simulations and a set of distance metrics. For that reason, it has recently been gaining popularity as an analysis tool in cosmology and astrophysics. Its drawback, however, is a slow convergence rate. We propose a novel method, which we call qABC, to accelerate ABC with Quantile Regression. In this method, we create a model of quantiles of distance measure as a function of input parameters. This model is trained on a small number of simulations and estimates which regions of the prior space are likely to be accepted into the posterior. Other regions are then immediately rejected. This procedure is then repeated as more simulations are available. We apply it to the practical problem of estimation of redshift distribution of cosmological samples, using forward modelling developed in previous work. The qABC method converges to nearly same posterior as the basic ABC. It uses, however, only 20% of the number of simulations compared to basic ABC, achieving a fivefold gain in execution time for our problem. For other problems the acceleration rate may vary; it depends on how close the prior is to the final posterior. We discuss possible improvements and extensions to this method.

A Bayesian model averaging approach for estimating the relative risk of mortality associated with heat waves in 105 U.S. cities.

PubMed

Bobb, Jennifer F; Dominici, Francesca; Peng, Roger D

2011-12-01

Estimating the risks heat waves pose to human health is a critical part of assessing the future impact of climate change. In this article, we propose a flexible class of time series models to estimate the relative risk of mortality associated with heat waves and conduct Bayesian model averaging (BMA) to account for the multiplicity of potential models. Applying these methods to data from 105 U.S. cities for the period 1987-2005, we identify those cities having a high posterior probability of increased mortality risk during heat waves, examine the heterogeneity of the posterior distributions of mortality risk across cities, assess sensitivity of the results to the selection of prior distributions, and compare our BMA results to a model selection approach. Our results show that no single model best predicts risk across the majority of cities, and that for some cities heat-wave risk estimation is sensitive to model choice. Although model averaging leads to posterior distributions with increased variance as compared to statistical inference conditional on a model obtained through model selection, we find that the posterior mean of heat wave mortality risk is robust to accounting for model uncertainty over a broad class of models. © 2011, The International Biometric Society.

Bayesian Analysis of Item Response Curves. Research Report 84-1. Mathematical Sciences Technical Report No. 132.

ERIC Educational Resources Information Center

Tsutakawa, Robert K.; Lin, Hsin Ying

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data…

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

On the use of Bayesian Monte-Carlo in evaluation of nuclear data

NASA Astrophysics Data System (ADS)

De Saint Jean, Cyrille; Archier, Pascal; Privas, Edwin; Noguere, Gilles

2017-09-01

As model parameters, necessary ingredients of theoretical models, are not always predicted by theory, a formal mathematical framework associated to the evaluation work is needed to obtain the best set of parameters (resonance parameters, optical models, fission barrier, average width, multigroup cross sections) with Bayesian statistical inference by comparing theory to experiment. The formal rule related to this methodology is to estimate the posterior density probability function of a set of parameters by solving an equation of the following type: pdf(posterior) ˜ pdf(prior) × a likelihood function. A fitting procedure can be seen as an estimation of the posterior density probability of a set of parameters (referred as x→?) knowing a prior information on these parameters and a likelihood which gives the probability density function of observing a data set knowing x→?. To solve this problem, two major paths could be taken: add approximations and hypothesis and obtain an equation to be solved numerically (minimum of a cost function or Generalized least Square method, referred as GLS) or use Monte-Carlo sampling of all prior distributions and estimate the final posterior distribution. Monte Carlo methods are natural solution for Bayesian inference problems. They avoid approximations (existing in traditional adjustment procedure based on chi-square minimization) and propose alternative in the choice of probability density distribution for priors and likelihoods. This paper will propose the use of what we are calling Bayesian Monte Carlo (referred as BMC in the rest of the manuscript) in the whole energy range from thermal, resonance and continuum range for all nuclear reaction models at these energies. Algorithms will be presented based on Monte-Carlo sampling and Markov chain. The objectives of BMC are to propose a reference calculation for validating the GLS calculations and approximations, to test probability density distributions effects and to provide the framework of finding global minimum if several local minimums exist. Application to resolved resonance, unresolved resonance and continuum evaluation as well as multigroup cross section data assimilation will be presented.

On the use of posterior predictive probabilities and prediction uncertainty to tailor informative sampling for parasitological surveillance in livestock.

PubMed

Musella, Vincenzo; Rinaldi, Laura; Lagazio, Corrado; Cringoli, Giuseppe; Biggeri, Annibale; Catelan, Dolores

2014-09-15

Model-based geostatistics and Bayesian approaches are appropriate in the context of Veterinary Epidemiology when point data have been collected by valid study designs. The aim is to predict a continuous infection risk surface. Little work has been done on the use of predictive infection probabilities at farm unit level. In this paper we show how to use predictive infection probability and related uncertainty from a Bayesian kriging model to draw a informative samples from the 8794 geo-referenced sheep farms of the Campania region (southern Italy). Parasitological data come from a first cross-sectional survey carried out to study the spatial distribution of selected helminths in sheep farms. A grid sampling was performed to select the farms for coprological examinations. Faecal samples were collected for 121 sheep farms and the presence of 21 different helminths were investigated using the FLOTAC technique. The 21 responses are very different in terms of geographical distribution and prevalence of infection. The observed prevalence range is from 0.83% to 96.69%. The distributions of the posterior predictive probabilities for all the 21 parasites are very heterogeneous. We show how the results of the Bayesian kriging model can be used to plan a second wave survey. Several alternatives can be chosen depending on the purposes of the second survey: weight by posterior predictive probabilities, their uncertainty or combining both information. The proposed Bayesian kriging model is simple, and the proposed samping strategy represents a useful tool to address targeted infection control treatments and surbveillance campaigns. It is easily extendable to other fields of research. Copyright © 2014 Elsevier B.V. All rights reserved.

Topics in Bayesian Hierarchical Modeling and its Monte Carlo Computations

NASA Astrophysics Data System (ADS)

Tak, Hyung Suk

The first chapter addresses a Beta-Binomial-Logit model that is a Beta-Binomial conjugate hierarchical model with covariate information incorporated via a logistic regression. Various researchers in the literature have unknowingly used improper posterior distributions or have given incorrect statements about posterior propriety because checking posterior propriety can be challenging due to the complicated functional form of a Beta-Binomial-Logit model. We derive data-dependent necessary and sufficient conditions for posterior propriety within a class of hyper-prior distributions that encompass those used in previous studies. Frequency coverage properties of several hyper-prior distributions are also investigated to see when and whether Bayesian interval estimates of random effects meet their nominal confidence levels. The second chapter deals with a time delay estimation problem in astrophysics. When the gravitational field of an intervening galaxy between a quasar and the Earth is strong enough to split light into two or more images, the time delay is defined as the difference between their travel times. The time delay can be used to constrain cosmological parameters and can be inferred from the time series of brightness data of each image. To estimate the time delay, we construct a Gaussian hierarchical model based on a state-space representation for irregularly observed time series generated by a latent continuous-time Ornstein-Uhlenbeck process. Our Bayesian approach jointly infers model parameters via a Gibbs sampler. We also introduce a profile likelihood of the time delay as an approximation of its marginal posterior distribution. The last chapter specifies a repelling-attracting Metropolis algorithm, a new Markov chain Monte Carlo method to explore multi-modal distributions in a simple and fast manner. This algorithm is essentially a Metropolis-Hastings algorithm with a proposal that consists of a downhill move in density that aims to make local modes repelling, followed by an uphill move in density that aims to make local modes attracting. The downhill move is achieved via a reciprocal Metropolis ratio so that the algorithm prefers downward movement. The uphill move does the opposite using the standard Metropolis ratio which prefers upward movement. This down-up movement in density increases the probability of a proposed move to a different mode.

Melanoma Cell Colony Expansion Parameters Revealed by Approximate Bayesian Computation

PubMed Central

Vo, Brenda N.; Drovandi, Christopher C.; Pettitt, Anthony N.; Pettet, Graeme J.

2015-01-01

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ. PMID:26642072

The Estimation of Tree Posterior Probabilities Using Conditional Clade Probability Distributions

PubMed Central

Larget, Bret

2013-01-01

In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample. [Bayesian phylogenetics; conditional clade distributions; improved accuracy; posterior probabilities of trees.] PMID:23479066

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.

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

Bertholon, François; Harant, Olivier; Bourlon, Bertrand

This article introduces a joined Bayesian estimation of gas samples issued from a gas chromatography column (GC) coupled with a NEMS sensor based on Giddings Eyring microscopic molecular stochastic model. The posterior distribution is sampled using a Monte Carlo Markov Chain and Gibbs sampling. Parameters are estimated using the posterior mean. This estimation scheme is finally applied on simulated and real datasets using this molecular stochastic forward model.

PyMC: Bayesian Stochastic Modelling in Python

PubMed Central

Patil, Anand; Huard, David; Fonnesbeck, Christopher J.

2010-01-01

This user guide describes a Python package, PyMC, that allows users to efficiently code a probabilistic model and draw samples from its posterior distribution using Markov chain Monte Carlo techniques. PMID:21603108

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

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

Lu, Dan; Ricciuto, Daniel M.; Walker, Anthony P.

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results inmore » a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. Here, the result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.« less

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

DOE PAGES

Lu, Dan; Ricciuto, Daniel M.; Walker, Anthony P.; ...

2017-09-27

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results inmore » a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. Here, the result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.« less

Estimation from incomplete multinomial data. Ph.D. Thesis - Harvard Univ.

NASA Technical Reports Server (NTRS)

Credeur, K. R.

1978-01-01

The vector of multinomial cell probabilities was estimated from incomplete data, incomplete in that it contains partially classified observations. Each such partially classified observation was observed to fall in one of two or more selected categories but was not classified further into a single category. The data were assumed to be incomplete at random. The estimation criterion was minimization of risk for quadratic loss. The estimators were the classical maximum likelihood estimate, the Bayesian posterior mode, and the posterior mean. An approximation was developed for the posterior mean. The Dirichlet, the conjugate prior for the multinomial distribution, was assumed for the prior distribution.

Effective Online Bayesian Phylogenetics via Sequential Monte Carlo with Guided Proposals

PubMed Central

Fourment, Mathieu; Claywell, Brian C; Dinh, Vu; McCoy, Connor; Matsen IV, Frederick A; Darling, Aaron E

2018-01-01

Abstract Modern infectious disease outbreak surveillance produces continuous streams of sequence data which require phylogenetic analysis as data arrives. Current software packages for Bayesian phylogenetic inference are unable to quickly incorporate new sequences as they become available, making them less useful for dynamically unfolding evolutionary stories. This limitation can be addressed by applying a class of Bayesian statistical inference algorithms called sequential Monte Carlo (SMC) to conduct online inference, wherein new data can be continuously incorporated to update the estimate of the posterior probability distribution. In this article, we describe and evaluate several different online phylogenetic sequential Monte Carlo (OPSMC) algorithms. We show that proposing new phylogenies with a density similar to the Bayesian prior suffers from poor performance, and we develop “guided” proposals that better match the proposal density to the posterior. Furthermore, we show that the simplest guided proposals can exhibit pathological behavior in some situations, leading to poor results, and that the situation can be resolved by heating the proposal density. The results demonstrate that relative to the widely used MCMC-based algorithm implemented in MrBayes, the total time required to compute a series of phylogenetic posteriors as sequences arrive can be significantly reduced by the use of OPSMC, without incurring a significant loss in accuracy. PMID:29186587

Bayesian Inference on the Radio-quietness of Gamma-ray Pulsars

NASA Astrophysics Data System (ADS)

Yu, Hoi-Fung; Hui, Chung Yue; Kong, Albert K. H.; Takata, Jumpei

2018-04-01

For the first time we demonstrate using a robust Bayesian approach to analyze the populations of radio-quiet (RQ) and radio-loud (RL) gamma-ray pulsars. We quantify their differences and obtain their distributions of the radio-cone opening half-angle δ and the magnetic inclination angle α by Bayesian inference. In contrast to the conventional frequentist point estimations that might be non-representative when the distribution is highly skewed or multi-modal, which is often the case when data points are scarce, Bayesian statistics displays the complete posterior distribution that the uncertainties can be readily obtained regardless of the skewness and modality. We found that the spin period, the magnetic field strength at the light cylinder, the spin-down power, the gamma-ray-to-X-ray flux ratio, and the spectral curvature significance of the two groups of pulsars exhibit significant differences at the 99% level. Using Bayesian inference, we are able to infer the values and uncertainties of δ and α from the distribution of RQ and RL pulsars. We found that δ is between 10° and 35° and the distribution of α is skewed toward large values.

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

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

NASA Astrophysics Data System (ADS)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

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.

On parametrized cold dense matter equation-of-state inference

NASA Astrophysics Data System (ADS)

Riley, Thomas E.; Raaijmakers, Geert; Watts, Anna L.

2018-07-01

Constraining the equation of state of cold dense matter in compact stars is a major science goal for observing programmes being conducted using X-ray, radio, and gravitational wave telescopes. We discuss Bayesian hierarchical inference of parametrized dense matter equations of state. In particular, we generalize and examine two inference paradigms from the literature: (i) direct posterior equation-of-state parameter estimation, conditioned on observations of a set of rotating compact stars; and (ii) indirect parameter estimation, via transformation of an intermediary joint posterior distribution of exterior spacetime parameters (such as gravitational masses and coordinate equatorial radii). We conclude that the former paradigm is not only tractable for large-scale analyses, but is principled and flexible from a Bayesian perspective while the latter paradigm is not. The thematic problem of Bayesian prior definition emerges as the crux of the difference between these paradigms. The second paradigm should in general only be considered as an ill-defined approach to the problem of utilizing archival posterior constraints on exterior spacetime parameters; we advocate for an alternative approach whereby such information is repurposed as an approximative likelihood function. We also discuss why conditioning on a piecewise-polytropic equation-of-state model - currently standard in the field of dense matter study - can easily violate conditions required for transformation of a probability density distribution between spaces of exterior (spacetime) and interior (source matter) parameters.

On parametrised cold dense matter equation of state inference

NASA Astrophysics Data System (ADS)

Riley, Thomas E.; Raaijmakers, Geert; Watts, Anna L.

2018-04-01

Constraining the equation of state of cold dense matter in compact stars is a major science goal for observing programmes being conducted using X-ray, radio, and gravitational wave telescopes. We discuss Bayesian hierarchical inference of parametrised dense matter equations of state. In particular we generalise and examine two inference paradigms from the literature: (i) direct posterior equation of state parameter estimation, conditioned on observations of a set of rotating compact stars; and (ii) indirect parameter estimation, via transformation of an intermediary joint posterior distribution of exterior spacetime parameters (such as gravitational masses and coordinate equatorial radii). We conclude that the former paradigm is not only tractable for large-scale analyses, but is principled and flexible from a Bayesian perspective whilst the latter paradigm is not. The thematic problem of Bayesian prior definition emerges as the crux of the difference between these paradigms. The second paradigm should in general only be considered as an ill-defined approach to the problem of utilising archival posterior constraints on exterior spacetime parameters; we advocate for an alternative approach whereby such information is repurposed as an approximative likelihood function. We also discuss why conditioning on a piecewise-polytropic equation of state model - currently standard in the field of dense matter study - can easily violate conditions required for transformation of a probability density distribution between spaces of exterior (spacetime) and interior (source matter) parameters.

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.

Annealed Importance Sampling for Neural Mass Models

PubMed Central

Penny, Will; Sengupta, Biswa

2016-01-01

Neural Mass Models provide a compact description of the dynamical activity of cell populations in neocortical regions. Moreover, models of regional activity can be connected together into networks, and inferences made about the strength of connections, using M/EEG data and Bayesian inference. To date, however, Bayesian methods have been largely restricted to the Variational Laplace (VL) algorithm which assumes that the posterior distribution is Gaussian and finds model parameters that are only locally optimal. This paper explores the use of Annealed Importance Sampling (AIS) to address these restrictions. We implement AIS using proposals derived from Langevin Monte Carlo (LMC) which uses local gradient and curvature information for efficient exploration of parameter space. In terms of the estimation of Bayes factors, VL and AIS agree about which model is best but report different degrees of belief. Additionally, AIS finds better model parameters and we find evidence of non-Gaussianity in their posterior distribution. PMID:26942606

Hydrologic Model Selection using Markov chain Monte Carlo methods

NASA Astrophysics Data System (ADS)

Marshall, L.; Sharma, A.; Nott, D.

2002-12-01

Estimation of parameter uncertainty (and in turn model uncertainty) allows assessment of the risk in likely applications of hydrological models. Bayesian statistical inference provides an ideal means of assessing parameter uncertainty whereby prior knowledge about the parameter is combined with information from the available data to produce a probability distribution (the posterior distribution) that describes uncertainty about the parameter and serves as a basis for selecting appropriate values for use in modelling applications. Widespread use of Bayesian techniques in hydrology has been hindered by difficulties in summarizing and exploring the posterior distribution. These difficulties have been largely overcome by recent advances in Markov chain Monte Carlo (MCMC) methods that involve random sampling of the posterior distribution. This study presents an adaptive MCMC sampling algorithm which has characteristics that are well suited to model parameters with a high degree of correlation and interdependence, as is often evident in hydrological models. The MCMC sampling technique is used to compare six alternative configurations of a commonly used conceptual rainfall-runoff model, the Australian Water Balance Model (AWBM), using 11 years of daily rainfall runoff data from the Bass river catchment in Australia. The alternative configurations considered fall into two classes - those that consider model errors to be independent of prior values, and those that model the errors as an autoregressive process. Each such class consists of three formulations that represent increasing levels of complexity (and parameterisation) of the original model structure. The results from this study point both to the importance of using Bayesian approaches in evaluating model performance, as well as the simplicity of the MCMC sampling framework that has the ability to bring such approaches within the reach of the applied hydrological community.

Identification of transmissivity fields using a Bayesian strategy and perturbative approach

NASA Astrophysics Data System (ADS)

Zanini, Andrea; Tanda, Maria Giovanna; Woodbury, Allan D.

2017-10-01

The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y* (Y = lnT) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the lnT has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities (σY2 = 1.0 and σY2 = 5.3). The estimated transmissivity fields were compared to the true one. The joint use of Y* and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds.

A Bayesian kriging approach for blending satellite and ground precipitation observations

USGS Publications Warehouse

Verdin, Andrew P.; Rajagopalan, Balaji; Kleiber, William; Funk, Christopher C.

2015-01-01

Drought and flood management practices require accurate estimates of precipitation. Gauge observations, however, are often sparse in regions with complicated terrain, clustered in valleys, and of poor quality. Consequently, the spatial extent of wet events is poorly represented. Satellite-derived precipitation data are an attractive alternative, though they tend to underestimate the magnitude of wet events due to their dependency on retrieval algorithms and the indirect relationship between satellite infrared observations and precipitation intensities. Here we offer a Bayesian kriging approach for blending precipitation gauge data and the Climate Hazards Group Infrared Precipitation satellite-derived precipitation estimates for Central America, Colombia, and Venezuela. First, the gauge observations are modeled as a linear function of satellite-derived estimates and any number of other variables—for this research we include elevation. Prior distributions are defined for all model parameters and the posterior distributions are obtained simultaneously via Markov chain Monte Carlo sampling. The posterior distributions of these parameters are required for spatial estimation, and thus are obtained prior to implementing the spatial kriging model. This functional framework is applied to model parameters obtained by sampling from the posterior distributions, and the residuals of the linear model are subject to a spatial kriging model. Consequently, the posterior distributions and uncertainties of the blended precipitation estimates are obtained. We demonstrate this method by applying it to pentadal and monthly total precipitation fields during 2009. The model's performance and its inherent ability to capture wet events are investigated. We show that this blending method significantly improves upon the satellite-derived estimates and is also competitive in its ability to represent wet events. This procedure also provides a means to estimate a full conditional distribution of the “true” observed precipitation value at each grid cell.

Simulation-based Bayesian inference for latent traits of item response models: Introduction to the ltbayes package for R.

PubMed

Johnson, Timothy R; Kuhn, Kristine M

2015-12-01

This paper introduces the ltbayes package for R. This package includes a suite of functions for investigating the posterior distribution of latent traits of item response models. These include functions for simulating realizations from the posterior distribution, profiling the posterior density or likelihood function, calculation of posterior modes or means, Fisher information functions and observed information, and profile likelihood confidence intervals. Inferences can be based on individual response patterns or sets of response patterns such as sum scores. Functions are included for several common binary and polytomous item response models, but the package can also be used with user-specified models. This paper introduces some background and motivation for the package, and includes several detailed examples of its use.

Neural Mechanisms for Integrating Prior Knowledge and Likelihood in Value-Based Probabilistic Inference

PubMed Central

Ting, Chih-Chung; Yu, Chia-Chen; Maloney, Laurence T.

2015-01-01

In Bayesian decision theory, knowledge about the probabilities of possible outcomes is captured by a prior distribution and a likelihood function. The prior reflects past knowledge and the likelihood summarizes current sensory information. The two combined (integrated) form a posterior distribution that allows estimation of the probability of different possible outcomes. In this study, we investigated the neural mechanisms underlying Bayesian integration using a novel lottery decision task in which both prior knowledge and likelihood information about reward probability were systematically manipulated on a trial-by-trial basis. Consistent with Bayesian integration, as sample size increased, subjects tended to weigh likelihood information more compared with prior information. Using fMRI in humans, we found that the medial prefrontal cortex (mPFC) correlated with the mean of the posterior distribution, a statistic that reflects the integration of prior knowledge and likelihood of reward probability. Subsequent analysis revealed that both prior and likelihood information were represented in mPFC and that the neural representations of prior and likelihood in mPFC reflected changes in the behaviorally estimated weights assigned to these different sources of information in response to changes in the environment. Together, these results establish the role of mPFC in prior-likelihood integration and highlight its involvement in representing and integrating these distinct sources of information. PMID:25632152

Bayesian statistical inference enhances the interpretation of contemporary randomized controlled trials.

PubMed

Wijeysundera, Duminda N; Austin, Peter C; Hux, Janet E; Beattie, W Scott; Laupacis, Andreas

2009-01-01

Randomized trials generally use "frequentist" statistics based on P-values and 95% confidence intervals. Frequentist methods have limitations that might be overcome, in part, by Bayesian inference. To illustrate these advantages, we re-analyzed randomized trials published in four general medical journals during 2004. We used Medline to identify randomized superiority trials with two parallel arms, individual-level randomization and dichotomous or time-to-event primary outcomes. Studies with P<0.05 in favor of the intervention were deemed "positive"; otherwise, they were "negative." We used several prior distributions and exact conjugate analyses to calculate Bayesian posterior probabilities for clinically relevant effects. Of 88 included studies, 39 were positive using a frequentist analysis. Although the Bayesian posterior probabilities of any benefit (relative risk or hazard ratio<1) were high in positive studies, these probabilities were lower and variable for larger benefits. The positive studies had only moderate probabilities for exceeding the effects that were assumed for calculating the sample size. By comparison, there were moderate probabilities of any benefit in negative studies. Bayesian and frequentist analyses complement each other when interpreting the results of randomized trials. Future reports of randomized trials should include both.

Accommodating Uncertainty in Prior Distributions

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

Picard, Richard Roy; Vander Wiel, Scott Alan

2017-01-19

A fundamental premise of Bayesian methodology is that a priori information is accurately summarized by a single, precisely de ned prior distribution. In many cases, especially involving informative priors, this premise is false, and the (mis)application of Bayes methods produces posterior quantities whose apparent precisions are highly misleading. We examine the implications of uncertainty in prior distributions, and present graphical methods for dealing with them.

Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Cheong, R. Y.; Gabda, D.

2017-09-01

Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.

A bayesian approach to classification criteria for spectacled eiders

USGS Publications Warehouse

Taylor, B.L.; Wade, P.R.; Stehn, R.A.; Cochrane, J.F.

1996-01-01

To facilitate decisions to classify species according to risk of extinction, we used Bayesian methods to analyze trend data for the Spectacled Eider, an arctic sea duck. Trend data from three independent surveys of the Yukon-Kuskokwim Delta were analyzed individually and in combination to yield posterior distributions for population growth rates. We used classification criteria developed by the recovery team for Spectacled Eiders that seek to equalize errors of under- or overprotecting the species. We conducted both a Bayesian decision analysis and a frequentist (classical statistical inference) decision analysis. Bayesian decision analyses are computationally easier, yield basically the same results, and yield results that are easier to explain to nonscientists. With the exception of the aerial survey analysis of the 10 most recent years, both Bayesian and frequentist methods indicated that an endangered classification is warranted. The discrepancy between surveys warrants further research. Although the trend data are abundance indices, we used a preliminary estimate of absolute abundance to demonstrate how to calculate extinction distributions using the joint probability distributions for population growth rate and variance in growth rate generated by the Bayesian analysis. Recent apparent increases in abundance highlight the need for models that apply to declining and then recovering species.

A Bayesian nonrigid registration method to enhance intraoperative target definition in image-guided prostate procedures through uncertainty characterization

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

Pursley, Jennifer; Risholm, Petter; Fedorov, Andriy

2012-11-15

Purpose: This study introduces a probabilistic nonrigid registration method for use in image-guided prostate brachytherapy. Intraoperative imaging for prostate procedures, usually transrectal ultrasound (TRUS), is typically inferior to diagnostic-quality imaging of the pelvis such as endorectal magnetic resonance imaging (MRI). MR images contain superior detail of the prostate boundaries and provide substructure features not otherwise visible. Previous efforts to register diagnostic prostate images with the intraoperative coordinate system have been deterministic and did not offer a measure of the registration uncertainty. The authors developed a Bayesian registration method to estimate the posterior distribution on deformations and provide a case-specific measuremore » of the associated registration uncertainty. Methods: The authors adapted a biomechanical-based probabilistic nonrigid method to register diagnostic to intraoperative images by aligning a physician's segmentations of the prostate in the two images. The posterior distribution was characterized with a Markov Chain Monte Carlo method; the maximum a posteriori deformation and the associated uncertainty were estimated from the collection of deformation samples drawn from the posterior distribution. The authors validated the registration method using a dataset created from ten patients with MRI-guided prostate biopsies who had both diagnostic and intraprocedural 3 Tesla MRI scans. The accuracy and precision of the estimated posterior distribution on deformations were evaluated from two predictive distance distributions: between the deformed central zone-peripheral zone (CZ-PZ) interface and the physician-labeled interface, and based on physician-defined landmarks. Geometric margins on the registration of the prostate's peripheral zone were determined from the posterior predictive distance to the CZ-PZ interface separately for the base, mid-gland, and apical regions of the prostate. Results: The authors observed variation in the shape and volume of the segmented prostate in diagnostic and intraprocedural images. The probabilistic method allowed us to convey registration results in terms of posterior distributions, with the dispersion providing a patient-specific estimate of the registration uncertainty. The median of the predictive distance distribution between the deformed prostate boundary and the segmented boundary was Less-Than-Or-Slanted-Equal-To 3 mm (95th percentiles within {+-}4 mm) for all ten patients. The accuracy and precision of the internal deformation was evaluated by comparing the posterior predictive distance distribution for the CZ-PZ interface for each patient, with the median distance ranging from -0.6 to 2.4 mm. Posterior predictive distances between naturally occurring landmarks showed registration errors of Less-Than-Or-Slanted-Equal-To 5 mm in any direction. The uncertainty was not a global measure, but instead was local and varied throughout the registration region. Registration uncertainties were largest in the apical region of the prostate. Conclusions: Using a Bayesian nonrigid registration method, the authors determined the posterior distribution on deformations between diagnostic and intraprocedural MR images and quantified the uncertainty in the registration results. The feasibility of this approach was tested and results were positive. The probabilistic framework allows us to evaluate both patient-specific and location-specific estimates of the uncertainty in the registration result. Although the framework was tested on MR-guided procedures, the preliminary results suggest that it may be applied to TRUS-guided procedures as well, where the addition of diagnostic MR information may have a larger impact on target definition and clinical guidance.« less

A Bayesian nonrigid registration method to enhance intraoperative target definition in image-guided prostate procedures through uncertainty characterization

PubMed Central

Pursley, Jennifer; Risholm, Petter; Fedorov, Andriy; Tuncali, Kemal; Fennessy, Fiona M.; Wells, William M.; Tempany, Clare M.; Cormack, Robert A.

2012-01-01

Purpose: This study introduces a probabilistic nonrigid registration method for use in image-guided prostate brachytherapy. Intraoperative imaging for prostate procedures, usually transrectal ultrasound (TRUS), is typically inferior to diagnostic-quality imaging of the pelvis such as endorectal magnetic resonance imaging (MRI). MR images contain superior detail of the prostate boundaries and provide substructure features not otherwise visible. Previous efforts to register diagnostic prostate images with the intraoperative coordinate system have been deterministic and did not offer a measure of the registration uncertainty. The authors developed a Bayesian registration method to estimate the posterior distribution on deformations and provide a case-specific measure of the associated registration uncertainty. Methods: The authors adapted a biomechanical-based probabilistic nonrigid method to register diagnostic to intraoperative images by aligning a physician's segmentations of the prostate in the two images. The posterior distribution was characterized with a Markov Chain Monte Carlo method; the maximum a posteriori deformation and the associated uncertainty were estimated from the collection of deformation samples drawn from the posterior distribution. The authors validated the registration method using a dataset created from ten patients with MRI-guided prostate biopsies who had both diagnostic and intraprocedural 3 Tesla MRI scans. The accuracy and precision of the estimated posterior distribution on deformations were evaluated from two predictive distance distributions: between the deformed central zone-peripheral zone (CZ-PZ) interface and the physician-labeled interface, and based on physician-defined landmarks. Geometric margins on the registration of the prostate's peripheral zone were determined from the posterior predictive distance to the CZ-PZ interface separately for the base, mid-gland, and apical regions of the prostate. Results: The authors observed variation in the shape and volume of the segmented prostate in diagnostic and intraprocedural images. The probabilistic method allowed us to convey registration results in terms of posterior distributions, with the dispersion providing a patient-specific estimate of the registration uncertainty. The median of the predictive distance distribution between the deformed prostate boundary and the segmented boundary was ⩽3 mm (95th percentiles within ±4 mm) for all ten patients. The accuracy and precision of the internal deformation was evaluated by comparing the posterior predictive distance distribution for the CZ-PZ interface for each patient, with the median distance ranging from −0.6 to 2.4 mm. Posterior predictive distances between naturally occurring landmarks showed registration errors of ⩽5 mm in any direction. The uncertainty was not a global measure, but instead was local and varied throughout the registration region. Registration uncertainties were largest in the apical region of the prostate. Conclusions: Using a Bayesian nonrigid registration method, the authors determined the posterior distribution on deformations between diagnostic and intraprocedural MR images and quantified the uncertainty in the registration results. The feasibility of this approach was tested and results were positive. The probabilistic framework allows us to evaluate both patient-specific and location-specific estimates of the uncertainty in the registration result. Although the framework was tested on MR-guided procedures, the preliminary results suggest that it may be applied to TRUS-guided procedures as well, where the addition of diagnostic MR information may have a larger impact on target definition and clinical guidance. PMID:23127078

Bayesian LASSO, scale space and decision making in association genetics.

PubMed

Pasanen, Leena; Holmström, Lasse; Sillanpää, Mikko J

2015-01-01

LASSO is a penalized regression method that facilitates model fitting in situations where there are as many, or even more explanatory variables than observations, and only a few variables are relevant in explaining the data. We focus on the Bayesian version of LASSO and consider four problems that need special attention: (i) controlling false positives, (ii) multiple comparisons, (iii) collinearity among explanatory variables, and (iv) the choice of the tuning parameter that controls the amount of shrinkage and the sparsity of the estimates. The particular application considered is association genetics, where LASSO regression can be used to find links between chromosome locations and phenotypic traits in a biological organism. However, the proposed techniques are relevant also in other contexts where LASSO is used for variable selection. We separate the true associations from false positives using the posterior distribution of the effects (regression coefficients) provided by Bayesian LASSO. We propose to solve the multiple comparisons problem by using simultaneous inference based on the joint posterior distribution of the effects. Bayesian LASSO also tends to distribute an effect among collinear variables, making detection of an association difficult. We propose to solve this problem by considering not only individual effects but also their functionals (i.e. sums and differences). Finally, whereas in Bayesian LASSO the tuning parameter is often regarded as a random variable, we adopt a scale space view and consider a whole range of fixed tuning parameters, instead. The effect estimates and the associated inference are considered for all tuning parameters in the selected range and the results are visualized with color maps that provide useful insights into data and the association problem considered. The methods are illustrated using two sets of artificial data and one real data set, all representing typical settings in association genetics.

Bayesian transformation cure frailty models with multivariate failure time data.

PubMed

Yin, Guosheng

2008-12-10

We propose a class of transformation cure frailty models to accommodate a survival fraction in multivariate failure time data. Established through a general power transformation, this family of cure frailty models includes the proportional hazards and the proportional odds modeling structures as two special cases. Within the Bayesian paradigm, we obtain the joint posterior distribution and the corresponding full conditional distributions of the model parameters for the implementation of Gibbs sampling. Model selection is based on the conditional predictive ordinate statistic and deviance information criterion. As an illustration, we apply the proposed method to a real data set from dentistry.

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.

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

Markov Chain Monte Carlo Inference of Parametric Dictionaries for Sparse Bayesian Approximations

PubMed Central

Chaspari, Theodora; Tsiartas, Andreas; Tsilifis, Panagiotis; Narayanan, Shrikanth

2016-01-01

Parametric dictionaries can increase the ability of sparse representations to meaningfully capture and interpret the underlying signal information, such as encountered in biomedical problems. Given a mapping function from the atom parameter space to the actual atoms, we propose a sparse Bayesian framework for learning the atom parameters, because of its ability to provide full posterior estimates, take uncertainty into account and generalize on unseen data. Inference is performed with Markov Chain Monte Carlo, that uses block sampling to generate the variables of the Bayesian problem. Since the parameterization of dictionary atoms results in posteriors that cannot be analytically computed, we use a Metropolis-Hastings-within-Gibbs framework, according to which variables with closed-form posteriors are generated with the Gibbs sampler, while the remaining ones with the Metropolis Hastings from appropriate candidate-generating densities. We further show that the corresponding Markov Chain is uniformly ergodic ensuring its convergence to a stationary distribution independently of the initial state. Results on synthetic data and real biomedical signals indicate that our approach offers advantages in terms of signal reconstruction compared to previously proposed Steepest Descent and Equiangular Tight Frame methods. This paper demonstrates the ability of Bayesian learning to generate parametric dictionaries that can reliably represent the exemplar data and provides the foundation towards inferring the entire variable set of the sparse approximation problem for signal denoising, adaptation and other applications. PMID:28649173

Bayesian inference on earthquake size distribution: a case study in Italy

NASA Astrophysics Data System (ADS)

Licia, Faenza; Carlo, Meletti; Laura, Sandri

2010-05-01

This paper is focused on the study of earthquake size statistical distribution by using Bayesian inference. The strategy consists in the definition of an a priori distribution based on instrumental seismicity, and modeled as a power law distribution. By using the observed historical data, the power law is then modified in order to obtain the posterior distribution. The aim of this paper is to define the earthquake size distribution using all the seismic database available (i.e., instrumental and historical catalogs) and a robust statistical technique. We apply this methodology to the Italian seismicity, dividing the territory in source zones as done for the seismic hazard assessment, taken here as a reference model. The results suggest that each area has its own peculiar trend: while the power law is able to capture the mean aspect of the earthquake size distribution, the posterior emphasizes different slopes in different areas. Our results are in general agreement with the ones used in the seismic hazard assessment in Italy. However, there are areas in which a flattening in the curve is shown, meaning a significant departure from the power law behavior and implying that there are some local aspects that a power law distribution is not able to capture.

An introduction to using Bayesian linear regression with clinical data.

PubMed

Baldwin, Scott A; Larson, Michael J

2017-11-01

Statistical training psychology focuses on frequentist methods. Bayesian methods are an alternative to standard frequentist methods. This article provides researchers with an introduction to fundamental ideas in Bayesian modeling. We use data from an electroencephalogram (EEG) and anxiety study to illustrate Bayesian models. Specifically, the models examine the relationship between error-related negativity (ERN), a particular event-related potential, and trait anxiety. Methodological topics covered include: how to set up a regression model in a Bayesian framework, specifying priors, examining convergence of the model, visualizing and interpreting posterior distributions, interval estimates, expected and predicted values, and model comparison tools. We also discuss situations where Bayesian methods can outperform frequentist methods as well has how to specify more complicated regression models. Finally, we conclude with recommendations about reporting guidelines for those using Bayesian methods in their own research. We provide data and R code for replicating our analyses. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Bayesian pick-the-winner design in a randomized phase II clinical trial.

PubMed

Chen, Dung-Tsa; Huang, Po-Yu; Lin, Hui-Yi; Chiappori, Alberto A; Gabrilovich, Dmitry I; Haura, Eric B; Antonia, Scott J; Gray, Jhanelle E

2017-10-24

Many phase II clinical trials evaluate unique experimental drugs/combinations through multi-arm design to expedite the screening process (early termination of ineffective drugs) and to identify the most effective drug (pick the winner) to warrant a phase III trial. Various statistical approaches have been developed for the pick-the-winner design but have been criticized for lack of objective comparison among the drug agents. We developed a Bayesian pick-the-winner design by integrating a Bayesian posterior probability with Simon two-stage design in a randomized two-arm clinical trial. The Bayesian posterior probability, as the rule to pick the winner, is defined as probability of the response rate in one arm higher than in the other arm. The posterior probability aims to determine the winner when both arms pass the second stage of the Simon two-stage design. When both arms are competitive (i.e., both passing the second stage), the Bayesian posterior probability performs better to correctly identify the winner compared with the Fisher exact test in the simulation study. In comparison to a standard two-arm randomized design, the Bayesian pick-the-winner design has a higher power to determine a clear winner. In application to two studies, the approach is able to perform statistical comparison of two treatment arms and provides a winner probability (Bayesian posterior probability) to statistically justify the winning arm. We developed an integrated design that utilizes Bayesian posterior probability, Simon two-stage design, and randomization into a unique setting. It gives objective comparisons between the arms to determine the winner.

Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation.

PubMed

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

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.

An approach based on Hierarchical Bayesian Graphical Models for measurement interpretation under uncertainty

NASA Astrophysics Data System (ADS)

Skataric, Maja; Bose, Sandip; Zeroug, Smaine; Tilke, Peter

2017-02-01

It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications. In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.

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.

Estimating the extent and distribution of new-onset adult asthma in British Columbia using frequentist and Bayesian approaches.

PubMed

Beach, Jeremy; Burstyn, Igor; Cherry, Nicola

2012-07-01

We previously described a method to identify the incidence of new-onset adult asthma (NOAA) in Alberta by industry and occupation, utilizing Workers' Compensation Board (WCB) and physician billing data. The aim of this study was to extend this method to data from British Columbia (BC) so as to compare the two provinces and to incorporate Bayesian methodology into estimates of risk. WCB claims for any reason 1995-2004 were linked to physician billing data. NOAA was defined as a billing for asthma (ICD-9 493) in the 12 months before a WCB claim without asthma in the previous 3 years. Incidence was calculated by occupation and industry. In a matched case-referent analysis, associations with exposures were examined using an asthma-specific job exposure matrix (JEM). Posterior distributions from the Alberta analysis and estimated misclassification parameters were used as priors in the Bayesian analysis of the BC data. Among 1 118 239 eligible WCB claims the incidence of NOAA was 1.4%. Sixteen occupations and 44 industries had a significantly increased risk; six industries had a decreased risk. The JEM identified wood dust [odds ratio (OR) 1.55, 95% confidence interval (CI) 1.08-2.24] and animal antigens (OR 1.66, 95% CI 1.17-2.36) as related to an increased risk of NOAA. Exposure to isocyanates was associated with decreased risk (OR 0.57, 95% CI 0.39-0.85). Bayesian analyses taking account of exposure misclassification and informative priors resulted in posterior distributions of ORs with lower boundary of 95% credible intervals >1.00 for almost all exposures. The distribution of NOAA in BC appeared somewhat similar to that in Alberta, except for isocyanates. Bayesian analyses allowed incorporation of prior evidence into risk estimates, permitting reconsideration of the apparently protective effect of isocyanate exposure.

Finite element model updating using the shadow hybrid Monte Carlo technique

NASA Astrophysics Data System (ADS)

Boulkaibet, I.; Mthembu, L.; Marwala, T.; Friswell, M. I.; Adhikari, S.

2015-02-01

Recent research in the field of finite element model updating (FEM) advocates the adoption of Bayesian analysis techniques to dealing with the uncertainties associated with these models. However, Bayesian formulations require the evaluation of the Posterior Distribution Function which may not be available in analytical form. This is the case in FEM updating. In such cases sampling methods can provide good approximations of the Posterior distribution when implemented in the Bayesian context. Markov Chain Monte Carlo (MCMC) algorithms are the most popular sampling tools used to sample probability distributions. However, the efficiency of these algorithms is affected by the complexity of the systems (the size of the parameter space). The Hybrid Monte Carlo (HMC) offers a very important MCMC approach to dealing with higher-dimensional complex problems. The HMC uses the molecular dynamics (MD) steps as the global Monte Carlo (MC) moves to reach areas of high probability where the gradient of the log-density of the Posterior acts as a guide during the search process. However, the acceptance rate of HMC is sensitive to the system size as well as the time step used to evaluate the MD trajectory. To overcome this limitation we propose the use of the Shadow Hybrid Monte Carlo (SHMC) algorithm. The SHMC algorithm is a modified version of the Hybrid Monte Carlo (HMC) and designed to improve sampling for large-system sizes and time steps. This is done by sampling from a modified Hamiltonian function instead of the normal Hamiltonian function. In this paper, the efficiency and accuracy of the SHMC method is tested on the updating of two real structures; an unsymmetrical H-shaped beam structure and a GARTEUR SM-AG19 structure and is compared to the application of the HMC algorithm on the same structures.

Approximate Bayesian estimation of extinction rate in the Finnish Daphnia magna metapopulation.

PubMed

Robinson, John D; Hall, David W; Wares, John P

2013-05-01

Approximate Bayesian computation (ABC) is useful for parameterizing complex models in population genetics. In this study, ABC was applied to simultaneously estimate parameter values for a model of metapopulation coalescence and test two alternatives to a strict metapopulation model in the well-studied network of Daphnia magna populations in Finland. The models shared four free parameters: the subpopulation genetic diversity (θS), the rate of gene flow among patches (4Nm), the founding population size (N0) and the metapopulation extinction rate (e) but differed in the distribution of extinction rates across habitat patches in the system. The three models had either a constant extinction rate in all populations (strict metapopulation), one population that was protected from local extinction (i.e. a persistent source), or habitat-specific extinction rates drawn from a distribution with specified mean and variance. Our model selection analysis favoured the model including a persistent source population over the two alternative models. Of the closest 750,000 data sets in Euclidean space, 78% were simulated under the persistent source model (estimated posterior probability = 0.769). This fraction increased to more than 85% when only the closest 150,000 data sets were considered (estimated posterior probability = 0.774). Approximate Bayesian computation was then used to estimate parameter values that might produce the observed set of summary statistics. Our analysis provided posterior distributions for e that included the point estimate obtained from previous data from the Finnish D. magna metapopulation. Our results support the use of ABC and population genetic data for testing the strict metapopulation model and parameterizing complex models of demography. © 2013 Blackwell Publishing Ltd.

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.

Inference of epidemiological parameters from household stratified data

PubMed Central

Walker, James N.; Ross, Joshua V.

2017-01-01

We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters—governing within-household transmission, recovery, and between-household transmission—from data of the day upon which each individual became infectious and the household in which each infection occurred, as might be available from First Few Hundred studies. Each method is a form of Bayesian Markov Chain Monte Carlo that allows us to calculate a joint posterior distribution for all parameters and hence the household reproduction number and the early growth rate of the epidemic. The first method performs exact Bayesian inference using a standard data-augmentation approach; the second performs approximate Bayesian inference based on a likelihood approximation derived from branching processes. These methods are compared for computational efficiency and posteriors from each are compared. The branching process is shown to be a good approximation and remains computationally efficient as the amount of data is increased. PMID:29045456

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.

Classical and Bayesian Seismic Yield Estimation: The 1998 Indian and Pakistani Tests

NASA Astrophysics Data System (ADS)

Shumway, R. H.

2001-10-01

- The nuclear tests in May, 1998, in India and Pakistan have stimulated a renewed interest in yield estimation, based on limited data from uncalibrated test sites. We study here the problem of estimating yields using classical and Bayesian methods developed by Shumway (1992), utilizing calibration data from the Semipalatinsk test site and measured magnitudes for the 1998 Indian and Pakistani tests given by Murphy (1998). Calibration is done using multivariate classical or Bayesian linear regression, depending on the availability of measured magnitude-yield data and prior information. Confidence intervals for the classical approach are derived applying an extension of Fieller's method suggested by Brown (1982). In the case where prior information is available, the posterior predictive magnitude densities are inverted to give posterior intervals for yield. Intervals obtained using the joint distribution of magnitudes are comparable to the single-magnitude estimates produced by Murphy (1998) and reinforce the conclusion that the announced yields of the Indian and Pakistani tests were too high.

Classical and Bayesian Seismic Yield Estimation: The 1998 Indian and Pakistani Tests

NASA Astrophysics Data System (ADS)

Shumway, R. H.

The nuclear tests in May, 1998, in India and Pakistan have stimulated a renewed interest in yield estimation, based on limited data from uncalibrated test sites. We study here the problem of estimating yields using classical and Bayesian methods developed by Shumway (1992), utilizing calibration data from the Semipalatinsk test site and measured magnitudes for the 1998 Indian and Pakistani tests given by Murphy (1998). Calibration is done using multivariate classical or Bayesian linear regression, depending on the availability of measured magnitude-yield data and prior information. Confidence intervals for the classical approach are derived applying an extension of Fieller's method suggested by Brown (1982). In the case where prior information is available, the posterior predictive magnitude densities are inverted to give posterior intervals for yield. Intervals obtained using the joint distribution of magnitudes are comparable to the single-magnitude estimates produced by Murphy (1998) and reinforce the conclusion that the announced yields of the Indian and Pakistani tests were too high.

Bayesian inference for the distribution of grams of marijuana in a joint.

PubMed

Ridgeway, Greg; Kilmer, Beau

2016-08-01

The average amount of marijuana in a joint is unknown, yet this figure is a critical quantity for creating credible measures of marijuana consumption. It is essential for projecting tax revenues post-legalization, estimating the size of illicit marijuana markets, and learning about how much marijuana users are consuming in order to understand health and behavioral consequences. Arrestee Drug Abuse Monitoring data collected between 2000 and 2010 contain relevant information on 10,628 marijuana transactions, joints and loose marijuana purchases, including the city in which the purchase occurred and the price paid for the marijuana. Using the Brown-Silverman drug pricing model to link marijuana price and weight, we are able to infer the distribution of grams of marijuana in a joint and provide a Bayesian posterior distribution for the mean weight of marijuana in a joint. We estimate that the mean weight of marijuana in a joint is 0.32g (95% Bayesian posterior interval: 0.30-0.35). Our estimate of the mean weight of marijuana in a joint is lower than figures commonly used to make estimates of marijuana consumption. These estimates can be incorporated into drug policy discussions to produce better understanding about illicit marijuana markets, the size of potential legalized marijuana markets, and health and behavior outcomes. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

MapReduce Based Parallel Bayesian Network for Manufacturing Quality Control

NASA Astrophysics Data System (ADS)

Zheng, Mao-Kuan; Ming, Xin-Guo; Zhang, Xian-Yu; Li, Guo-Ming

2017-09-01

Increasing complexity of industrial products and manufacturing processes have challenged conventional statistics based quality management approaches in the circumstances of dynamic production. A Bayesian network and big data analytics integrated approach for manufacturing process quality analysis and control is proposed. Based on Hadoop distributed architecture and MapReduce parallel computing model, big volume and variety quality related data generated during the manufacturing process could be dealt with. Artificial intelligent algorithms, including Bayesian network learning, classification and reasoning, are embedded into the Reduce process. Relying on the ability of the Bayesian network in dealing with dynamic and uncertain problem and the parallel computing power of MapReduce, Bayesian network of impact factors on quality are built based on prior probability distribution and modified with posterior probability distribution. A case study on hull segment manufacturing precision management for ship and offshore platform building shows that computing speed accelerates almost directly proportionally to the increase of computing nodes. It is also proved that the proposed model is feasible for locating and reasoning of root causes, forecasting of manufacturing outcome, and intelligent decision for precision problem solving. The integration of bigdata analytics and BN method offers a whole new perspective in manufacturing quality control.

Conceptual issues in Bayesian divergence time estimation

PubMed Central

2016-01-01

Bayesian inference of species divergence times is an unusual statistical problem, because the divergence time parameters are not identifiable unless both fossil calibrations and sequence data are available. Commonly used marginal priors on divergence times derived from fossil calibrations may conflict with node order on the phylogenetic tree causing a change in the prior on divergence times for a particular topology. Care should be taken to avoid confusing this effect with changes due to informative sequence data. This effect is illustrated with examples. A topology-consistent prior that preserves the marginal priors is defined and examples are constructed. Conflicts between fossil calibrations and relative branch lengths (based on sequence data) can cause estimates of divergence times that are grossly incorrect, yet have a narrow posterior distribution. An example of this effect is given; it is recommended that overly narrow posterior distributions of divergence times should be carefully scrutinized. This article is part of the themed issue ‘Dating species divergences using rocks and clocks’. PMID:27325831

Conceptual issues in Bayesian divergence time estimation.

PubMed

Rannala, Bruce

2016-07-19

Bayesian inference of species divergence times is an unusual statistical problem, because the divergence time parameters are not identifiable unless both fossil calibrations and sequence data are available. Commonly used marginal priors on divergence times derived from fossil calibrations may conflict with node order on the phylogenetic tree causing a change in the prior on divergence times for a particular topology. Care should be taken to avoid confusing this effect with changes due to informative sequence data. This effect is illustrated with examples. A topology-consistent prior that preserves the marginal priors is defined and examples are constructed. Conflicts between fossil calibrations and relative branch lengths (based on sequence data) can cause estimates of divergence times that are grossly incorrect, yet have a narrow posterior distribution. An example of this effect is given; it is recommended that overly narrow posterior distributions of divergence times should be carefully scrutinized.This article is part of the themed issue 'Dating species divergences using rocks and clocks'. © 2016 The Author(s).

Bayesian methods for characterizing unknown parameters of material models

DOE PAGES

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

2016-02-04

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods for characterizing unknown parameters of material models

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

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Uncertainty analysis of gross primary production partitioned from net ecosystem exchange measurements

NASA Astrophysics Data System (ADS)

Raj, R.; Hamm, N. A. S.; van der Tol, C.; Stein, A.

2015-08-01

Gross primary production (GPP), separated from flux tower measurements of net ecosystem exchange (NEE) of CO2, is used increasingly to validate process-based simulators and remote sensing-derived estimates of simulated GPP at various time steps. Proper validation should include the uncertainty associated with this separation at different time steps. This can be achieved by using a Bayesian framework. In this study, we estimated the uncertainty in GPP at half hourly time steps. We used a non-rectangular hyperbola (NRH) model to separate GPP from flux tower measurements of NEE at the Speulderbos forest site, The Netherlands. The NRH model included the variables that influence GPP, in particular radiation, and temperature. In addition, the NRH model provided a robust empirical relationship between radiation and GPP by including the degree of curvature of the light response curve. Parameters of the NRH model were fitted to the measured NEE data for every 10-day period during the growing season (April to October) in 2009. Adopting a Bayesian approach, we defined the prior distribution of each NRH parameter. Markov chain Monte Carlo (MCMC) simulation was used to update the prior distribution of each NRH parameter. This allowed us to estimate the uncertainty in the separated GPP at half-hourly time steps. This yielded the posterior distribution of GPP at each half hour and allowed the quantification of uncertainty. The time series of posterior distributions thus obtained allowed us to estimate the uncertainty at daily time steps. We compared the informative with non-informative prior distributions of the NRH parameters. The results showed that both choices of prior produced similar posterior distributions GPP. This will provide relevant and important information for the validation of process-based simulators in the future. Furthermore, the obtained posterior distributions of NEE and the NRH parameters are of interest for a range of applications.

Bayesian assessment of uncertainty in aerosol size distributions and index of refraction retrieved from multiwavelength lidar measurements.

PubMed

Herman, Benjamin R; Gross, Barry; Moshary, Fred; Ahmed, Samir

2008-04-01

We investigate the assessment of uncertainty in the inference of aerosol size distributions from backscatter and extinction measurements that can be obtained from a modern elastic/Raman lidar system with a Nd:YAG laser transmitter. To calculate the uncertainty, an analytic formula for the correlated probability density function (PDF) describing the error for an optical coefficient ratio is derived based on a normally distributed fractional error in the optical coefficients. Assuming a monomodal lognormal particle size distribution of spherical, homogeneous particles with a known index of refraction, we compare the assessment of uncertainty using a more conventional forward Monte Carlo method with that obtained from a Bayesian posterior PDF assuming a uniform prior PDF and show that substantial differences between the two methods exist. In addition, we use the posterior PDF formalism, which was extended to include an unknown refractive index, to find credible sets for a variety of optical measurement scenarios. We find the uncertainty is greatly reduced with the addition of suitable extinction measurements in contrast to the inclusion of extra backscatter coefficients, which we show to have a minimal effect and strengthens similar observations based on numerical regularization methods.

Uncertainty Quantification of Hypothesis Testing for the Integrated Knowledge Engine

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

Cuellar, Leticia

2012-05-31

The Integrated Knowledge Engine (IKE) is a tool of Bayesian analysis, based on Bayesian Belief Networks or Bayesian networks for short. A Bayesian network is a graphical model (directed acyclic graph) that allows representing the probabilistic structure of many variables assuming a localized type of dependency called the Markov property. The Markov property in this instance makes any node or random variable to be independent of any non-descendant node given information about its parent. A direct consequence of this property is that it is relatively easy to incorporate new evidence and derive the appropriate consequences, which in general is notmore » an easy or feasible task. Typically we use Bayesian networks as predictive models for a small subset of the variables, either the leave nodes or the root nodes. In IKE, since most applications deal with diagnostics, we are interested in predicting the likelihood of the root nodes given new observations on any of the children nodes. The root nodes represent the various possible outcomes of the analysis, and an important problem is to determine when we have gathered enough evidence to lean toward one of these particular outcomes. This document presents criteria to decide when the evidence gathered is sufficient to draw a particular conclusion or decide in favor of a particular outcome by quantifying the uncertainty in the conclusions that are drawn from the data. The material in this document is organized as follows: Section 2 presents briefly a forensics Bayesian network, and we explore evaluating the information provided by new evidence by looking first at the posterior distribution of the nodes of interest, and then at the corresponding posterior odds ratios. Section 3 presents a third alternative: Bayes Factors. In section 4 we finalize by showing the relation between the posterior odds ratios and Bayes factors and showing examples these cases, and in section 5 we conclude by providing clear guidelines of how to use these for the type of Bayesian networks used in IKE.« less

Basics of Bayesian methods.

PubMed

Ghosh, Sujit K

2010-01-01

Bayesian methods are rapidly becoming popular tools for making statistical inference in various fields of science including biology, engineering, finance, and genetics. One of the key aspects of Bayesian inferential method is its logical foundation that provides a coherent framework to utilize not only empirical but also scientific information available to a researcher. Prior knowledge arising from scientific background, expert judgment, or previously collected data is used to build a prior distribution which is then combined with current data via the likelihood function to characterize the current state of knowledge using the so-called posterior distribution. Bayesian methods allow the use of models of complex physical phenomena that were previously too difficult to estimate (e.g., using asymptotic approximations). Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models based on hierarchical conditional distributions that can be estimated even with limited amounts of data. Furthermore, advances in numerical integration methods, particularly those based on Monte Carlo methods, have made it possible to compute the optimal Bayes estimators. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of this chapter is to bridge the gap by offering elementary to advanced concepts that emphasize linkages between standard approaches and full probability modeling via Bayesian methods.

Daniel Goodman’s empirical approach to Bayesian statistics

USGS Publications Warehouse

Gerrodette, Tim; Ward, Eric; Taylor, Rebecca L.; Schwarz, Lisa K.; Eguchi, Tomoharu; Wade, Paul; Himes Boor, Gina

2016-01-01

Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.

An offline approach for output-only Bayesian identification of stochastic nonlinear systems using unscented Kalman filtering

NASA Astrophysics Data System (ADS)

Erazo, Kalil; Nagarajaiah, Satish

2017-06-01

In this paper an offline approach for output-only Bayesian identification of stochastic nonlinear systems is presented. The approach is based on a re-parameterization of the joint posterior distribution of the parameters that define a postulated state-space stochastic model class. In the re-parameterization the state predictive distribution is included, marginalized, and estimated recursively in a state estimation step using an unscented Kalman filter, bypassing state augmentation as required by existing online methods. In applications expectations of functions of the parameters are of interest, which requires the evaluation of potentially high-dimensional integrals; Markov chain Monte Carlo is adopted to sample the posterior distribution and estimate the expectations. The proposed approach is suitable for nonlinear systems subjected to non-stationary inputs whose realization is unknown, and that are modeled as stochastic processes. Numerical verification and experimental validation examples illustrate the effectiveness and advantages of the approach, including: (i) an increased numerical stability with respect to augmented-state unscented Kalman filtering, avoiding divergence of the estimates when the forcing input is unmeasured; (ii) the ability to handle arbitrary prior and posterior distributions. The experimental validation of the approach is conducted using data from a large-scale structure tested on a shake table. It is shown that the approach is robust to inherent modeling errors in the description of the system and forcing input, providing accurate prediction of the dynamic response when the excitation history is unknown.

Predictability of depression severity based on posterior alpha oscillations.

PubMed

Jiang, H; Popov, T; Jylänki, P; Bi, K; Yao, Z; Lu, Q; Jensen, O; van Gerven, M A J

2016-04-01

We aimed to integrate neural data and an advanced machine learning technique to predict individual major depressive disorder (MDD) patient severity. MEG data was acquired from 22 MDD patients and 22 healthy controls (HC) resting awake with eyes closed. Individual power spectra were calculated by a Fourier transform. Sources were reconstructed via beamforming technique. Bayesian linear regression was applied to predict depression severity based on the spatial distribution of oscillatory power. In MDD patients, decreased theta (4-8 Hz) and alpha (8-14 Hz) power was observed in fronto-central and posterior areas respectively, whereas increased beta (14-30 Hz) power was observed in fronto-central regions. In particular, posterior alpha power was negatively related to depression severity. The Bayesian linear regression model showed significant depression severity prediction performance based on the spatial distribution of both alpha (r=0.68, p=0.0005) and beta power (r=0.56, p=0.007) respectively. Our findings point to a specific alteration of oscillatory brain activity in MDD patients during rest as characterized from MEG data in terms of spectral and spatial distribution. The proposed model yielded a quantitative and objective estimation for the depression severity, which in turn has a potential for diagnosis and monitoring of the recovery process. Copyright © 2016 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Robust Bayesian clustering.

PubMed

Archambeau, Cédric; Verleysen, Michel

2007-01-01

A new variational Bayesian learning algorithm for Student-t mixture models is introduced. This algorithm leads to (i) robust density estimation, (ii) robust clustering and (iii) robust automatic model selection. Gaussian mixture models are learning machines which are based on a divide-and-conquer approach. They are commonly used for density estimation and clustering tasks, but are sensitive to outliers. The Student-t distribution has heavier tails than the Gaussian distribution and is therefore less sensitive to any departure of the empirical distribution from Gaussianity. As a consequence, the Student-t distribution is suitable for constructing robust mixture models. In this work, we formalize the Bayesian Student-t mixture model as a latent variable model in a different way from Svensén and Bishop [Svensén, M., & Bishop, C. M. (2005). Robust Bayesian mixture modelling. Neurocomputing, 64, 235-252]. The main difference resides in the fact that it is not necessary to assume a factorized approximation of the posterior distribution on the latent indicator variables and the latent scale variables in order to obtain a tractable solution. Not neglecting the correlations between these unobserved random variables leads to a Bayesian model having an increased robustness. Furthermore, it is expected that the lower bound on the log-evidence is tighter. Based on this bound, the model complexity, i.e. the number of components in the mixture, can be inferred with a higher confidence.

Fast and Accurate Learning When Making Discrete Numerical Estimates.

PubMed

Sanborn, Adam N; Beierholm, Ulrik R

2016-04-01

Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates.

Fast and Accurate Learning When Making Discrete Numerical Estimates

PubMed Central

Sanborn, Adam N.; Beierholm, Ulrik R.

2016-01-01

Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates. PMID:27070155

Bayesian sample size calculations in phase II clinical trials using a mixture of informative priors.

PubMed

Gajewski, Byron J; Mayo, Matthew S

2006-08-15

A number of researchers have discussed phase II clinical trials from a Bayesian perspective. A recent article by Mayo and Gajewski focuses on sample size calculations, which they determine by specifying an informative prior distribution and then calculating a posterior probability that the true response will exceed a prespecified target. In this article, we extend these sample size calculations to include a mixture of informative prior distributions. The mixture comes from several sources of information. For example consider information from two (or more) clinicians. The first clinician is pessimistic about the drug and the second clinician is optimistic. We tabulate the results for sample size design using the fact that the simple mixture of Betas is a conjugate family for the Beta- Binomial model. We discuss the theoretical framework for these types of Bayesian designs and show that the Bayesian designs in this paper approximate this theoretical framework. Copyright 2006 John Wiley & Sons, Ltd.

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

Reed, K F; Arhonditsis, G B; France, J; Kebreab, E

2016-08-01

Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

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.

Use of Bayes theorem to correct size-specific sampling bias in growth data.

PubMed

Troynikov, V S

1999-03-01

The bayesian decomposition of posterior distribution was used to develop a likelihood function to correct bias in the estimates of population parameters from data collected randomly with size-specific selectivity. Positive distributions with time as a parameter were used for parametrization of growth data. Numerical illustrations are provided. The alternative applications of the likelihood to estimate selectivity parameters are discussed.

BAT - The Bayesian analysis toolkit

NASA Astrophysics Data System (ADS)

Caldwell, Allen; Kollár, Daniel; Kröninger, Kevin

2009-11-01

We describe the development of a new toolkit for data analysis. The analysis package is based on Bayes' Theorem, and is realized with the use of Markov Chain Monte Carlo. This gives access to the full posterior probability distribution. Parameter estimation, limit setting and uncertainty propagation are implemented in a straightforward manner.

Bayesian bivariate meta-analysis of correlated effects: Impact of the prior distributions on the between-study correlation, borrowing of strength, and joint inferences

PubMed Central

Bujkiewicz, Sylwia; Riley, Richard D

2016-01-01

Multivariate random-effects meta-analysis allows the joint synthesis of correlated results from multiple studies, for example, for multiple outcomes or multiple treatment groups. In a Bayesian univariate meta-analysis of one endpoint, the importance of specifying a sensible prior distribution for the between-study variance is well understood. However, in multivariate meta-analysis, there is little guidance about the choice of prior distributions for the variances or, crucially, the between-study correlation, ρB; for the latter, researchers often use a Uniform(−1,1) distribution assuming it is vague. In this paper, an extensive simulation study and a real illustrative example is used to examine the impact of various (realistically) vague prior distributions for ρB and the between-study variances within a Bayesian bivariate random-effects meta-analysis of two correlated treatment effects. A range of diverse scenarios are considered, including complete and missing data, to examine the impact of the prior distributions on posterior results (for treatment effect and between-study correlation), amount of borrowing of strength, and joint predictive distributions of treatment effectiveness in new studies. Two key recommendations are identified to improve the robustness of multivariate meta-analysis results. First, the routine use of a Uniform(−1,1) prior distribution for ρB should be avoided, if possible, as it is not necessarily vague. Instead, researchers should identify a sensible prior distribution, for example, by restricting values to be positive or negative as indicated by prior knowledge. Second, it remains critical to use sensible (e.g. empirically based) prior distributions for the between-study variances, as an inappropriate choice can adversely impact the posterior distribution for ρB, which may then adversely affect inferences such as joint predictive probabilities. These recommendations are especially important with a small number of studies and missing data. PMID:26988929

Bayesian analysis of time-series data under case-crossover designs: posterior equivalence and inference.

PubMed

Li, Shi; Mukherjee, Bhramar; Batterman, Stuart; Ghosh, Malay

2013-12-01

Case-crossover designs are widely used to study short-term exposure effects on the risk of acute adverse health events. While the frequentist literature on this topic is vast, there is no Bayesian work in this general area. The contribution of this paper is twofold. First, the paper establishes Bayesian equivalence results that require characterization of the set of priors under which the posterior distributions of the risk ratio parameters based on a case-crossover and time-series analysis are identical. Second, the paper studies inferential issues under case-crossover designs in a Bayesian framework. Traditionally, a conditional logistic regression is used for inference on risk-ratio parameters in case-crossover studies. We consider instead a more general full likelihood-based approach which makes less restrictive assumptions on the risk functions. Formulation of a full likelihood leads to growth in the number of parameters proportional to the sample size. We propose a semi-parametric Bayesian approach using a Dirichlet process prior to handle the random nuisance parameters that appear in a full likelihood formulation. We carry out a simulation study to compare the Bayesian methods based on full and conditional likelihood with the standard frequentist approaches for case-crossover and time-series analysis. The proposed methods are illustrated through the Detroit Asthma Morbidity, Air Quality and Traffic study, which examines the association between acute asthma risk and ambient air pollutant concentrations. © 2013, The International Biometric Society.

Posterior consistency in conditional distribution estimation

PubMed Central

Pati, Debdeep; Dunson, David B.; Tokdar, Surya T.

2014-01-01

A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as posterior consistency. Estimation of an uncountable collection of conditional distributions across different regions of the predictor space is a challenging problem, which differs in some important ways from density and mean regression estimation problems. Defining various topologies on the space of conditional distributions, we provide sufficient conditions for posterior consistency focusing on a broad class of priors formulated as predictor-dependent mixtures of Gaussian kernels. This theory is illustrated by showing that the conditions are satisfied for a class of generalized stick-breaking process mixtures in which the stick-breaking lengths are monotone, differentiable functions of a continuous stochastic process. We also provide a set of sufficient conditions for the case where stick-breaking lengths are predictor independent, such as those arising from a fixed Dirichlet process prior. PMID:25067858

The behavior of Metropolis-coupled Markov chains when sampling rugged phylogenetic distributions.

PubMed

Brown, Jeremy M; Thomson, Robert C

2018-02-15

Bayesian phylogenetic inference involves sampling from posterior distributions of trees, which sometimes exhibit local optima, or peaks, separated by regions of low posterior density. Markov chain Monte Carlo (MCMC) algorithms are the most widely used numerical method for generating samples from these posterior distributions, but they are susceptible to entrapment on individual optima in rugged distributions when they are unable to easily cross through or jump across regions of low posterior density. Ruggedness of posterior distributions can result from a variety of factors, including unmodeled variation in evolutionary processes and unrecognized variation in the true topology across sites or genes. Ruggedness can also become exaggerated when constraints are placed on topologies that require the presence or absence of particular bipartitions (often referred to as positive or negative constraints, respectively). These types of constraints are frequently employed when conducting tests of topological hypotheses (Bergsten et al. 2013; Brown and Thomson 2017). Negative constraints can lead to particularly rugged distributions when the data strongly support a forbidden clade, because monophyly of the clade can be disrupted by inserting outgroup taxa in many different ways. However, topological moves between the alternative disruptions are very difficult, because they require swaps between the inserted outgroup taxa while the data constrain taxa from the forbidden clade to remain close together on the tree. While this precise form of ruggedness is particular to negative constraints, trees with high posterior density can be separated by similarly complicated topological rearrangements, even in the absence of constraints.

A Bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites

USGS Publications Warehouse

Nichols, J.M.; Link, W.A.; Murphy, K.D.; Olson, C.C.

2010-01-01

This work discusses a Bayesian approach to approximating the distribution of parameters governing nonlinear structural systems. Specifically, we use a Markov Chain Monte Carlo method for sampling the posterior parameter distributions thus producing both point and interval estimates for parameters. The method is first used to identify both linear and nonlinear parameters in a multiple degree-of-freedom structural systems using free-decay vibrations. The approach is then applied to the problem of identifying the location, size, and depth of delamination in a model composite beam. The influence of additive Gaussian noise on the response data is explored with respect to the quality of the resulting parameter estimates.

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.

Entropic Inference

NASA Astrophysics Data System (ADS)

Caticha, Ariel

2011-03-01

In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), includes as special cases both MaxEnt and Bayes' rule, and therefore unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme.

General Metropolis-Hastings jump diffusions for automatic target recognition in infrared scenes

NASA Astrophysics Data System (ADS)

Lanterman, Aaron D.; Miller, Michael I.; Snyder, Donald L.

1997-04-01

To locate and recognize ground-based targets in forward- looking IR (FLIR) images, 3D faceted models with associated pose parameters are formulated to accommodate the variability found in FLIR imagery. Taking a Bayesian approach, scenes are simulated from the emissive characteristics of the CAD models and compared with the collected data by a likelihood function based on sensor statistics. This likelihood is combined with a prior distribution defined over the set of possible scenes to form a posterior distribution. To accommodate scenes with variable numbers of targets, the posterior distribution is defined over parameter vectors of varying dimension. An inference algorithm based on Metropolis-Hastings jump- diffusion processes empirically samples from the posterior distribution, generating configurations of templates and transformations that match the collected sensor data with high probability. The jumps accommodate the addition and deletion of targets and the estimation of target identities; diffusions refine the hypotheses by drifting along the gradient of the posterior distribution with respect to the orientation and position parameters. Previous results on jumps strategies analogous to the Metropolis acceptance/rejection algorithm, with proposals drawn from the prior and accepted based on the likelihood, are extended to encompass general Metropolis-Hastings proposal densities. In particular, the algorithm proposes moves by drawing from the posterior distribution over computationally tractible subsets of the parameter space. The algorithm is illustrated by an implementation on a Silicon Graphics Onyx/Reality Engine.

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.

Bayesian model checking: A comparison of tests

NASA Astrophysics Data System (ADS)

Lucy, L. B.

2018-06-01

Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability density functions agree closely with posterior predictive p-values. The former can therefore serve as an effective proxy for the difficult-to-calculate posterior predictive p-values.

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

CytoBayesJ: software tools for Bayesian analysis of cytogenetic radiation dosimetry data.

PubMed

Ainsbury, Elizabeth A; Vinnikov, Volodymyr; Puig, Pedro; Maznyk, Nataliya; Rothkamm, Kai; Lloyd, David C

2013-08-30

A number of authors have suggested that a Bayesian approach may be most appropriate for analysis of cytogenetic radiation dosimetry data. In the Bayesian framework, probability of an event is described in terms of previous expectations and uncertainty. Previously existing, or prior, information is used in combination with experimental results to infer probabilities or the likelihood that a hypothesis is true. It has been shown that the Bayesian approach increases both the accuracy and quality assurance of radiation dose estimates. New software entitled CytoBayesJ has been developed with the aim of bringing Bayesian analysis to cytogenetic biodosimetry laboratory practice. CytoBayesJ takes a number of Bayesian or 'Bayesian like' methods that have been proposed in the literature and presents them to the user in the form of simple user-friendly tools, including testing for the most appropriate model for distribution of chromosome aberrations and calculations of posterior probability distributions. The individual tools are described in detail and relevant examples of the use of the methods and the corresponding CytoBayesJ software tools are given. In this way, the suitability of the Bayesian approach to biological radiation dosimetry is highlighted and its wider application encouraged by providing a user-friendly software interface and manual in English and Russian. Copyright © 2013 Elsevier B.V. All rights reserved.

Bayesian view of single-qubit clocks, and an energy versus accuracy tradeoff

NASA Astrophysics Data System (ADS)

Gopalkrishnan, Manoj; Kandula, Varshith; Sriram, Praveen; Deshpande, Abhishek; Muralidharan, Bhaskaran

2017-09-01

We bring a Bayesian approach to the analysis of clocks. Using exponential distributions as priors for clocks, we analyze how well one can keep time with a single qubit freely precessing under a magnetic field. We find that, at least with a single qubit, quantum mechanics does not allow exact timekeeping, in contrast to classical mechanics, which does. We find the design of the single-qubit clock that leads to maximum accuracy. Further, we find an energy versus accuracy tradeoff—the energy cost is at least kBT times the improvement in accuracy as measured by the entropy reduction in going from the prior distribution to the posterior distribution. We propose a physical realization of the single-qubit clock using charge transport across a capacitively coupled quantum dot.

Bayesian tomography by interacting Markov chains

NASA Astrophysics Data System (ADS)

Romary, T.

2017-12-01

In seismic tomography, we seek to determine the velocity of the undergound from noisy first arrival travel time observations. In most situations, this is an ill posed inverse problem that admits several unperfect solutions. Given an a priori distribution over the parameters of the velocity model, the Bayesian formulation allows to state this problem as a probabilistic one, with a solution under the form of a posterior distribution. The posterior distribution is generally high dimensional and may exhibit multimodality. Moreover, as it is known only up to a constant, the only sensible way to addressthis problem is to try to generate simulations from the posterior. The natural tools to perform these simulations are Monte Carlo Markov chains (MCMC). Classical implementations of MCMC algorithms generally suffer from slow mixing: the generated states are slow to enter the stationary regime, that is to fit the observations, and when one mode of the posterior is eventually identified, it may become difficult to visit others. Using a varying temperature parameter relaxing the constraint on the data may help to enter the stationary regime. Besides, the sequential nature of MCMC makes them ill fitted toparallel implementation. Running a large number of chains in parallel may be suboptimal as the information gathered by each chain is not mutualized. Parallel tempering (PT) can be seen as a first attempt to make parallel chains at different temperatures communicate but only exchange information between current states. In this talk, I will show that PT actually belongs to a general class of interacting Markov chains algorithm. I will also show that this class enables to design interacting schemes that can take advantage of the whole history of the chain, by authorizing exchanges toward already visited states. The algorithms will be illustrated with toy examples and an application to first arrival traveltime tomography.

An agglomerative hierarchical clustering approach to visualisation in Bayesian clustering problems

PubMed Central

Dawson, Kevin J.; Belkhir, Khalid

2009-01-01

Clustering problems (including the clustering of individuals into outcrossing populations, hybrid generations, full-sib families and selfing lines) have recently received much attention in population genetics. In these clustering problems, the parameter of interest is a partition of the set of sampled individuals, - the sample partition. In a fully Bayesian approach to clustering problems of this type, our knowledge about the sample partition is represented by a probability distribution on the space of possible sample partitions. Since the number of possible partitions grows very rapidly with the sample size, we can not visualise this probability distribution in its entirety, unless the sample is very small. As a solution to this visualisation problem, we recommend using an agglomerative hierarchical clustering algorithm, which we call the exact linkage algorithm. This algorithm is a special case of the maximin clustering algorithm that we introduced previously. The exact linkage algorithm is now implemented in our software package Partition View. The exact linkage algorithm takes the posterior co-assignment probabilities as input, and yields as output a rooted binary tree, - or more generally, a forest of such trees. Each node of this forest defines a set of individuals, and the node height is the posterior co-assignment probability of this set. This provides a useful visual representation of the uncertainty associated with the assignment of individuals to categories. It is also a useful starting point for a more detailed exploration of the posterior distribution in terms of the co-assignment probabilities. PMID:19337306

A Bayesian approach to meta-analysis of plant pathology studies.

PubMed

Mila, A L; Ngugi, H K

2011-01-01

Bayesian statistical methods are used for meta-analysis in many disciplines, including medicine, molecular biology, and engineering, but have not yet been applied for quantitative synthesis of plant pathology studies. In this paper, we illustrate the key concepts of Bayesian statistics and outline the differences between Bayesian and classical (frequentist) methods in the way parameters describing population attributes are considered. We then describe a Bayesian approach to meta-analysis and present a plant pathological example based on studies evaluating the efficacy of plant protection products that induce systemic acquired resistance for the management of fire blight of apple. In a simple random-effects model assuming a normal distribution of effect sizes and no prior information (i.e., a noninformative prior), the results of the Bayesian meta-analysis are similar to those obtained with classical methods. Implementing the same model with a Student's t distribution and a noninformative prior for the effect sizes, instead of a normal distribution, yields similar results for all but acibenzolar-S-methyl (Actigard) which was evaluated only in seven studies in this example. Whereas both the classical (P = 0.28) and the Bayesian analysis with a noninformative prior (95% credibility interval [CRI] for the log response ratio: -0.63 to 0.08) indicate a nonsignificant effect for Actigard, specifying a t distribution resulted in a significant, albeit variable, effect for this product (CRI: -0.73 to -0.10). These results confirm the sensitivity of the analytical outcome (i.e., the posterior distribution) to the choice of prior in Bayesian meta-analyses involving a limited number of studies. We review some pertinent literature on more advanced topics, including modeling of among-study heterogeneity, publication bias, analyses involving a limited number of studies, and methods for dealing with missing data, and show how these issues can be approached in a Bayesian framework. Bayesian meta-analysis can readily include information not easily incorporated in classical methods, and allow for a full evaluation of competing models. Given the power and flexibility of Bayesian methods, we expect them to become widely adopted for meta-analysis of plant pathology studies.

Bayesian calibration of the Community Land Model using surrogates

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

Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi

2014-02-01

We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural errormore » in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.« less

Estimation of gross land-use change and its uncertainty using a Bayesian data assimilation approach

NASA Astrophysics Data System (ADS)

Levy, Peter; van Oijen, Marcel; Buys, Gwen; Tomlinson, Sam

2018-03-01

We present a method for estimating land-use change using a Bayesian data assimilation approach. The approach provides a general framework for combining multiple disparate data sources with a simple model. This allows us to constrain estimates of gross land-use change with reliable national-scale census data, whilst retaining the detailed information available from several other sources. Eight different data sources, with three different data structures, were combined in our posterior estimate of land use and land-use change, and other data sources could easily be added in future. The tendency for observations to underestimate gross land-use change is accounted for by allowing for a skewed distribution in the likelihood function. The data structure produced has high temporal and spatial resolution, and is appropriate for dynamic process-based modelling. Uncertainty is propagated appropriately into the output, so we have a full posterior distribution of output and parameters. The data are available in the widely used netCDF file format from http://eidc.ceh.ac.uk/.

A general framework for updating belief distributions.

PubMed

Bissiri, P G; Holmes, C C; Walker, S G

2016-11-01

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution. More importantly, there are settings where the parameter of interest does not directly index a family of density functions and thus the Bayesian approach to learning about such parameters is currently regarded as problematic. Our framework uses loss functions to connect information in the data to functionals of interest. The updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions. Importantly, the procedure coincides with Bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings. Connections to other inference frameworks are highlighted.

How Much Can We Learn from a Single Chromatographic Experiment? A Bayesian Perspective.

PubMed

Wiczling, Paweł; Kaliszan, Roman

2016-01-05

In this work, we proposed and investigated a Bayesian inference procedure to find the desired chromatographic conditions based on known analyte properties (lipophilicity, pKa, and polar surface area) using one preliminary experiment. A previously developed nonlinear mixed effect model was used to specify the prior information about a new analyte with known physicochemical properties. Further, the prior (no preliminary data) and posterior predictive distribution (prior + one experiment) were determined sequentially to search towards the desired separation. The following isocratic high-performance reversed-phase liquid chromatographic conditions were sought: (1) retention time of a single analyte within the range of 4-6 min and (2) baseline separation of two analytes with retention times within the range of 4-10 min. The empirical posterior Bayesian distribution of parameters was estimated using the "slice sampling" Markov Chain Monte Carlo (MCMC) algorithm implemented in Matlab. The simulations with artificial analytes and experimental data of ketoprofen and papaverine were used to test the proposed methodology. The simulation experiment showed that for a single and two randomly selected analytes, there is 97% and 74% probability of obtaining a successful chromatogram using none or one preliminary experiment. The desired separation for ketoprofen and papaverine was established based on a single experiment. It was confirmed that the search for a desired separation rarely requires a large number of chromatographic analyses at least for a simple optimization problem. The proposed Bayesian-based optimization scheme is a powerful method of finding a desired chromatographic separation based on a small number of preliminary experiments.

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

Objectively combining AR5 instrumental period and paleoclimate climate sensitivity evidence

NASA Astrophysics Data System (ADS)

Lewis, Nicholas; Grünwald, Peter

2018-03-01

Combining instrumental period evidence regarding equilibrium climate sensitivity with largely independent paleoclimate proxy evidence should enable a more constrained sensitivity estimate to be obtained. Previous, subjective Bayesian approaches involved selection of a prior probability distribution reflecting the investigators' beliefs about climate sensitivity. Here a recently developed approach employing two different statistical methods—objective Bayesian and frequentist likelihood-ratio—is used to combine instrumental period and paleoclimate evidence based on data presented and assessments made in the IPCC Fifth Assessment Report. Probabilistic estimates from each source of evidence are represented by posterior probability density functions (PDFs) of physically-appropriate form that can be uniquely factored into a likelihood function and a noninformative prior distribution. The three-parameter form is shown accurately to fit a wide range of estimated climate sensitivity PDFs. The likelihood functions relating to the probabilistic estimates from the two sources are multiplicatively combined and a prior is derived that is noninformative for inference from the combined evidence. A posterior PDF that incorporates the evidence from both sources is produced using a single-step approach, which avoids the order-dependency that would arise if Bayesian updating were used. Results are compared with an alternative approach using the frequentist signed root likelihood ratio method. Results from these two methods are effectively identical, and provide a 5-95% range for climate sensitivity of 1.1-4.05 K (median 1.87 K).

Estimating the Effective Sample Size of Tree Topologies from Bayesian Phylogenetic Analyses

PubMed Central

Lanfear, Robert; Hua, Xia; Warren, Dan L.

2016-01-01

Bayesian phylogenetic analyses estimate posterior distributions of phylogenetic tree topologies and other parameters using Markov chain Monte Carlo (MCMC) methods. Before making inferences from these distributions, it is important to assess their adequacy. To this end, the effective sample size (ESS) estimates how many truly independent samples of a given parameter the output of the MCMC represents. The ESS of a parameter is frequently much lower than the number of samples taken from the MCMC because sequential samples from the chain can be non-independent due to autocorrelation. Typically, phylogeneticists use a rule of thumb that the ESS of all parameters should be greater than 200. However, we have no method to calculate an ESS of tree topology samples, despite the fact that the tree topology is often the parameter of primary interest and is almost always central to the estimation of other parameters. That is, we lack a method to determine whether we have adequately sampled one of the most important parameters in our analyses. In this study, we address this problem by developing methods to estimate the ESS for tree topologies. We combine these methods with two new diagnostic plots for assessing posterior samples of tree topologies, and compare their performance on simulated and empirical data sets. Combined, the methods we present provide new ways to assess the mixing and convergence of phylogenetic tree topologies in Bayesian MCMC analyses. PMID:27435794

Posterior Predictive Model Checking in Bayesian Networks

ERIC Educational Resources Information Center

Crawford, Aaron

2014-01-01

This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex…

Competing risk models in reliability systems, an exponential distribution model with Bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, I.

2018-03-01

The exponential distribution is the most widely used reliability analysis. This distribution is very suitable for representing the lengths of life of many cases and is available in a simple statistical form. The characteristic of this distribution is a constant hazard rate. The exponential distribution is the lower rank of the Weibull distributions. In this paper our effort is to introduce the basic notions that constitute an exponential competing risks model in reliability analysis using Bayesian analysis approach and presenting their analytic methods. The cases are limited to the models with independent causes of failure. A non-informative prior distribution is used in our analysis. This model describes the likelihood function and follows with the description of the posterior function and the estimations of the point, interval, hazard function, and reliability. The net probability of failure if only one specific risk is present, crude probability of failure due to a specific risk in the presence of other causes, and partial crude probabilities are also included.

Adaptive Annealed Importance Sampling for Multimodal Posterior Exploration and Model Selection with Application to Extrasolar Planet Detection

NASA Astrophysics Data System (ADS)

Liu, Bin

2014-07-01

We describe an algorithm that can adaptively provide mixture summaries of multimodal posterior distributions. The parameter space of the involved posteriors ranges in size from a few dimensions to dozens of dimensions. This work was motivated by an astrophysical problem called extrasolar planet (exoplanet) detection, wherein the computation of stochastic integrals that are required for Bayesian model comparison is challenging. The difficulty comes from the highly nonlinear models that lead to multimodal posterior distributions. We resort to importance sampling (IS) to estimate the integrals, and thus translate the problem to be how to find a parametric approximation of the posterior. To capture the multimodal structure in the posterior, we initialize a mixture proposal distribution and then tailor its parameters elaborately to make it resemble the posterior to the greatest extent possible. We use the effective sample size (ESS) calculated based on the IS draws to measure the degree of approximation. The bigger the ESS is, the better the proposal resembles the posterior. A difficulty within this tailoring operation lies in the adjustment of the number of mixing components in the mixture proposal. Brute force methods just preset it as a large constant, which leads to an increase in the required computational resources. We provide an iterative delete/merge/add process, which works in tandem with an expectation-maximization step to tailor such a number online. The efficiency of our proposed method is tested via both simulation studies and real exoplanet data analysis.

A model to systematically employ professional judgment in the Bayesian Decision Analysis for a semiconductor industry exposure assessment.

PubMed

Torres, Craig; Jones, Rachael; Boelter, Fred; Poole, James; Dell, Linda; Harper, Paul

2014-01-01

Bayesian Decision Analysis (BDA) uses Bayesian statistics to integrate multiple types of exposure information and classify exposures within the exposure rating categorization scheme promoted in American Industrial Hygiene Association (AIHA) publications. Prior distributions for BDA may be developed from existing monitoring data, mathematical models, or professional judgment. Professional judgments may misclassify exposures. We suggest that a structured qualitative risk assessment (QLRA) method can provide consistency and transparency in professional judgments. In this analysis, we use a structured QLRA method to define prior distributions (priors) for BDA. We applied this approach at three semiconductor facilities in South Korea, and present an evaluation of the performance of structured QLRA for determination of priors, and an evaluation of occupational exposures using BDA. Specifically, the structured QLRA was applied to chemical agents in similar exposure groups to identify provisional risk ratings. Standard priors were developed for each risk rating before review of historical monitoring data. Newly collected monitoring data were used to update priors informed by QLRA or historical monitoring data, and determine the posterior distribution. Exposure ratings were defined by the rating category with the highest probability--i.e., the most likely. We found the most likely exposure rating in the QLRA-informed priors to be consistent with historical and newly collected monitoring data, and the posterior exposure ratings developed with QLRA-informed priors to be equal to or greater than those developed with data-informed priors in 94% of comparisons. Overall, exposures at these facilities are consistent with well-controlled work environments. That is, the 95th percentile of exposure distributions are ≤50% of the occupational exposure limit (OEL) for all chemical-SEG combinations evaluated; and are ≤10% of the limit for 94% of chemical-SEG combinations evaluated.

Bayesian selection of misspecified models is overconfident and may cause spurious posterior probabilities for phylogenetic trees.

PubMed

Yang, Ziheng; Zhu, Tianqi

2018-02-20

The Bayesian method is noted to produce spuriously high posterior probabilities for phylogenetic trees in analysis of large datasets, but the precise reasons for this overconfidence are unknown. In general, the performance of Bayesian selection of misspecified models is poorly understood, even though this is of great scientific interest since models are never true in real data analysis. Here we characterize the asymptotic behavior of Bayesian model selection and show that when the competing models are equally wrong, Bayesian model selection exhibits surprising and polarized behaviors in large datasets, supporting one model with full force while rejecting the others. If one model is slightly less wrong than the other, the less wrong model will eventually win when the amount of data increases, but the method may become overconfident before it becomes reliable. We suggest that this extreme behavior may be a major factor for the spuriously high posterior probabilities for evolutionary trees. The philosophical implications of our results to the application of Bayesian model selection to evaluate opposing scientific hypotheses are yet to be explored, as are the behaviors of non-Bayesian methods in similar situations.

Computational Toxicology of Chloroform: Reverse Dosimetry Using Bayesian Inference, Markov Chain Monte Carlo Simulation, and Human Biomonitoring Data

PubMed Central

Lyons, Michael A.; Yang, Raymond S.H.; Mayeno, Arthur N.; Reisfeld, Brad

2008-01-01

Background One problem of interpreting population-based biomonitoring data is the reconstruction of corresponding external exposure in cases where no such data are available. Objectives We demonstrate the use of a computational framework that integrates physiologically based pharmacokinetic (PBPK) modeling, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of environmental chloroform source concentrations consistent with human biomonitoring data. The biomonitoring data consist of chloroform blood concentrations measured as part of the Third National Health and Nutrition Examination Survey (NHANES III), and for which no corresponding exposure data were collected. Methods We used a combined PBPK and shower exposure model to consider several routes and sources of exposure: ingestion of tap water, inhalation of ambient household air, and inhalation and dermal absorption while showering. We determined posterior distributions for chloroform concentration in tap water and ambient household air using U.S. Environmental Protection Agency Total Exposure Assessment Methodology (TEAM) data as prior distributions for the Bayesian analysis. Results Posterior distributions for exposure indicate that 95% of the population represented by the NHANES III data had likely chloroform exposures ≤ 67 μg/L in tap water and ≤ 0.02 μg/L in ambient household air. Conclusions Our results demonstrate the application of computer simulation to aid in the interpretation of human biomonitoring data in the context of the exposure–health evaluation–risk assessment continuum. These results should be considered as a demonstration of the method and can be improved with the addition of more detailed data. PMID:18709138

Bayesian truncation errors in chiral effective field theory: model checking and accounting for correlations

NASA Astrophysics Data System (ADS)

Melendez, Jordan; Wesolowski, Sarah; Furnstahl, Dick

2017-09-01

Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. A Bayesian model yields posterior probability distribution functions for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. As a general example of a statistical approach to truncation errors, the model was applied to chiral EFT for neutron-proton scattering using various semi-local potentials of Epelbaum, Krebs, and Meißner (EKM). Here we discuss how our model can learn correlation information from the data and how to perform Bayesian model checking to validate that the EFT is working as advertised. Supported in part by NSF PHY-1614460 and DOE NUCLEI SciDAC DE-SC0008533.

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

The utility of Bayesian predictive probabilities for interim monitoring of clinical trials

PubMed Central

Connor, Jason T.; Ayers, Gregory D; Alvarez, JoAnn

2014-01-01

Background Bayesian predictive probabilities can be used for interim monitoring of clinical trials to estimate the probability of observing a statistically significant treatment effect if the trial were to continue to its predefined maximum sample size. Purpose We explore settings in which Bayesian predictive probabilities are advantageous for interim monitoring compared to Bayesian posterior probabilities, p-values, conditional power, or group sequential methods. Results For interim analyses that address prediction hypotheses, such as futility monitoring and efficacy monitoring with lagged outcomes, only predictive probabilities properly account for the amount of data remaining to be observed in a clinical trial and have the flexibility to incorporate additional information via auxiliary variables. Limitations Computational burdens limit the feasibility of predictive probabilities in many clinical trial settings. The specification of prior distributions brings additional challenges for regulatory approval. Conclusions The use of Bayesian predictive probabilities enables the choice of logical interim stopping rules that closely align with the clinical decision making process. PMID:24872363

Hepatitis disease detection using Bayesian theory

NASA Astrophysics Data System (ADS)

Maseleno, Andino; Hidayati, Rohmah Zahroh

2017-02-01

This paper presents hepatitis disease diagnosis using a Bayesian theory for better understanding of the theory. In this research, we used a Bayesian theory for detecting hepatitis disease and displaying the result of diagnosis process. Bayesian algorithm theory is rediscovered and perfected by Laplace, the basic idea is using of the known prior probability and conditional probability density parameter, based on Bayes theorem to calculate the corresponding posterior probability, and then obtained the posterior probability to infer and make decisions. Bayesian methods combine existing knowledge, prior probabilities, with additional knowledge derived from new data, the likelihood function. The initial symptoms of hepatitis which include malaise, fever and headache. The probability of hepatitis given the presence of malaise, fever, and headache. The result revealed that a Bayesian theory has successfully identified the existence of hepatitis disease.

Bayesian structural inference for hidden processes.

PubMed

Strelioff, Christopher C; Crutchfield, James P

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ε-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ε-machines, irrespective of estimated transition probabilities. Properties of ε-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Bayesian structural inference for hidden processes

NASA Astrophysics Data System (ADS)

Strelioff, Christopher C.; Crutchfield, James P.

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ɛ-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ɛ-machines, irrespective of estimated transition probabilities. Properties of ɛ-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Bayesian nonparametric regression with varying residual density

PubMed Central

Pati, Debdeep; Dunson, David B.

2013-01-01

We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized PSB (sPSB) location-scale mixtures. Both priors restrict the residual density to be symmetric about zero, with the sPSB prior more flexible in allowing multimodal densities. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function under the sPSB prior, generalizing existing theory focused on parametric residual distributions. The PSB and sPSB priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating Gaussian processes in the stick-breaking components. This leads to a robust Bayesian regression procedure that automatically down-weights outliers and influential observations in a locally-adaptive manner. Posterior computation relies on an efficient data augmentation exact block Gibbs sampler. The methods are illustrated using simulated and real data applications. PMID:24465053

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.

Model Diagnostics for Bayesian Networks

ERIC Educational Resources Information Center

Sinharay, Sandip

2006-01-01

Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…

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.

Dimension-independent likelihood-informed MCMC

DOE PAGES

Cui, Tiangang; Law, Kody J. H.; Marzouk, Youssef M.

2015-10-08

Many Bayesian inference problems require exploring the posterior distribution of highdimensional parameters that represent the discretization of an underlying function. Our work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. There are two distinct lines of research that intersect in the methods we develop here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian informationmore » and any associated lowdimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Finally, we use two nonlinear inverse problems in order to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.« less

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.

A Bayesian Approach to Evaluating Consistency between Climate Model Output and Observations

NASA Astrophysics Data System (ADS)

Braverman, A. J.; Cressie, N.; Teixeira, J.

2010-12-01

Like other scientific and engineering problems that involve physical modeling of complex systems, climate models can be evaluated and diagnosed by comparing their output to observations of similar quantities. Though the global remote sensing data record is relatively short by climate research standards, these data offer opportunities to evaluate model predictions in new ways. For example, remote sensing data are spatially and temporally dense enough to provide distributional information that goes beyond simple moments to allow quantification of temporal and spatial dependence structures. In this talk, we propose a new method for exploiting these rich data sets using a Bayesian paradigm. For a collection of climate models, we calculate posterior probabilities its members best represent the physical system each seeks to reproduce. The posterior probability is based on the likelihood that a chosen summary statistic, computed from observations, would be obtained when the model's output is considered as a realization from a stochastic process. By exploring how posterior probabilities change with different statistics, we may paint a more quantitative and complete picture of the strengths and weaknesses of the models relative to the observations. We demonstrate our method using model output from the CMIP archive, and observations from NASA's Atmospheric Infrared Sounder.

Distributed multisensory integration in a recurrent network model through supervised learning

NASA Astrophysics Data System (ADS)

Wang, He; Wong, K. Y. Michael

Sensory integration between different modalities has been extensively studied. It is suggested that the brain integrates signals from different modalities in a Bayesian optimal way. However, how the Bayesian rule is implemented in a neural network remains under debate. In this work we propose a biologically plausible recurrent network model, which can perform Bayesian multisensory integration after trained by supervised learning. Our model is composed of two modules, each for one modality. We assume that each module is a recurrent network, whose activity represents the posterior distribution of each stimulus. The feedforward input on each module is the likelihood of each modality. Two modules are integrated through cross-links, which are feedforward connections from the other modality, and reciprocal connections, which are recurrent connections between different modules. By stochastic gradient descent, we successfully trained the feedforward and recurrent coupling matrices simultaneously, both of which resembles the Mexican-hat. We also find that there are more than one set of coupling matrices that can approximate the Bayesian theorem well. Specifically, reciprocal connections and cross-links will compensate each other if one of them is removed. Even though trained with two inputs, the network's performance with only one input is in good accordance with what is predicted by the Bayesian theorem.

ADAPTIVE ANNEALED IMPORTANCE SAMPLING FOR MULTIMODAL POSTERIOR EXPLORATION AND MODEL SELECTION WITH APPLICATION TO EXTRASOLAR PLANET DETECTION

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

Liu, Bin, E-mail: bins@ieee.org

2014-07-01

We describe an algorithm that can adaptively provide mixture summaries of multimodal posterior distributions. The parameter space of the involved posteriors ranges in size from a few dimensions to dozens of dimensions. This work was motivated by an astrophysical problem called extrasolar planet (exoplanet) detection, wherein the computation of stochastic integrals that are required for Bayesian model comparison is challenging. The difficulty comes from the highly nonlinear models that lead to multimodal posterior distributions. We resort to importance sampling (IS) to estimate the integrals, and thus translate the problem to be how to find a parametric approximation of the posterior.more » To capture the multimodal structure in the posterior, we initialize a mixture proposal distribution and then tailor its parameters elaborately to make it resemble the posterior to the greatest extent possible. We use the effective sample size (ESS) calculated based on the IS draws to measure the degree of approximation. The bigger the ESS is, the better the proposal resembles the posterior. A difficulty within this tailoring operation lies in the adjustment of the number of mixing components in the mixture proposal. Brute force methods just preset it as a large constant, which leads to an increase in the required computational resources. We provide an iterative delete/merge/add process, which works in tandem with an expectation-maximization step to tailor such a number online. The efficiency of our proposed method is tested via both simulation studies and real exoplanet data analysis.« less

Model-based Bayesian inference for ROC data analysis

NASA Astrophysics Data System (ADS)

Lei, Tianhu; Bae, K. Ty

2013-03-01

This paper presents a study of model-based Bayesian inference to Receiver Operating Characteristics (ROC) data. The model is a simple version of general non-linear regression model. Different from Dorfman model, it uses a probit link function with a covariate variable having zero-one two values to express binormal distributions in a single formula. Model also includes a scale parameter. Bayesian inference is implemented by Markov Chain Monte Carlo (MCMC) method carried out by Bayesian analysis Using Gibbs Sampling (BUGS). Contrast to the classical statistical theory, Bayesian approach considers model parameters as random variables characterized by prior distributions. With substantial amount of simulated samples generated by sampling algorithm, posterior distributions of parameters as well as parameters themselves can be accurately estimated. MCMC-based BUGS adopts Adaptive Rejection Sampling (ARS) protocol which requires the probability density function (pdf) which samples are drawing from be log concave with respect to the targeted parameters. Our study corrects a common misconception and proves that pdf of this regression model is log concave with respect to its scale parameter. Therefore, ARS's requirement is satisfied and a Gaussian prior which is conjugate and possesses many analytic and computational advantages is assigned to the scale parameter. A cohort of 20 simulated data sets and 20 simulations from each data set are used in our study. Output analysis and convergence diagnostics for MCMC method are assessed by CODA package. Models and methods by using continuous Gaussian prior and discrete categorical prior are compared. Intensive simulations and performance measures are given to illustrate our practice in the framework of model-based Bayesian inference using MCMC method.

Bayesian approach to analyzing holograms of colloidal particles.

PubMed

Dimiduk, Thomas G; Manoharan, Vinothan N

2016-10-17

We demonstrate a Bayesian approach to tracking and characterizing colloidal particles from in-line digital holograms. We model the formation of the hologram using Lorenz-Mie theory. We then use a tempered Markov-chain Monte Carlo method to sample the posterior probability distributions of the model parameters: particle position, size, and refractive index. Compared to least-squares fitting, our approach allows us to more easily incorporate prior information about the parameters and to obtain more accurate uncertainties, which are critical for both particle tracking and characterization experiments. Our approach also eliminates the need to supply accurate initial guesses for the parameters, so it requires little tuning.

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.

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.

A Bayesian predictive two-stage design for phase II clinical trials.

PubMed

Sambucini, Valeria

2008-04-15

In this paper, we propose a Bayesian two-stage design for phase II clinical trials, which represents a predictive version of the single threshold design (STD) recently introduced by Tan and Machin. The STD two-stage sample sizes are determined specifying a minimum threshold for the posterior probability that the true response rate exceeds a pre-specified target value and assuming that the observed response rate is slightly higher than the target. Unlike the STD, we do not refer to a fixed experimental outcome, but take into account the uncertainty about future data. In both stages, the design aims to control the probability of getting a large posterior probability that the true response rate exceeds the target value. Such a probability is expressed in terms of prior predictive distributions of the data. The performance of the design is based on the distinction between analysis and design priors, recently introduced in the literature. The properties of the method are studied when all the design parameters vary.

Spectral decompositions of multiple time series: a Bayesian non-parametric approach.

PubMed

Macaro, Christian; Prado, Raquel

2014-01-01

We consider spectral decompositions of multiple time series that arise in studies where the interest lies in assessing the influence of two or more factors. We write the spectral density of each time series as a sum of the spectral densities associated to the different levels of the factors. We then use Whittle's approximation to the likelihood function and follow a Bayesian non-parametric approach to obtain posterior inference on the spectral densities based on Bernstein-Dirichlet prior distributions. The prior is strategically important as it carries identifiability conditions for the models and allows us to quantify our degree of confidence in such conditions. A Markov chain Monte Carlo (MCMC) algorithm for posterior inference within this class of frequency-domain models is presented.We illustrate the approach by analyzing simulated and real data via spectral one-way and two-way models. In particular, we present an analysis of functional magnetic resonance imaging (fMRI) brain responses measured in individuals who participated in a designed experiment to study pain perception in humans.

Efficient Mean Field Variational Algorithm for Data Assimilation (Invited)

NASA Astrophysics Data System (ADS)

Vrettas, M. D.; Cornford, D.; Opper, M.

2013-12-01

Data assimilation algorithms combine available observations of physical systems with the assumed model dynamics in a systematic manner, to produce better estimates of initial conditions for prediction. Broadly they can be categorized in three main approaches: (a) sequential algorithms, (b) sampling methods and (c) variational algorithms which transform the density estimation problem to an optimization problem. However, given finite computational resources, only a handful of ensemble Kalman filters and 4DVar algorithms have been applied operationally to very high dimensional geophysical applications, such as weather forecasting. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the ';optimal' posterior distribution over the continuous time states, within a family of non-stationary Gaussian processes. Our initial work on variational Bayesian approaches to data assimilation, unlike the well-known 4DVar method which seeks only the most probable solution, computes the best time varying Gaussian process approximation to the posterior smoothing distribution for dynamical systems that can be represented by stochastic differential equations. This approach was based on minimising the Kullback-Leibler divergence, over paths, between the true posterior and our Gaussian process approximation. Whilst the observations were informative enough to keep the posterior smoothing density close to Gaussian the algorithm proved very effective on low dimensional systems (e.g. O(10)D). However for higher dimensional systems, the high computational demands make the algorithm prohibitively expensive. To overcome the difficulties presented in the original framework and make our approach more efficient in higher dimensional systems we have been developing a new mean field version of the algorithm which treats the state variables at any given time as being independent in the posterior approximation, while still accounting for their relationships in the mean solution arising from the original system dynamics. Here we present this new mean field approach, illustrating its performance on a range of benchmark data assimilation problems whose dimensionality varies from O(10) to O(10^3)D. We emphasise that the variational Bayesian approach we adopt, unlike other variational approaches, provides a natural bound on the marginal likelihood of the observations given the model parameters which also allows for inference of (hyper-) parameters such as observational errors, parameters in the dynamical model and model error representation. We also stress that since our approach is intrinsically parallel it can be implemented very efficiently to address very long data assimilation time windows. Moreover, like most traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem therefore its complexity can be tuned to the available computational resources. We finish with a sketch of possible future directions.

A Bayesian-based multilevel factorial analysis method for analyzing parameter uncertainty of hydrological model

NASA Astrophysics Data System (ADS)

Liu, Y. R.; Li, Y. P.; Huang, G. H.; Zhang, J. L.; Fan, Y. R.

2017-10-01

In this study, a Bayesian-based multilevel factorial analysis (BMFA) method is developed to assess parameter uncertainties and their effects on hydrological model responses. In BMFA, Differential Evolution Adaptive Metropolis (DREAM) algorithm is employed to approximate the posterior distributions of model parameters with Bayesian inference; factorial analysis (FA) technique is used for measuring the specific variations of hydrological responses in terms of posterior distributions to investigate the individual and interactive effects of parameters on model outputs. BMFA is then applied to a case study of the Jinghe River watershed in the Loess Plateau of China to display its validity and applicability. The uncertainties of four sensitive parameters, including soil conservation service runoff curve number to moisture condition II (CN2), soil hydraulic conductivity (SOL_K), plant available water capacity (SOL_AWC), and soil depth (SOL_Z), are investigated. Results reveal that (i) CN2 has positive effect on peak flow, implying that the concentrated rainfall during rainy season can cause infiltration-excess surface flow, which is an considerable contributor to peak flow in this watershed; (ii) SOL_K has positive effect on average flow, implying that the widely distributed cambisols can lead to medium percolation capacity; (iii) the interaction between SOL_AWC and SOL_Z has noticeable effect on the peak flow and their effects are dependent upon each other, which discloses that soil depth can significant influence the processes of plant uptake of soil water in this watershed. Based on the above findings, the significant parameters and the relationship among uncertain parameters can be specified, such that hydrological model's capability for simulating/predicting water resources of the Jinghe River watershed can be improved.

New seismogenic stress fields for southern Italy from a Bayesian approach

NASA Astrophysics Data System (ADS)

Totaro, Cristina; Orecchio, Barbara; Presti, Debora; Scolaro, Silvia; Neri, Giancarlo

2017-04-01

A new database of high-quality waveform inversion focal mechanism has been compiled for southern Italy by integrating the highest quality solutions, available from literature and catalogues, and 146 newly-computed ones. All the selected focal mechanisms are (i) coming from the Italian CMT, Regional CMT and TDMT catalogues (Pondrelli et al., PEPI 2006, PEPI 2011; http://www.ingv.it), or (ii) computed by using the Cut And Paste (CAP) method (Zhao & Helmberger, BSSA 1994; Zhu & Helmberger, BSSA 1996). Specific tests have been carried out in order to evaluate the robustness of the obtained solutions (e.g., by varying both seismic network configuration and Earth structure parameters) and to estimate uncertainties on the focal mechanism parameters. Only the resulting highest-quality solutions have been enclosed in the database, that has then been used for computation of posterior density distributions of stress tensor components by a Bayesian method (Arnold & Townend, GJI 2007). This algorithm furnishes the posterior density function of the principal components of stress tensor (maximum σ1, intermediate σ2, and minimum σ3 compressive stress, respectively) and the stress-magnitude ratio (R). Before stress computation, we applied the k-means clustering algorithm to subdivide the focal mechanism catalog on the basis of earthquake locations. This approach allows identifying the sectors to be investigated without any "a priori" constraint from faulting type distribution. The large amount of data and the application of the Bayesian algorithm allowed us to provide a more accurate local-to-regional scale stress distribution that has shed new light on the kinematics and dynamics of this very complex area, where lithospheric unit configuration and geodynamic engines are still strongly debated. The new high-quality information here furnished will then represent very useful tools and constraints for future geophysical analyses and geodynamic modeling.

A Bayesian Supertree Model for Genome-Wide Species Tree Reconstruction

PubMed Central

De Oliveira Martins, Leonardo; Mallo, Diego; Posada, David

2016-01-01

Current phylogenomic data sets highlight the need for species tree methods able to deal with several sources of gene tree/species tree incongruence. At the same time, we need to make most use of all available data. Most species tree methods deal with single processes of phylogenetic discordance, namely, gene duplication and loss, incomplete lineage sorting (ILS) or horizontal gene transfer. In this manuscript, we address the problem of species tree inference from multilocus, genome-wide data sets regardless of the presence of gene duplication and loss and ILS therefore without the need to identify orthologs or to use a single individual per species. We do this by extending the idea of Maximum Likelihood (ML) supertrees to a hierarchical Bayesian model where several sources of gene tree/species tree disagreement can be accounted for in a modular manner. We implemented this model in a computer program called guenomu whose inputs are posterior distributions of unrooted gene tree topologies for multiple gene families, and whose output is the posterior distribution of rooted species tree topologies. We conducted extensive simulations to evaluate the performance of our approach in comparison with other species tree approaches able to deal with more than one leaf from the same species. Our method ranked best under simulated data sets, in spite of ignoring branch lengths, and performed well on empirical data, as well as being fast enough to analyze relatively large data sets. Our Bayesian supertree method was also very successful in obtaining better estimates of gene trees, by reducing the uncertainty in their distributions. In addition, our results show that under complex simulation scenarios, gene tree parsimony is also a competitive approach once we consider its speed, in contrast to more sophisticated models. PMID:25281847

Bayesian functional integral method for inferring continuous data from discrete measurements.

PubMed

Heuett, William J; Miller, Bernard V; Racette, Susan B; Holloszy, John O; Chow, Carson C; Periwal, Vipul

2012-02-08

Inference of the insulin secretion rate (ISR) from C-peptide measurements as a quantification of pancreatic β-cell function is clinically important in diseases related to reduced insulin sensitivity and insulin action. ISR derived from C-peptide concentration is an example of nonparametric Bayesian model selection where a proposed ISR time-course is considered to be a "model". An inferred value of inaccessible continuous variables from discrete observable data is often problematic in biology and medicine, because it is a priori unclear how robust the inference is to the deletion of data points, and a closely related question, how much smoothness or continuity the data actually support. Predictions weighted by the posterior distribution can be cast as functional integrals as used in statistical field theory. Functional integrals are generally difficult to evaluate, especially for nonanalytic constraints such as positivity of the estimated parameters. We propose a computationally tractable method that uses the exact solution of an associated likelihood function as a prior probability distribution for a Markov-chain Monte Carlo evaluation of the posterior for the full model. As a concrete application of our method, we calculate the ISR from actual clinical C-peptide measurements in human subjects with varying degrees of insulin sensitivity. Our method demonstrates the feasibility of functional integral Bayesian model selection as a practical method for such data-driven inference, allowing the data to determine the smoothing timescale and the width of the prior probability distribution on the space of models. In particular, our model comparison method determines the discrete time-step for interpolation of the unobservable continuous variable that is supported by the data. Attempts to go to finer discrete time-steps lead to less likely models. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Quantifying MCMC exploration of phylogenetic tree space.

PubMed

Whidden, Chris; Matsen, Frederick A

2015-05-01

In order to gain an understanding of the effectiveness of phylogenetic Markov chain Monte Carlo (MCMC), it is important to understand how quickly the empirical distribution of the MCMC converges to the posterior distribution. In this article, we investigate this problem on phylogenetic tree topologies with a metric that is especially well suited to the task: the subtree prune-and-regraft (SPR) metric. This metric directly corresponds to the minimum number of MCMC rearrangements required to move between trees in common phylogenetic MCMC implementations. We develop a novel graph-based approach to analyze tree posteriors and find that the SPR metric is much more informative than simpler metrics that are unrelated to MCMC moves. In doing so, we show conclusively that topological peaks do occur in Bayesian phylogenetic posteriors from real data sets as sampled with standard MCMC approaches, investigate the efficiency of Metropolis-coupled MCMC (MCMCMC) in traversing the valleys between peaks, and show that conditional clade distribution (CCD) can have systematic problems when there are multiple peaks. © The Author(s) 2015. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.

A Surrogate-based Adaptive Sampling Approach for History Matching and Uncertainty Quantification

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

Li, Weixuan; Zhang, Dongxiao; Lin, Guang

A critical procedure in reservoir simulations is history matching (or data assimilation in a broader sense), which calibrates model parameters such that the simulation results are consistent with field measurements, and hence improves the credibility of the predictions given by the simulations. Often there exist non-unique combinations of parameter values that all yield the simulation results matching the measurements. For such ill-posed history matching problems, Bayesian theorem provides a theoretical foundation to represent different solutions and to quantify the uncertainty with the posterior PDF. Lacking an analytical solution in most situations, the posterior PDF may be characterized with a samplemore » of realizations, each representing a possible scenario. A novel sampling algorithm is presented here for the Bayesian solutions to history matching problems. We aim to deal with two commonly encountered issues: 1) as a result of the nonlinear input-output relationship in a reservoir model, the posterior distribution could be in a complex form, such as multimodal, which violates the Gaussian assumption required by most of the commonly used data assimilation approaches; 2) a typical sampling method requires intensive model evaluations and hence may cause unaffordable computational cost. In the developed algorithm, we use a Gaussian mixture model as the proposal distribution in the sampling process, which is simple but also flexible to approximate non-Gaussian distributions and is particularly efficient when the posterior is multimodal. Also, a Gaussian process is utilized as a surrogate model to speed up the sampling process. Furthermore, an iterative scheme of adaptive surrogate refinement and re-sampling ensures sampling accuracy while keeping the computational cost at a minimum level. The developed approach is demonstrated with an illustrative example and shows its capability in handling the above-mentioned issues. Multimodal posterior of the history matching problem is captured and are used to give a reliable production prediction with uncertainty quantification. The new algorithm reveals a great improvement in terms of computational efficiency comparing previously studied approaches for the sample problem.« less

The Efficacy of Consensus Tree Methods for Summarizing Phylogenetic Relationships from a Posterior Sample of Trees Estimated from Morphological Data.

PubMed

O'Reilly, Joseph E; Donoghue, Philip C J

2018-03-01

Consensus trees are required to summarize trees obtained through MCMC sampling of a posterior distribution, providing an overview of the distribution of estimated parameters such as topology, branch lengths, and divergence times. Numerous consensus tree construction methods are available, each presenting a different interpretation of the tree sample. The rise of morphological clock and sampled-ancestor methods of divergence time estimation, in which times and topology are coestimated, has increased the popularity of the maximum clade credibility (MCC) consensus tree method. The MCC method assumes that the sampled, fully resolved topology with the highest clade credibility is an adequate summary of the most probable clades, with parameter estimates from compatible sampled trees used to obtain the marginal distributions of parameters such as clade ages and branch lengths. Using both simulated and empirical data, we demonstrate that MCC trees, and trees constructed using the similar maximum a posteriori (MAP) method, often include poorly supported and incorrect clades when summarizing diffuse posterior samples of trees. We demonstrate that the paucity of information in morphological data sets contributes to the inability of MCC and MAP trees to accurately summarise of the posterior distribution. Conversely, majority-rule consensus (MRC) trees represent a lower proportion of incorrect nodes when summarizing the same posterior samples of trees. Thus, we advocate the use of MRC trees, in place of MCC or MAP trees, in attempts to summarize the results of Bayesian phylogenetic analyses of morphological data.

The Efficacy of Consensus Tree Methods for Summarizing Phylogenetic Relationships from a Posterior Sample of Trees Estimated from Morphological Data

PubMed Central

O’Reilly, Joseph E; Donoghue, Philip C J

2018-01-01

Abstract Consensus trees are required to summarize trees obtained through MCMC sampling of a posterior distribution, providing an overview of the distribution of estimated parameters such as topology, branch lengths, and divergence times. Numerous consensus tree construction methods are available, each presenting a different interpretation of the tree sample. The rise of morphological clock and sampled-ancestor methods of divergence time estimation, in which times and topology are coestimated, has increased the popularity of the maximum clade credibility (MCC) consensus tree method. The MCC method assumes that the sampled, fully resolved topology with the highest clade credibility is an adequate summary of the most probable clades, with parameter estimates from compatible sampled trees used to obtain the marginal distributions of parameters such as clade ages and branch lengths. Using both simulated and empirical data, we demonstrate that MCC trees, and trees constructed using the similar maximum a posteriori (MAP) method, often include poorly supported and incorrect clades when summarizing diffuse posterior samples of trees. We demonstrate that the paucity of information in morphological data sets contributes to the inability of MCC and MAP trees to accurately summarise of the posterior distribution. Conversely, majority-rule consensus (MRC) trees represent a lower proportion of incorrect nodes when summarizing the same posterior samples of trees. Thus, we advocate the use of MRC trees, in place of MCC or MAP trees, in attempts to summarize the results of Bayesian phylogenetic analyses of morphological data. PMID:29106675

Information-Based Analysis of Data Assimilation (Invited)

NASA Astrophysics Data System (ADS)

Nearing, G. S.; Gupta, H. V.; Crow, W. T.; Gong, W.

2013-12-01

Data assimilation is defined as the Bayesian conditioning of uncertain model simulations on observations for the purpose of reducing uncertainty about model states. Practical data assimilation methods make the application of Bayes' law tractable either by employing assumptions about the prior, posterior and likelihood distributions (e.g., the Kalman family of filters) or by using resampling methods (e.g., bootstrap filter). We propose to quantify the efficiency of these approximations in an OSSE setting using information theory and, in an OSSE or real-world validation setting, to measure the amount - and more importantly, the quality - of information extracted from observations during data assimilation. To analyze DA assumptions, uncertainty is quantified as the Shannon-type entropy of a discretized probability distribution. The maximum amount of information that can be extracted from observations about model states is the mutual information between states and observations, which is equal to the reduction in entropy in our estimate of the state due to Bayesian filtering. The difference between this potential and the actual reduction in entropy due to Kalman (or other type of) filtering measures the inefficiency of the filter assumptions. Residual uncertainty in DA posterior state estimates can be attributed to three sources: (i) non-injectivity of the observation operator, (ii) noise in the observations, and (iii) filter approximations. The contribution of each of these sources is measurable in an OSSE setting. The amount of information extracted from observations by data assimilation (or system identification, including parameter estimation) can also be measured by Shannon's theory. Since practical filters are approximations of Bayes' law, it is important to know whether the information that is extracted form observations by a filter is reliable. We define information as either good or bad, and propose to measure these two types of information using partial Kullback-Leibler divergences. Defined this way, good and bad information sum to total information. This segregation of information into good and bad components requires a validation target distribution; in a DA OSSE setting, this can be the true Bayesian posterior, but in a real-world setting the validation target might be determined by a set of in situ observations.

Reweighting Data in the Spirit of Tukey: Using Bayesian Posterior Probabilities as Rasch Residuals for Studying Misfit

ERIC Educational Resources Information Center

Dardick, William R.; Mislevy, Robert J.

2016-01-01

A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

A hierarchical Bayesian method for vibration-based time domain force reconstruction problems

NASA Astrophysics Data System (ADS)

Li, Qiaofeng; Lu, Qiuhai

2018-05-01

Traditional force reconstruction techniques require prior knowledge on the force nature to determine the regularization term. When such information is unavailable, the inappropriate term is easily chosen and the reconstruction result becomes unsatisfactory. In this paper, we propose a novel method to automatically determine the appropriate q as in ℓq regularization and reconstruct the force history. The method incorporates all to-be-determined variables such as the force history, precision parameters and q into a hierarchical Bayesian formulation. The posterior distributions of variables are evaluated by a Metropolis-within-Gibbs sampler. The point estimates of variables and their uncertainties are given. Simulations of a cantilever beam and a space truss under various loading conditions validate the proposed method in providing adaptive determination of q and better reconstruction performance than existing Bayesian methods.

Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes simulations: A data-driven, physics-informed Bayesian approach

NASA Astrophysics Data System (ADS)

Xiao, H.; Wu, J.-L.; Wang, J.-X.; Sun, R.; Roy, C. J.

2016-11-01

Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has potential implications in many fields in which the governing equations are well understood but the model uncertainty comes from unresolved physical processes.

Bayesian inference of galaxy formation from the K-band luminosity function of galaxies: tensions between theory and observation

NASA Astrophysics Data System (ADS)

Lu, Yu; Mo, H. J.; Katz, Neal; Weinberg, Martin D.

2012-04-01

We conduct Bayesian model inferences from the observed K-band luminosity function of galaxies in the local Universe, using the semi-analytic model (SAM) of galaxy formation introduced in Lu et al. The prior distributions for the 14 free parameters include a large range of possible models. We find that some of the free parameters, e.g. the characteristic scales for quenching star formation in both high-mass and low-mass haloes, are already tightly constrained by the single data set. The posterior distribution includes the model parameters adopted in other SAMs. By marginalizing over the posterior distribution, we make predictions that include the full inferential uncertainties for the colour-magnitude relation, the Tully-Fisher relation, the conditional stellar mass function of galaxies in haloes of different masses, the H I mass function, the redshift evolution of the stellar mass function of galaxies and the global star formation history. Using posterior predictive checking with the available observational results, we find that the model family (i) predicts a Tully-Fisher relation that is curved; (ii) significantly overpredicts the satellite fraction; (iii) vastly overpredicts the H I mass function; (iv) predicts high-z stellar mass functions that have too many low-mass galaxies and too few high-mass ones and (v) predicts a redshift evolution of the stellar mass density and the star formation history that are in moderate disagreement. These results suggest that some important processes are still missing in the current model family, and we discuss a number of possible solutions to solve the discrepancies, such as interactions between galaxies and dark matter haloes, tidal stripping, the bimodal accretion of gas, preheating and a redshift-dependent initial mass function.

Detection of mastitis in dairy cattle by use of mixture models for repeated somatic cell scores: a Bayesian approach via Gibbs sampling.

PubMed

Odegård, J; Jensen, J; Madsen, P; Gianola, D; Klemetsdal, G; Heringstad, B

2003-11-01

The distribution of somatic cell scores could be regarded as a mixture of at least two components depending on a cow's udder health status. A heteroscedastic two-component Bayesian normal mixture model with random effects was developed and implemented via Gibbs sampling. The model was evaluated using datasets consisting of simulated somatic cell score records. Somatic cell score was simulated as a mixture representing two alternative udder health statuses ("healthy" or "diseased"). Animals were assigned randomly to the two components according to the probability of group membership (Pm). Random effects (additive genetic and permanent environment), when included, had identical distributions across mixture components. Posterior probabilities of putative mastitis were estimated for all observations, and model adequacy was evaluated using measures of sensitivity, specificity, and posterior probability of misclassification. Fitting different residual variances in the two mixture components caused some bias in estimation of parameters. When the components were difficult to disentangle, so were their residual variances, causing bias in estimation of Pm and of location parameters of the two underlying distributions. When all variance components were identical across mixture components, the mixture model analyses returned parameter estimates essentially without bias and with a high degree of precision. Including random effects in the model increased the probability of correct classification substantially. No sizable differences in probability of correct classification were found between models in which a single cow effect (ignoring relationships) was fitted and models where this effect was split into genetic and permanent environmental components, utilizing relationship information. When genetic and permanent environmental effects were fitted, the between-replicate variance of estimates of posterior means was smaller because the model accounted for random genetic drift.

Multiple model cardinalized probability hypothesis density filter

NASA Astrophysics Data System (ADS)

Georgescu, Ramona; Willett, Peter

2011-09-01

The Probability Hypothesis Density (PHD) filter propagates the first-moment approximation to the multi-target Bayesian posterior distribution while the Cardinalized PHD (CPHD) filter propagates both the posterior likelihood of (an unlabeled) target state and the posterior probability mass function of the number of targets. Extensions of the PHD filter to the multiple model (MM) framework have been published and were implemented either with a Sequential Monte Carlo or a Gaussian Mixture approach. In this work, we introduce the multiple model version of the more elaborate CPHD filter. We present the derivation of the prediction and update steps of the MMCPHD particularized for the case of two target motion models and proceed to show that in the case of a single model, the new MMCPHD equations reduce to the original CPHD equations.

Back to Normal! Gaussianizing posterior distributions for cosmological probes

NASA Astrophysics Data System (ADS)

Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.

2014-05-01

We present a method to map multivariate non-Gaussian posterior probability densities into Gaussian ones via nonlinear Box-Cox transformations, and generalizations thereof. This is analogous to the search for normal parameters in the CMB, but can in principle be applied to any probability density that is continuous and unimodal. The search for the optimally Gaussianizing transformation amongst the Box-Cox family is performed via a maximum likelihood formalism. We can judge the quality of the found transformation a posteriori: qualitatively via statistical tests of Gaussianity, and more illustratively by how well it reproduces the credible regions. The method permits an analytical reconstruction of the posterior from a sample, e.g. a Markov chain, and simplifies the subsequent joint analysis with other experiments. Furthermore, it permits the characterization of a non-Gaussian posterior in a compact and efficient way. The expression for the non-Gaussian posterior can be employed to find analytic formulae for the Bayesian evidence, and consequently be used for model comparison.

Markov Chain Monte Carlo Bayesian Learning for Neural Networks

NASA Technical Reports Server (NTRS)

Goodrich, Michael S.

2011-01-01

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

Bayesian hierarchical functional data analysis via contaminated informative priors.

PubMed

Scarpa, Bruno; Dunson, David B

2009-09-01

A variety of flexible approaches have been proposed for functional data analysis, allowing both the mean curve and the distribution about the mean to be unknown. Such methods are most useful when there is limited prior information. Motivated by applications to modeling of temperature curves in the menstrual cycle, this article proposes a flexible approach for incorporating prior information in semiparametric Bayesian analyses of hierarchical functional data. The proposed approach is based on specifying the distribution of functions as a mixture of a parametric hierarchical model and a nonparametric contamination. The parametric component is chosen based on prior knowledge, while the contamination is characterized as a functional Dirichlet process. In the motivating application, the contamination component allows unanticipated curve shapes in unhealthy menstrual cycles. Methods are developed for posterior computation, and the approach is applied to data from a European fecundability study.

A Bayesian method for inferring transmission chains in a partially observed epidemic.

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

Marzouk, Youssef M.; Ray, Jaideep

2008-10-01

We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historicalmore » data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.« less

Bayesian isotonic density regression

PubMed Central

Wang, Lianming; Dunson, David B.

2011-01-01

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model can be accurately approximated. This article develops a new class of density regression models that incorporate stochastic-ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor. Theory is developed showing large support. Methods are developed for hypothesis testing, with posterior computation relying on a simple Gibbs sampler. Frequentist properties are illustrated in a simulation study, and an epidemiology application is considered. PMID:22822259

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 operational modal analysis with asynchronous data, Part II: Posterior uncertainty

NASA Astrophysics Data System (ADS)

Zhu, Yi-Chen; Au, Siu-Kui

2018-01-01

A Bayesian modal identification method has been proposed in the companion paper that allows the most probable values of modal parameters to be determined using asynchronous ambient vibration data. This paper investigates the identification uncertainty of modal parameters in terms of their posterior covariance matrix. Computational issues are addressed. Analytical expressions are derived to allow the posterior covariance matrix to be evaluated accurately and efficiently. Synthetic, laboratory and field data examples are presented to verify the consistency, investigate potential modelling error and demonstrate practical applications.

Bayesian analysis of physiologically based toxicokinetic and toxicodynamic models.

PubMed

Hack, C Eric

2006-04-17

Physiologically based toxicokinetic (PBTK) and toxicodynamic (TD) models of bromate in animals and humans would improve our ability to accurately estimate the toxic doses in humans based on available animal studies. These mathematical models are often highly parameterized and must be calibrated in order for the model predictions of internal dose to adequately fit the experimentally measured doses. Highly parameterized models are difficult to calibrate and it is difficult to obtain accurate estimates of uncertainty or variability in model parameters with commonly used frequentist calibration methods, such as maximum likelihood estimation (MLE) or least squared error approaches. The Bayesian approach called Markov chain Monte Carlo (MCMC) analysis can be used to successfully calibrate these complex models. Prior knowledge about the biological system and associated model parameters is easily incorporated in this approach in the form of prior parameter distributions, and the distributions are refined or updated using experimental data to generate posterior distributions of parameter estimates. The goal of this paper is to give the non-mathematician a brief description of the Bayesian approach and Markov chain Monte Carlo analysis, how this technique is used in risk assessment, and the issues associated with this approach.

Bayesian analysis of U.S. hurricane climate

USGS Publications Warehouse

Elsner, James B.; Bossak, Brian H.

2001-01-01

Predictive climate distributions of U.S. landfalling hurricanes are estimated from observational records over the period 1851–2000. The approach is Bayesian, combining the reliable records of hurricane activity during the twentieth century with the less precise accounts of activity during the nineteenth century to produce a best estimate of the posterior distribution on the annual rates. The methodology provides a predictive distribution of future activity that serves as a climatological benchmark. Results are presented for the entire coast as well as for the Gulf Coast, Florida, and the East Coast. Statistics on the observed annual counts of U.S. hurricanes, both for the entire coast and by region, are similar within each of the three consecutive 50-yr periods beginning in 1851. However, evidence indicates that the records during the nineteenth century are less precise. Bayesian theory provides a rational approach for defining hurricane climate that uses all available information and that makes no assumption about whether the 150-yr record of hurricanes has been adequately or uniformly monitored. The analysis shows that the number of major hurricanes expected to reach the U.S. coast over the next 30 yr is 18 and the number of hurricanes expected to hit Florida is 20.

BCM: toolkit for Bayesian analysis of Computational Models using samplers.

PubMed

Thijssen, Bram; Dijkstra, Tjeerd M H; Heskes, Tom; Wessels, Lodewyk F A

2016-10-21

Computational models in biology are characterized by a large degree of uncertainty. This uncertainty can be analyzed with Bayesian statistics, however, the sampling algorithms that are frequently used for calculating Bayesian statistical estimates are computationally demanding, and each algorithm has unique advantages and disadvantages. It is typically unclear, before starting an analysis, which algorithm will perform well on a given computational model. We present BCM, a toolkit for the Bayesian analysis of Computational Models using samplers. It provides efficient, multithreaded implementations of eleven algorithms for sampling from posterior probability distributions and for calculating marginal likelihoods. BCM includes tools to simplify the process of model specification and scripts for visualizing the results. The flexible architecture allows it to be used on diverse types of biological computational models. In an example inference task using a model of the cell cycle based on ordinary differential equations, BCM is significantly more efficient than existing software packages, allowing more challenging inference problems to be solved. BCM represents an efficient one-stop-shop for computational modelers wishing to use sampler-based Bayesian statistics.

A Bayesian approach for parameter estimation and prediction using a computationally intensive model

DOE PAGES

Higdon, Dave; McDonnell, Jordan D.; Schunck, Nicolas; ...

2015-02-05

Bayesian methods have been successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based modelmore » $$\\eta (\\theta )$$, where θ denotes the uncertain, best input setting. Hence the statistical model is of the form $$y=\\eta (\\theta )+\\epsilon ,$$ where $$\\epsilon $$ accounts for measurement, and possibly other, error sources. When nonlinearity is present in $$\\eta (\\cdot )$$, the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model $$\\eta (\\cdot )$$. This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. Lastly, we also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory.« less

Maximum Entropy Discrimination Poisson Regression for Software Reliability Modeling.

PubMed

Chatzis, Sotirios P; Andreou, Andreas S

2015-11-01

Reliably predicting software defects is one of the most significant tasks in software engineering. Two of the major components of modern software reliability modeling approaches are: 1) extraction of salient features for software system representation, based on appropriately designed software metrics and 2) development of intricate regression models for count data, to allow effective software reliability data modeling and prediction. Surprisingly, research in the latter frontier of count data regression modeling has been rather limited. More specifically, a lack of simple and efficient algorithms for posterior computation has made the Bayesian approaches appear unattractive, and thus underdeveloped in the context of software reliability modeling. In this paper, we try to address these issues by introducing a novel Bayesian regression model for count data, based on the concept of max-margin data modeling, effected in the context of a fully Bayesian model treatment with simple and efficient posterior distribution updates. Our novel approach yields a more discriminative learning technique, making more effective use of our training data during model inference. In addition, it allows of better handling uncertainty in the modeled data, which can be a significant problem when the training data are limited. We derive elegant inference algorithms for our model under the mean-field paradigm and exhibit its effectiveness using the publicly available benchmark data sets.

Inference of emission rates from multiple sources using Bayesian probability theory.

PubMed

Yee, Eugene; Flesch, Thomas K

2010-03-01

The determination of atmospheric emission rates from multiple sources using inversion (regularized least-squares or best-fit technique) is known to be very susceptible to measurement and model errors in the problem, rendering the solution unusable. In this paper, a new perspective is offered for this problem: namely, it is argued that the problem should be addressed as one of inference rather than inversion. Towards this objective, Bayesian probability theory is used to estimate the emission rates from multiple sources. The posterior probability distribution for the emission rates is derived, accounting fully for the measurement errors in the concentration data and the model errors in the dispersion model used to interpret the data. The Bayesian inferential methodology for emission rate recovery is validated against real dispersion data, obtained from a field experiment involving various source-sensor geometries (scenarios) consisting of four synthetic area sources and eight concentration sensors. The recovery of discrete emission rates from three different scenarios obtained using Bayesian inference and singular value decomposition inversion are compared and contrasted.

Bayesian analyses of seasonal runoff forecasts

NASA Astrophysics Data System (ADS)

Krzysztofowicz, R.; Reese, S.

1991-12-01

Forecasts of seasonal snowmelt runoff volume provide indispensable information for rational decision making by water project operators, irrigation district managers, and farmers in the western United States. Bayesian statistical models and communication frames have been researched in order to enhance the forecast information disseminated to the users, and to characterize forecast skill from the decision maker's point of view. Four products are presented: (i) a Bayesian Processor of Forecasts, which provides a statistical filter for calibrating the forecasts, and a procedure for estimating the posterior probability distribution of the seasonal runoff; (ii) the Bayesian Correlation Score, a new measure of forecast skill, which is related monotonically to the ex ante economic value of forecasts for decision making; (iii) a statistical predictor of monthly cumulative runoffs within the snowmelt season, conditional on the total seasonal runoff forecast; and (iv) a framing of the forecast message that conveys the uncertainty associated with the forecast estimates to the users. All analyses are illustrated with numerical examples of forecasts for six gauging stations from the period 1971 1988.

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.

Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin; Feeney, Stephen

2018-07-01

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data space suffers from the curse of dimensionality and requires compression of the data to a small number of summary statistics to be tractable. In this paper, we use massive asymptotically optimal data compression to reduce the dimensionality of the data space to just one number per parameter, providing a natural and optimal framework for summary statistic choice for likelihood-free inference. Secondly, we present the first cosmological application of Density Estimation Likelihood-Free Inference (DELFI), which learns a parametrized model for joint distribution of data and parameters, yielding both the parameter posterior and the model evidence. This approach is conceptually simple, requires less tuning than traditional Approximate Bayesian Computation approaches to likelihood-free inference and can give high-fidelity posteriors from orders of magnitude fewer forward simulations. As an additional bonus, it enables parameter inference and Bayesian model comparison simultaneously. We demonstrate DELFI with massive data compression on an analysis of the joint light-curve analysis supernova data, as a simple validation case study. We show that high-fidelity posterior inference is possible for full-scale cosmological data analyses with as few as ˜104 simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological data sets.

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

DOE PAGES

Li, Weixuan; Lin, Guang

2015-03-21

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle thesemore » challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.« less

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

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

Li, Weixuan; Lin, Guang, E-mail: guanglin@purdue.edu

2015-08-01

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle thesemore » challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.« less

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

Estimating Tree Height-Diameter Models with the Bayesian Method

PubMed Central

Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2. PMID:24711733

Estimating tree height-diameter models with the Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification

NASA Astrophysics Data System (ADS)

Arnst, M.; Abello Álvarez, B.; Ponthot, J.-P.; Boman, R.

2017-11-01

This paper is concerned with the characterization and the propagation of errors associated with data limitations in polynomial-chaos-based stochastic methods for uncertainty quantification. Such an issue can arise in uncertainty quantification when only a limited amount of data is available. When the available information does not suffice to accurately determine the probability distributions that must be assigned to the uncertain variables, the Bayesian method for assigning these probability distributions becomes attractive because it allows the stochastic model to account explicitly for insufficiency of the available information. In previous work, such applications of the Bayesian method had already been implemented by using the Metropolis-Hastings and Gibbs Markov Chain Monte Carlo (MCMC) methods. In this paper, we present an alternative implementation, which uses an alternative MCMC method built around an Itô stochastic differential equation (SDE) that is ergodic for the Bayesian posterior. We draw together from the mathematics literature a number of formal properties of this Itô SDE that lend support to its use in the implementation of the Bayesian method, and we describe its discretization, including the choice of the free parameters, by using the implicit Euler method. We demonstrate the proposed methodology on a problem of uncertainty quantification in a complex nonlinear engineering application relevant to metal forming.

A Pragmatic Bayesian Perspective on Correlation Analysis. The exoplanetary gravity - stellar activity case

NASA Astrophysics Data System (ADS)

Figueira, P.; Faria, J. P.; Adibekyan, V. Zh.; Oshagh, M.; Santos, N. C.

2016-11-01

We apply the Bayesian framework to assess the presence of a correlation between two quantities. To do so, we estimate the probability distribution of the parameter of interest, ρ, characterizing the strength of the correlation. We provide an implementation of these ideas and concepts using python programming language and the pyMC module in a very short (˜ 130 lines of code, heavily commented) and user-friendly program. We used this tool to assess the presence and properties of the correlation between planetary surface gravity and stellar activity level as measured by the log(R^' }_{ {HK}}) indicator. The results of the Bayesian analysis are qualitatively similar to those obtained via p-value analysis, and support the presence of a correlation in the data. The results are more robust in their derivation and more informative, revealing interesting features such as asymmetric posterior distributions or markedly different credible intervals, and allowing for a deeper exploration. We encourage the reader interested in this kind of problem to apply our code to his/her own scientific problems. The full understanding of what the Bayesian framework is can only be gained through the insight that comes by handling priors, assessing the convergence of Monte Carlo runs, and a multitude of other practical problems. We hope to contribute so that Bayesian analysis becomes a tool in the toolkit of researchers, and they understand by experience its advantages and limitations.

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.

INFERRING THE ECCENTRICITY DISTRIBUTION

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

Hogg, David W.; Bovy, Jo; Myers, Adam D., E-mail: david.hogg@nyu.ed

2010-12-20

Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. Here, we develop and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, inferring the true eccentricity distribution, taking as input the likelihood functions for the individual star eccentricities, or samplings of the posterior probability distributions for the eccentricities (under a given, uninformative prior). The method is a simple implementationmore » of a hierarchical Bayesian model; it can also be seen as a kind of heteroscedastic deconvolution. It can be applied to any quantity measured with finite precision-other orbital parameters, or indeed any astronomical measurements of any kind, including magnitudes, distances, or photometric redshifts-so long as the measurements have been communicated as a likelihood function or a posterior sampling.« less

Bayesian Community Detection in the Space of Group-Level Functional Differences

PubMed Central

Venkataraman, Archana; Yang, Daniel Y.-J.; Pelphrey, Kevin A.; Duncan, James S.

2017-01-01

We propose a unified Bayesian framework to detect both hyper- and hypo-active communities within whole-brain fMRI data. Specifically, our model identifies dense subgraphs that exhibit population-level differences in functional synchrony between a control and clinical group. We derive a variational EM algorithm to solve for the latent posterior distributions and parameter estimates, which subsequently inform us about the afflicted network topology. We demonstrate that our method provides valuable insights into the neural mechanisms underlying social dysfunction in autism, as verified by the Neurosynth meta-analytic database. In contrast, both univariate testing and community detection via recursive edge elimination fail to identify stable functional communities associated with the disorder. PMID:26955022

Bayesian Community Detection in the Space of Group-Level Functional Differences.

PubMed

Venkataraman, Archana; Yang, Daniel Y-J; Pelphrey, Kevin A; Duncan, James S

2016-08-01

We propose a unified Bayesian framework to detect both hyper- and hypo-active communities within whole-brain fMRI data. Specifically, our model identifies dense subgraphs that exhibit population-level differences in functional synchrony between a control and clinical group. We derive a variational EM algorithm to solve for the latent posterior distributions and parameter estimates, which subsequently inform us about the afflicted network topology. We demonstrate that our method provides valuable insights into the neural mechanisms underlying social dysfunction in autism, as verified by the Neurosynth meta-analytic database. In contrast, both univariate testing and community detection via recursive edge elimination fail to identify stable functional communities associated with the disorder.

cosmoabc: Likelihood-free inference for cosmology

NASA Astrophysics Data System (ADS)

Ishida, Emille E. O.; Vitenti, Sandro D. P.; Penna-Lima, Mariana; Trindade, Arlindo M.; Cisewski, Jessi; M.; de Souza, Rafael; Cameron, Ewan; Busti, Vinicius C.

2015-05-01

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogs. cosmoabc is a Python Approximate Bayesian Computation (ABC) sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code can be coupled to an external simulator to allow incorporation of arbitrary distance and prior functions. When coupled with the numcosmo library, it has been used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function.

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.

Bayesian analysis of experimental epidemics of foot-and-mouth disease.

PubMed Central

Streftaris, George; Gibson, Gavin J.

2004-01-01

We investigate the transmission dynamics of a certain type of foot-and-mouth disease (FMD) virus under experimental conditions. Previous analyses of experimental data from FMD outbreaks in non-homogeneously mixing populations of sheep have suggested a decline in viraemic level through serial passage of the virus, but these do not take into account possible variation in the length of the chain of viral transmission for each animal, which is implicit in the non-observed transmission process. We consider a susceptible-exposed-infectious-removed non-Markovian compartmental model for partially observed epidemic processes, and we employ powerful methodology (Markov chain Monte Carlo) for statistical inference, to address epidemiological issues under a Bayesian framework that accounts for all available information and associated uncertainty in a coherent approach. The analysis allows us to investigate the posterior distribution of the hidden transmission history of the epidemic, and thus to determine the effect of the length of the infection chain on the recorded viraemic levels, based on the posterior distribution of a p-value. Parameter estimates of the epidemiological characteristics of the disease are also obtained. The results reveal a possible decline in viraemia in one of the two experimental outbreaks. Our model also suggests that individual infectivity is related to the level of viraemia. PMID:15306359

A probabilistic model framework for evaluating year-to-year variation in crop productivity

NASA Astrophysics Data System (ADS)

Yokozawa, M.; Iizumi, T.; Tao, F.

2008-12-01

Most models describing the relation between crop productivity and weather condition have so far been focused on mean changes of crop yield. For keeping stable food supply against abnormal weather as well as climate change, evaluating the year-to-year variations in crop productivity rather than the mean changes is more essential. We here propose a new framework of probabilistic model based on Bayesian inference and Monte Carlo simulation. As an example, we firstly introduce a model on paddy rice production in Japan. It is called PRYSBI (Process- based Regional rice Yield Simulator with Bayesian Inference; Iizumi et al., 2008). The model structure is the same as that of SIMRIW, which was developed and used widely in Japan. The model includes three sub- models describing phenological development, biomass accumulation and maturing of rice crop. These processes are formulated to include response nature of rice plant to weather condition. This model inherently was developed to predict rice growth and yield at plot paddy scale. We applied it to evaluate the large scale rice production with keeping the same model structure. Alternatively, we assumed the parameters as stochastic variables. In order to let the model catch up actual yield at larger scale, model parameters were determined based on agricultural statistical data of each prefecture of Japan together with weather data averaged over the region. The posterior probability distribution functions (PDFs) of parameters included in the model were obtained using Bayesian inference. The MCMC (Markov Chain Monte Carlo) algorithm was conducted to numerically solve the Bayesian theorem. For evaluating the year-to-year changes in rice growth/yield under this framework, we firstly iterate simulations with set of parameter values sampled from the estimated posterior PDF of each parameter and then take the ensemble mean weighted with the posterior PDFs. We will also present another example for maize productivity in China. The framework proposed here provides us information on uncertainties, possibilities and limitations on future improvements in crop model as well.

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

Data Envelopment Analysis in the Presence of Measurement Error: Case Study from the National Database of Nursing Quality Indicators® (NDNQI®)

PubMed Central

Gajewski, Byron J.; Lee, Robert; Dunton, Nancy

2012-01-01

Data Envelopment Analysis (DEA) is the most commonly used approach for evaluating healthcare efficiency (Hollingsworth, 2008), but a long-standing concern is that DEA assumes that data are measured without error. This is quite unlikely, and DEA and other efficiency analysis techniques may yield biased efficiency estimates if it is not realized (Gajewski, Lee, Bott, Piamjariyakul and Taunton, 2009; Ruggiero, 2004). We propose to address measurement error systematically using a Bayesian method (Bayesian DEA). We will apply Bayesian DEA to data from the National Database of Nursing Quality Indicators® (NDNQI®) to estimate nursing units’ efficiency. Several external reliability studies inform the posterior distribution of the measurement error on the DEA variables. We will discuss the case of generalizing the approach to situations where an external reliability study is not feasible. PMID:23328796

Bayesian models based on test statistics for multiple hypothesis testing problems.

PubMed

Ji, Yuan; Lu, Yiling; Mills, Gordon B

2008-04-01

We propose a Bayesian method for the problem of multiple hypothesis testing that is routinely encountered in bioinformatics research, such as the differential gene expression analysis. Our algorithm is based on modeling the distributions of test statistics under both null and alternative hypotheses. We substantially reduce the complexity of the process of defining posterior model probabilities by modeling the test statistics directly instead of modeling the full data. Computationally, we apply a Bayesian FDR approach to control the number of rejections of null hypotheses. To check if our model assumptions for the test statistics are valid for various bioinformatics experiments, we also propose a simple graphical model-assessment tool. Using extensive simulations, we demonstrate the performance of our models and the utility of the model-assessment tool. In the end, we apply the proposed methodology to an siRNA screening and a gene expression experiment.

A Bayesian sequential processor approach to spectroscopic portal system decisions

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

Sale, K; Candy, J; Breitfeller, E

The development of faster more reliable techniques to detect radioactive contraband in a portal type scenario is an extremely important problem especially in this era of constant terrorist threats. Towards this goal the development of a model-based, Bayesian sequential data processor for the detection problem is discussed. In the sequential processor each datum (detector energy deposit and pulse arrival time) is used to update the posterior probability distribution over the space of model parameters. The nature of the sequential processor approach is that a detection is produced as soon as it is statistically justified by the data rather than waitingmore » for a fixed counting interval before any analysis is performed. In this paper the Bayesian model-based approach, physics and signal processing models and decision functions are discussed along with the first results of our research.« less

Bayesian tomography and integrated data analysis in fusion diagnostics

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

Li, Dong, E-mail: lid@swip.ac.cn; Dong, Y. B.; Deng, Wei

2016-11-15

In this article, a Bayesian tomography method using non-stationary Gaussian process for a prior has been introduced. The Bayesian formalism allows quantities which bear uncertainty to be expressed in the probabilistic form so that the uncertainty of a final solution can be fully resolved from the confidence interval of a posterior probability. Moreover, a consistency check of that solution can be performed by checking whether the misfits between predicted and measured data are reasonably within an assumed data error. In particular, the accuracy of reconstructions is significantly improved by using the non-stationary Gaussian process that can adapt to the varyingmore » smoothness of emission distribution. The implementation of this method to a soft X-ray diagnostics on HL-2A has been used to explore relevant physics in equilibrium and MHD instability modes. This project is carried out within a large size inference framework, aiming at an integrated analysis of heterogeneous diagnostics.« less

Bayesian median regression for temporal gene expression data

NASA Astrophysics Data System (ADS)

Yu, Keming; Vinciotti, Veronica; Liu, Xiaohui; 't Hoen, Peter A. C.

2007-09-01

Most of the existing methods for the identification of biologically interesting genes in a temporal expression profiling dataset do not fully exploit the temporal ordering in the dataset and are based on normality assumptions for the gene expression. In this paper, we introduce a Bayesian median regression model to detect genes whose temporal profile is significantly different across a number of biological conditions. The regression model is defined by a polynomial function where both time and condition effects as well as interactions between the two are included. MCMC-based inference returns the posterior distribution of the polynomial coefficients. From this a simple Bayes factor test is proposed to test for significance. The estimation of the median rather than the mean, and within a Bayesian framework, increases the robustness of the method compared to a Hotelling T2-test previously suggested. This is shown on simulated data and on muscular dystrophy gene expression data.

Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: A data-driven, physics-informed Bayesian approach

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

Xiao, H., E-mail: hengxiao@vt.edu; Wu, J.-L.; Wang, J.-X.

Despite their well-known limitations, Reynolds-Averaged Navier–Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations.more » Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has potential implications in many fields in which the governing equations are well understood but the model uncertainty comes from unresolved physical processes. - Highlights: • Proposed a physics–informed framework to quantify uncertainty in RANS simulations. • Framework incorporates physical prior knowledge and observation data. • Based on a rigorous Bayesian framework yet fully utilizes physical model. • Applicable for many complex physical systems beyond turbulent flows.« less

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.

The impact of the rate prior on Bayesian estimation of divergence times with multiple Loci.

PubMed

Dos Reis, Mario; Zhu, Tianqi; Yang, Ziheng

2014-07-01

Bayesian methods provide a powerful way to estimate species divergence times by combining information from molecular sequences with information from the fossil record. With the explosive increase of genomic data, divergence time estimation increasingly uses data of multiple loci (genes or site partitions). Widely used computer programs to estimate divergence times use independent and identically distributed (i.i.d.) priors on the substitution rates for different loci. The i.i.d. prior is problematic. As the number of loci (L) increases, the prior variance of the average rate across all loci goes to zero at the rate 1/L. As a consequence, the rate prior dominates posterior time estimates when many loci are analyzed, and if the rate prior is misspecified, the estimated divergence times will converge to wrong values with very narrow credibility intervals. Here we develop a new prior on the locus rates based on the Dirichlet distribution that corrects the problematic behavior of the i.i.d. prior. We use computer simulation and real data analysis to highlight the differences between the old and new priors. For a dataset for six primate species, we show that with the old i.i.d. prior, if the prior rate is too high (or too low), the estimated divergence times are too young (or too old), outside the bounds imposed by the fossil calibrations. In contrast, with the new Dirichlet prior, posterior time estimates are insensitive to the rate prior and are compatible with the fossil calibrations. We re-analyzed a phylogenomic data set of 36 mammal species and show that using many fossil calibrations can alleviate the adverse impact of a misspecified rate prior to some extent. We recommend the use of the new Dirichlet prior in Bayesian divergence time estimation. [Bayesian inference, divergence time, relaxed clock, rate prior, partition analysis.]. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.

Predicting uncertainty in future marine ice sheet volume using Bayesian statistical methods

NASA Astrophysics Data System (ADS)

Davis, A. D.

2015-12-01

The marine ice instability can trigger rapid retreat of marine ice streams. Recent observations suggest that marine ice systems in West Antarctica have begun retreating. However, unknown ice dynamics, computationally intensive mathematical models, and uncertain parameters in these models make predicting retreat rate and ice volume difficult. In this work, we fuse current observational data with ice stream/shelf models to develop probabilistic predictions of future grounded ice sheet volume. Given observational data (e.g., thickness, surface elevation, and velocity) and a forward model that relates uncertain parameters (e.g., basal friction and basal topography) to these observations, we use a Bayesian framework to define a posterior distribution over the parameters. A stochastic predictive model then propagates uncertainties in these parameters to uncertainty in a particular quantity of interest (QoI)---here, the volume of grounded ice at a specified future time. While the Bayesian approach can in principle characterize the posterior predictive distribution of the QoI, the computational cost of both the forward and predictive models makes this effort prohibitively expensive. To tackle this challenge, we introduce a new Markov chain Monte Carlo method that constructs convergent approximations of the QoI target density in an online fashion, yielding accurate characterizations of future ice sheet volume at significantly reduced computational cost.Our second goal is to attribute uncertainty in these Bayesian predictions to uncertainties in particular parameters. Doing so can help target data collection, for the purpose of constraining the parameters that contribute most strongly to uncertainty in the future volume of grounded ice. For instance, smaller uncertainties in parameters to which the QoI is highly sensitive may account for more variability in the prediction than larger uncertainties in parameters to which the QoI is less sensitive. We use global sensitivity analysis to help answer this question, and make the computation of sensitivity indices computationally tractable using a combination of polynomial chaos and Monte Carlo techniques.

Comparing Bayesian estimates of genetic differentiation of molecular markers and quantitative traits: an application to Pinus sylvestris.

PubMed

Waldmann, P; García-Gil, M R; Sillanpää, M J

2005-06-01

Comparison of the level of differentiation at neutral molecular markers (estimated as F(ST) or G(ST)) with the level of differentiation at quantitative traits (estimated as Q(ST)) has become a standard tool for inferring that there is differential selection between populations. We estimated Q(ST) of timing of bud set from a latitudinal cline of Pinus sylvestris with a Bayesian hierarchical variance component method utilizing the information on the pre-estimated population structure from neutral molecular markers. Unfortunately, the between-family variances differed substantially between populations that resulted in a bimodal posterior of Q(ST) that could not be compared in any sensible way with the unimodal posterior of the microsatellite F(ST). In order to avoid publishing studies with flawed Q(ST) estimates, we recommend that future studies should present heritability estimates for each trait and population. Moreover, to detect variance heterogeneity in frequentist methods (ANOVA and REML), it is of essential importance to check also that the residuals are normally distributed and do not follow any systematically deviating trends.

Supernova Cosmology Inference with Probabilistic Photometric Redshifts (SCIPPR)

NASA Astrophysics Data System (ADS)

Peters, Christina; Malz, Alex; Hlozek, Renée

2018-01-01

The Bayesian Estimation Applied to Multiple Species (BEAMS) framework employs probabilistic supernova type classifications to do photometric SN cosmology. This work extends BEAMS to replace high-confidence spectroscopic redshifts with photometric redshift probability density functions, a capability that will be essential in the era the Large Synoptic Survey Telescope and other next-generation photometric surveys where it will not be possible to perform spectroscopic follow up on every SN. We present the Supernova Cosmology Inference with Probabilistic Photometric Redshifts (SCIPPR) Bayesian hierarchical model for constraining the cosmological parameters from photometric lightcurves and host galaxy photometry, which includes selection effects and is extensible to uncertainty in the redshift-dependent supernova type proportions. We create a pair of realistic mock catalogs of joint posteriors over supernova type, redshift, and distance modulus informed by photometric supernova lightcurves and over redshift from simulated host galaxy photometry. We perform inference under our model to obtain a joint posterior probability distribution over the cosmological parameters and compare our results with other methods, namely: a spectroscopic subset, a subset of high probability photometrically classified supernovae, and reducing the photometric redshift probability to a single measurement and error bar.

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.

Bayesian Posterior Odds Ratios: Statistical Tools for Collaborative Evaluations

ERIC Educational Resources Information Center

Hicks, Tyler; Rodríguez-Campos, Liliana; Choi, Jeong Hoon

2018-01-01

To begin statistical analysis, Bayesians quantify their confidence in modeling hypotheses with priors. A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices…

A Development of Nonstationary Regional Frequency Analysis Model with Large-scale Climate Information: Its Application to Korean Watershed

NASA Astrophysics Data System (ADS)

Kim, Jin-Young; Kwon, Hyun-Han; Kim, Hung-Soo

2015-04-01

The existing regional frequency analysis has disadvantages in that it is difficult to consider geographical characteristics in estimating areal rainfall. In this regard, this study aims to develop a hierarchical Bayesian model based nonstationary regional frequency analysis in that spatial patterns of the design rainfall with geographical information (e.g. latitude, longitude and altitude) are explicitly incorporated. This study assumes that the parameters of Gumbel (or GEV distribution) are a function of geographical characteristics within a general linear regression framework. Posterior distribution of the regression parameters are estimated by Bayesian Markov Chain Monte Carlo (MCMC) method, and the identified functional relationship is used to spatially interpolate the parameters of the distributions by using digital elevation models (DEM) as inputs. The proposed model is applied to derive design rainfalls over the entire Han-river watershed. It was found that the proposed Bayesian regional frequency analysis model showed similar results compared to L-moment based regional frequency analysis. In addition, the model showed an advantage in terms of quantifying uncertainty of the design rainfall and estimating the area rainfall considering geographical information. Finally, comprehensive discussion on design rainfall in the context of nonstationary will be presented. KEYWORDS: Regional frequency analysis, Nonstationary, Spatial information, Bayesian Acknowledgement This research was supported by a grant (14AWMP-B082564-01) from Advanced Water Management Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government.

A Fast Surrogate-facilitated Data-driven Bayesian Approach to Uncertainty Quantification of a Regional Groundwater Flow Model with Structural Error

NASA Astrophysics Data System (ADS)

Xu, T.; Valocchi, A. J.; Ye, M.; Liang, F.

2016-12-01

Due to simplification and/or misrepresentation of the real aquifer system, numerical groundwater flow and solute transport models are usually subject to model structural error. During model calibration, the hydrogeological parameters may be overly adjusted to compensate for unknown structural error. This may result in biased predictions when models are used to forecast aquifer response to new forcing. In this study, we extend a fully Bayesian method [Xu and Valocchi, 2015] to calibrate a real-world, regional groundwater flow model. The method uses a data-driven error model to describe model structural error and jointly infers model parameters and structural error. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models. The surrogate models are constructed using machine learning techniques to emulate the response simulated by the computationally expensive groundwater model. We demonstrate in the real-world case study that explicitly accounting for model structural error yields parameter posterior distributions that are substantially different from those derived by the classical Bayesian calibration that does not account for model structural error. In addition, the Bayesian with error model method gives significantly more accurate prediction along with reasonable credible intervals.

A Gibbs sampler for Bayesian analysis of site-occupancy data

USGS Publications Warehouse

Dorazio, Robert M.; Rodriguez, Daniel Taylor

2012-01-01

1. A Bayesian analysis of site-occupancy data containing covariates of species occurrence and species detection probabilities is usually completed using Markov chain Monte Carlo methods in conjunction with software programs that can implement those methods for any statistical model, not just site-occupancy models. Although these software programs are quite flexible, considerable experience is often required to specify a model and to initialize the Markov chain so that summaries of the posterior distribution can be estimated efficiently and accurately. 2. As an alternative to these programs, we develop a Gibbs sampler for Bayesian analysis of site-occupancy data that include covariates of species occurrence and species detection probabilities. This Gibbs sampler is based on a class of site-occupancy models in which probabilities of species occurrence and detection are specified as probit-regression functions of site- and survey-specific covariate measurements. 3. To illustrate the Gibbs sampler, we analyse site-occupancy data of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly species in Switzerland. Our analysis includes a comparison of results based on Bayesian and classical (non-Bayesian) methods of inference. We also provide code (based on the R software program) for conducting Bayesian and classical analyses of site-occupancy data.

A Bayesian hierarchical latent trait model for estimating rater bias and reliability in large-scale performance assessment

PubMed Central

2018-01-01

We propose a novel approach to modelling rater effects in scoring-based assessment. The approach is based on a Bayesian hierarchical model and simulations from the posterior distribution. We apply it to large-scale essay assessment data over a period of 5 years. Empirical results suggest that the model provides a good fit for both the total scores and when applied to individual rubrics. We estimate the median impact of rater effects on the final grade to be ± 2 points on a 50 point scale, while 10% of essays would receive a score at least ± 5 different from their actual quality. Most of the impact is due to rater unreliability, not rater bias. PMID:29614129

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

Bayesian imperfect information analysis for clinical recurrent data

PubMed Central

Chang, Chih-Kuang; Chang, Chi-Chang

2015-01-01

In medical research, clinical practice must often be undertaken with imperfect information from limited resources. This study applied Bayesian imperfect information-value analysis to realistic situations to produce likelihood functions and posterior distributions, to a clinical decision-making problem for recurrent events. In this study, three kinds of failure models are considered, and our methods illustrated with an analysis of imperfect information from a trial of immunotherapy in the treatment of chronic granulomatous disease. In addition, we present evidence toward a better understanding of the differing behaviors along with concomitant variables. Based on the results of simulations, the imperfect information value of the concomitant variables was evaluated and different realistic situations were compared to see which could yield more accurate results for medical decision-making. PMID:25565853

Quantifying parameter uncertainty in stochastic models using the Box Cox transformation

NASA Astrophysics Data System (ADS)

Thyer, Mark; Kuczera, George; Wang, Q. J.

2002-08-01

The Box-Cox transformation is widely used to transform hydrological data to make it approximately Gaussian. Bayesian evaluation of parameter uncertainty in stochastic models using the Box-Cox transformation is hindered by the fact that there is no analytical solution for the posterior distribution. However, the Markov chain Monte Carlo method known as the Metropolis algorithm can be used to simulate the posterior distribution. This method properly accounts for the nonnegativity constraint implicit in the Box-Cox transformation. Nonetheless, a case study using the AR(1) model uncovered a practical problem with the implementation of the Metropolis algorithm. The use of a multivariate Gaussian jump distribution resulted in unacceptable convergence behaviour. This was rectified by developing suitable parameter transformations for the mean and variance of the AR(1) process to remove the strong nonlinear dependencies with the Box-Cox transformation parameter. Applying this methodology to the Sydney annual rainfall data and the Burdekin River annual runoff data illustrates the efficacy of these parameter transformations and demonstrate the value of quantifying parameter uncertainty.

Statistical analysis of modal parameters of a suspension bridge based on Bayesian spectral density approach and SHM data

NASA Astrophysics Data System (ADS)

Li, Zhijun; Feng, Maria Q.; Luo, Longxi; Feng, Dongming; Xu, Xiuli

2018-01-01

Uncertainty of modal parameters estimation appear in structural health monitoring (SHM) practice of civil engineering to quite some significant extent due to environmental influences and modeling errors. Reasonable methodologies are needed for processing the uncertainty. Bayesian inference can provide a promising and feasible identification solution for the purpose of SHM. However, there are relatively few researches on the application of Bayesian spectral method in the modal identification using SHM data sets. To extract modal parameters from large data sets collected by SHM system, the Bayesian spectral density algorithm was applied to address the uncertainty of mode extraction from output-only response of a long-span suspension bridge. The posterior most possible values of modal parameters and their uncertainties were estimated through Bayesian inference. A long-term variation and statistical analysis was performed using the sensor data sets collected from the SHM system of the suspension bridge over a one-year period. The t location-scale distribution was shown to be a better candidate function for frequencies of lower modes. On the other hand, the burr distribution provided the best fitting to the higher modes which are sensitive to the temperature. In addition, wind-induced variation of modal parameters was also investigated. It was observed that both the damping ratios and modal forces increased during the period of typhoon excitations. Meanwhile, the modal damping ratios exhibit significant correlation with the spectral intensities of the corresponding modal forces.

Aerosol-type retrieval and uncertainty quantification from OMI data

NASA Astrophysics Data System (ADS)

Kauppi, Anu; Kolmonen, Pekka; Laine, Marko; Tamminen, Johanna

2017-11-01

We discuss uncertainty quantification for aerosol-type selection in satellite-based atmospheric aerosol retrieval. The retrieval procedure uses precalculated aerosol microphysical models stored in look-up tables (LUTs) and top-of-atmosphere (TOA) spectral reflectance measurements to solve the aerosol characteristics. The forward model approximations cause systematic differences between the modelled and observed reflectance. Acknowledging this model discrepancy as a source of uncertainty allows us to produce more realistic uncertainty estimates and assists the selection of the most appropriate LUTs for each individual retrieval.This paper focuses on the aerosol microphysical model selection and characterisation of uncertainty in the retrieved aerosol type and aerosol optical depth (AOD). The concept of model evidence is used as a tool for model comparison. The method is based on Bayesian inference approach, in which all uncertainties are described as a posterior probability distribution. When there is no single best-matching aerosol microphysical model, we use a statistical technique based on Bayesian model averaging to combine AOD posterior probability densities of the best-fitting models to obtain an averaged AOD estimate. We also determine the shared evidence of the best-matching models of a certain main aerosol type in order to quantify how plausible it is that it represents the underlying atmospheric aerosol conditions.The developed method is applied to Ozone Monitoring Instrument (OMI) measurements using a multiwavelength approach for retrieving the aerosol type and AOD estimate with uncertainty quantification for cloud-free over-land pixels. Several larger pixel set areas were studied in order to investigate the robustness of the developed method. We evaluated the retrieved AOD by comparison with ground-based measurements at example sites. We found that the uncertainty of AOD expressed by posterior probability distribution reflects the difficulty in model selection. The posterior probability distribution can provide a comprehensive characterisation of the uncertainty in this kind of problem for aerosol-type selection. As a result, the proposed method can account for the model error and also include the model selection uncertainty in the total uncertainty budget.

Appraisal of jump distributions in ensemble-based sampling algorithms

NASA Astrophysics Data System (ADS)

Dejanic, Sanda; Scheidegger, Andreas; Rieckermann, Jörg; Albert, Carlo

2017-04-01

Sampling Bayesian posteriors of model parameters is often required for making model-based probabilistic predictions. For complex environmental models, standard Monte Carlo Markov Chain (MCMC) methods are often infeasible because they require too many sequential model runs. Therefore, we focused on ensemble methods that use many Markov chains in parallel, since they can be run on modern cluster architectures. Little is known about how to choose the best performing sampler, for a given application. A poor choice can lead to an inappropriate representation of posterior knowledge. We assessed two different jump moves, the stretch and the differential evolution move, underlying, respectively, the software packages EMCEE and DREAM, which are popular in different scientific communities. For the assessment, we used analytical posteriors with features as they often occur in real posteriors, namely high dimensionality, strong non-linear correlations or multimodality. For posteriors with non-linear features, standard convergence diagnostics based on sample means can be insufficient. Therefore, we resorted to an entropy-based convergence measure. We assessed the samplers by means of their convergence speed, robustness and effective sample sizes. For posteriors with strongly non-linear features, we found that the stretch move outperforms the differential evolution move, w.r.t. all three aspects.

Robust Bayesian hypocentre and uncertainty region estimation: the effect of heavy-tailed distributions and prior information in cases with poor, inconsistent and insufficient arrival times

NASA Astrophysics Data System (ADS)

Martinsson, J.

2013-03-01

We propose methods for robust Bayesian inference of the hypocentre in presence of poor, inconsistent and insufficient phase arrival times. The objectives are to increase the robustness, the accuracy and the precision by introducing heavy-tailed distributions and an informative prior distribution of the seismicity. The effects of the proposed distributions are studied under real measurement conditions in two underground mine networks and validated using 53 blasts with known hypocentres. To increase the robustness against poor, inconsistent or insufficient arrivals, a Gaussian Mixture Model is used as a hypocentre prior distribution to describe the seismically active areas, where the parameters are estimated based on previously located events in the region. The prior is truncated to constrain the solution to valid geometries, for example below the ground surface, excluding known cavities, voids and fractured zones. To reduce the sensitivity to outliers, different heavy-tailed distributions are evaluated to model the likelihood distribution of the arrivals given the hypocentre and the origin time. Among these distributions, the multivariate t-distribution is shown to produce the overall best performance, where the tail-mass adapts to the observed data. Hypocentre and uncertainty region estimates are based on simulations from the posterior distribution using Markov Chain Monte Carlo techniques. Velocity graphs (equivalent to traveltime graphs) are estimated using blasts from known locations, and applied to reduce the main uncertainties and thereby the final estimation error. To focus on the behaviour and the performance of the proposed distributions, a basic single-event Bayesian procedure is considered in this study for clarity. Estimation results are shown with different distributions, with and without prior distribution of seismicity, with wrong prior distribution, with and without error compensation, with and without error description, with insufficient arrival times and in presence of significant outliers. A particular focus is on visual results and comparisons to give a better understanding of the Bayesian advantage and to show the effects of heavy-tailed distributions and informative prior information on real data.

HELP: XID+, the probabilistic de-blender for Herschel SPIRE maps

NASA Astrophysics Data System (ADS)

Hurley, P. D.; Oliver, S.; Betancourt, M.; Clarke, C.; Cowley, W. I.; Duivenvoorden, S.; Farrah, D.; Griffin, M.; Lacey, C.; Le Floc'h, E.; Papadopoulos, A.; Sargent, M.; Scudder, J. M.; Vaccari, M.; Valtchanov, I.; Wang, L.

2017-01-01

We have developed a new prior-based source extraction tool, XID+, to carry out photometry in the Herschel SPIRE (Spectral and Photometric Imaging Receiver) maps at the positions of known sources. XID+ is developed using a probabilistic Bayesian framework that provides a natural framework in which to include prior information, and uses the Bayesian inference tool Stan to obtain the full posterior probability distribution on flux estimates. In this paper, we discuss the details of XID+ and demonstrate the basic capabilities and performance by running it on simulated SPIRE maps resembling the COSMOS field, and comparing to the current prior-based source extraction tool DESPHOT. Not only we show that XID+ performs better on metrics such as flux accuracy and flux uncertainty accuracy, but we also illustrate how obtaining the posterior probability distribution can help overcome some of the issues inherent with maximum-likelihood-based source extraction routines. We run XID+ on the COSMOS SPIRE maps from Herschel Multi-Tiered Extragalactic Survey using a 24-μm catalogue as a positional prior, and a uniform flux prior ranging from 0.01 to 1000 mJy. We show the marginalized SPIRE colour-colour plot and marginalized contribution to the cosmic infrared background at the SPIRE wavelengths. XID+ is a core tool arising from the Herschel Extragalactic Legacy Project (HELP) and we discuss how additional work within HELP providing prior information on fluxes can and will be utilized. The software is available at https://github.com/H-E-L-P/XID_plus. We also provide the data product for COSMOS. We believe this is the first time that the full posterior probability of galaxy photometry has been provided as a data product.

A Bayesian approach to tracking patients having changing pharmacokinetic parameters

NASA Technical Reports Server (NTRS)

Bayard, David S.; Jelliffe, Roger W.

2004-01-01

This paper considers the updating of Bayesian posterior densities for pharmacokinetic models associated with patients having changing parameter values. For estimation purposes it is proposed to use the Interacting Multiple Model (IMM) estimation algorithm, which is currently a popular algorithm in the aerospace community for tracking maneuvering targets. The IMM algorithm is described, and compared to the multiple model (MM) and Maximum A-Posteriori (MAP) Bayesian estimation methods, which are presently used for posterior updating when pharmacokinetic parameters do not change. Both the MM and MAP Bayesian estimation methods are used in their sequential forms, to facilitate tracking of changing parameters. Results indicate that the IMM algorithm is well suited for tracking time-varying pharmacokinetic parameters in acutely ill and unstable patients, incurring only about half of the integrated error compared to the sequential MM and MAP methods on the same example.

Multivariate Copula Analysis Toolbox (MvCAT): Describing dependence and underlying uncertainty using a Bayesian framework

NASA Astrophysics Data System (ADS)

Sadegh, Mojtaba; Ragno, Elisa; AghaKouchak, Amir

2017-06-01

We present a newly developed Multivariate Copula Analysis Toolbox (MvCAT) which includes a wide range of copula families with different levels of complexity. MvCAT employs a Bayesian framework with a residual-based Gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties. The contribution of this paper is threefold: (a) providing a Bayesian framework to approximate the predictive uncertainties of fitted copulas, (b) introducing a hybrid-evolution Markov Chain Monte Carlo (MCMC) approach designed for numerical estimation of the posterior distribution of copula parameters, and (c) enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties. We show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima. The proposed method, however, addresses this limitation and improves describing the dependence structure. MvCAT also enables evaluation of uncertainties relative to the length of record, which is fundamental to a wide range of applications such as multivariate frequency analysis.

Critically evaluating the theory and performance of Bayesian analysis of macroevolutionary mixtures

PubMed Central

Moore, Brian R.; Höhna, Sebastian; May, Michael R.; Rannala, Bruce; Huelsenbeck, John P.

2016-01-01

Bayesian analysis of macroevolutionary mixtures (BAMM) has recently taken the study of lineage diversification by storm. BAMM estimates the diversification-rate parameters (speciation and extinction) for every branch of a study phylogeny and infers the number and location of diversification-rate shifts across branches of a tree. Our evaluation of BAMM reveals two major theoretical errors: (i) the likelihood function (which estimates the model parameters from the data) is incorrect, and (ii) the compound Poisson process prior model (which describes the prior distribution of diversification-rate shifts across branches) is incoherent. Using simulation, we demonstrate that these theoretical issues cause statistical pathologies; posterior estimates of the number of diversification-rate shifts are strongly influenced by the assumed prior, and estimates of diversification-rate parameters are unreliable. Moreover, the inability to correctly compute the likelihood or to correctly specify the prior for rate-variable trees precludes the use of Bayesian approaches for testing hypotheses regarding the number and location of diversification-rate shifts using BAMM. PMID:27512038

Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

NASA Astrophysics Data System (ADS)

Hadjidoukas, P. E.; Angelikopoulos, P.; Papadimitriou, C.; Koumoutsakos, P.

2015-03-01

We present Π4U, an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.

Marginally specified priors for non-parametric Bayesian estimation

PubMed Central

Kessler, David C.; Hoff, Peter D.; Dunson, David B.

2014-01-01

Summary Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for non-parametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard non-parametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables. PMID:25663813

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.

Estimation of selection intensity under overdominance by Bayesian methods.

PubMed

Buzbas, Erkan Ozge; Joyce, Paul; Abdo, Zaid

2009-01-01

A balanced pattern in the allele frequencies of polymorphic loci is a potential sign of selection, particularly of overdominance. Although this type of selection is of some interest in population genetics, there exists no likelihood based approaches specifically tailored to make inference on selection intensity. To fill this gap, we present Bayesian methods to estimate selection intensity under k-allele models with overdominance. Our model allows for an arbitrary number of loci and alleles within a locus. The neutral and selected variability within each locus are modeled with corresponding k-allele models. To estimate the posterior distribution of the mean selection intensity in a multilocus region, a hierarchical setup between loci is used. The methods are demonstrated with data at the Human Leukocyte Antigen loci from world-wide populations.

Bayesian experimental design for models with intractable likelihoods.

PubMed

Drovandi, Christopher C; Pettitt, Anthony N

2013-12-01

In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables. © 2013, The International Biometric Society.

Inference on cancer screening exam accuracy using population-level administrative data.

PubMed

Jiang, H; Brown, P E; Walter, S D

2016-01-15

This paper develops a model for cancer screening and cancer incidence data, accommodating the partially unobserved disease status, clustered data structures, general covariate effects, and dependence between exams. The true unobserved cancer and detection status of screening participants are treated as latent variables, and a Markov Chain Monte Carlo algorithm is used to estimate the Bayesian posterior distributions of the diagnostic error rates and disease prevalence. We show how the Bayesian approach can be used to draw inferences about screening exam properties and disease prevalence while allowing for the possibility of conditional dependence between two exams. The techniques are applied to the estimation of the diagnostic accuracy of mammography and clinical breast examination using data from the Ontario Breast Screening Program in Canada. Copyright © 2015 John Wiley & Sons, Ltd.

Reconstructing gravitational wave source parameters via direct comparisons to numerical relativity II: Applications

NASA Astrophysics Data System (ADS)

O'Shaughnessy, Richard; Lange, Jacob; Healy, James; Carlos, Lousto; Shoemaker, Deirdre; Lovelace, Geoffrey; Scheel, Mark

2016-03-01

In this talk, we apply a procedure to reconstruct the parameters of sufficiently massive coalescing compact binaries via direct comparison with numerical relativity simulations. We illustrate how to use only comparisons between synthetic data and these simulations to reconstruct properties of a synthetic candidate source. We demonstrate using selected examples that we can reconstruct posterior distributions obtained by other Bayesian methods with our sparse grid. We describe how followup simulations can corroborate and improve our understanding of a candidate signal.

A Bayesian Analysis of a Randomized Clinical Trial Comparing Antimetabolite Therapies for Non-Infectious Uveitis.

PubMed

Browne, Erica N; Rathinam, Sivakumar R; Kanakath, Anuradha; Thundikandy, Radhika; Babu, Manohar; Lietman, Thomas M; Acharya, Nisha R

2017-02-01

To conduct a Bayesian analysis of a randomized clinical trial (RCT) for non-infectious uveitis using expert opinion as a subjective prior belief. A RCT was conducted to determine which antimetabolite, methotrexate or mycophenolate mofetil, is more effective as an initial corticosteroid-sparing agent for the treatment of intermediate, posterior, and pan-uveitis. Before the release of trial results, expert opinion on the relative effectiveness of these two medications was collected via online survey. Members of the American Uveitis Society executive committee were invited to provide an estimate for the relative decrease in efficacy with a 95% credible interval (CrI). A prior probability distribution was created from experts' estimates. A Bayesian analysis was performed using the constructed expert prior probability distribution and the trial's primary outcome. A total of 11 of the 12 invited uveitis specialists provided estimates. Eight of 11 experts (73%) believed mycophenolate mofetil is more effective. The group prior belief was that the odds of treatment success for patients taking mycophenolate mofetil were 1.4-fold the odds of those taking methotrexate (95% CrI 0.03-45.0). The odds of treatment success with mycophenolate mofetil compared to methotrexate was 0.4 from the RCT (95% confidence interval 0.1-1.2) and 0.7 (95% CrI 0.2-1.7) from the Bayesian analysis. A Bayesian analysis combining expert belief with the trial's result did not indicate preference for one drug. However, the wide credible interval leaves open the possibility of a substantial treatment effect. This suggests clinical equipoise necessary to allow a larger, more definitive RCT.

A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework

PubMed Central

Aslam, Muhammad; Tahir, Muhammad; Hussain, Zawar; Al-Zahrani, Bander

2015-01-01

To study lifetimes of certain engineering processes, a lifetime model which can accommodate the nature of such processes is desired. The mixture models of underlying lifetime distributions are intuitively more appropriate and appealing to model the heterogeneous nature of process as compared to simple models. This paper is about studying a 3-component mixture of the Rayleigh distributionsin Bayesian perspective. The censored sampling environment is considered due to its popularity in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under different scenarios. In case the case that no or little prior information is available, elicitation of hyperparameters is given. To examine, numerically, the performance of the Bayes estimators using non-informative and informative priors under different loss functions, we have simulated their statistical properties for different sample sizes and test termination times. In addition, to highlight the practical significance, an illustrative example based on a real-life engineering data is also given. PMID:25993475

A Bayesian Poisson-lognormal Model for Count Data for Multiple-Trait Multiple-Environment Genomic-Enabled Prediction

PubMed Central

Montesinos-López, Osval A.; Montesinos-López, Abelardo; Crossa, José; Toledo, Fernando H.; Montesinos-López, José C.; Singh, Pawan; Juliana, Philomin; Salinas-Ruiz, Josafhat

2017-01-01

When a plant scientist wishes to make genomic-enabled predictions of multiple traits measured in multiple individuals in multiple environments, the most common strategy for performing the analysis is to use a single trait at a time taking into account genotype × environment interaction (G × E), because there is a lack of comprehensive models that simultaneously take into account the correlated counting traits and G × E. For this reason, in this study we propose a multiple-trait and multiple-environment model for count data. The proposed model was developed under the Bayesian paradigm for which we developed a Markov Chain Monte Carlo (MCMC) with noninformative priors. This allows obtaining all required full conditional distributions of the parameters leading to an exact Gibbs sampler for the posterior distribution. Our model was tested with simulated data and a real data set. Results show that the proposed multi-trait, multi-environment model is an attractive alternative for modeling multiple count traits measured in multiple environments. PMID:28364037

A Bayesian observer replicates convexity context effects in figure-ground perception.

PubMed

Goldreich, Daniel; Peterson, Mary A

2012-01-01

Peterson and Salvagio (2008) demonstrated convexity context effects in figure-ground perception. Subjects shown displays consisting of unfamiliar alternating convex and concave regions identified the convex regions as foreground objects progressively more frequently as the number of regions increased; this occurred only when the concave regions were homogeneously colored. The origins of these effects have been unclear. Here, we present a two-free-parameter Bayesian observer that replicates convexity context effects. The Bayesian observer incorporates two plausible expectations regarding three-dimensional scenes: (1) objects tend to be convex rather than concave, and (2) backgrounds tend (more than foreground objects) to be homogeneously colored. The Bayesian observer estimates the probability that a depicted scene is three-dimensional, and that the convex regions are figures. It responds stochastically by sampling from its posterior distributions. Like human observers, the Bayesian observer shows convexity context effects only for images with homogeneously colored concave regions. With optimal parameter settings, it performs similarly to the average human subject on the four display types tested. We propose that object convexity and background color homogeneity are environmental regularities exploited by human visual perception; vision achieves figure-ground perception by interpreting ambiguous images in light of these and other expected regularities in natural scenes.

Fully Bayesian inference for structural MRI: application to segmentation and statistical analysis of T2-hypointensities.

PubMed

Schmidt, Paul; Schmid, Volker J; Gaser, Christian; Buck, Dorothea; Bührlen, Susanne; Förschler, Annette; Mühlau, Mark

2013-01-01

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: [Formula: see text]; range, [Formula: see text]). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data.

Bayesian propensity scores for high-dimensional causal inference: A comparison of drug-eluting to bare-metal coronary stents.

PubMed

Spertus, Jacob V; Normand, Sharon-Lise T

2018-04-23

High-dimensional data provide many potential confounders that may bolster the plausibility of the ignorability assumption in causal inference problems. Propensity score methods are powerful causal inference tools, which are popular in health care research and are particularly useful for high-dimensional data. Recent interest has surrounded a Bayesian treatment of propensity scores in order to flexibly model the treatment assignment mechanism and summarize posterior quantities while incorporating variance from the treatment model. We discuss methods for Bayesian propensity score analysis of binary treatments, focusing on modern methods for high-dimensional Bayesian regression and the propagation of uncertainty. We introduce a novel and simple estimator for the average treatment effect that capitalizes on conjugacy of the beta and binomial distributions. Through simulations, we show the utility of horseshoe priors and Bayesian additive regression trees paired with our new estimator, while demonstrating the importance of including variance from the treatment regression model. An application to cardiac stent data with almost 500 confounders and 9000 patients illustrates approaches and facilitates comparison with existing alternatives. As measured by a falsifiability endpoint, we improved confounder adjustment compared with past observational research of the same problem. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Clinical Outcome Prediction in Aneurysmal Subarachnoid Hemorrhage Using Bayesian Neural Networks with Fuzzy Logic Inferences

PubMed Central

Lo, Benjamin W. Y.; Macdonald, R. Loch; Baker, Andrew; Levine, Mitchell A. H.

2013-01-01

Objective. The novel clinical prediction approach of Bayesian neural networks with fuzzy logic inferences is created and applied to derive prognostic decision rules in cerebral aneurysmal subarachnoid hemorrhage (aSAH). Methods. The approach of Bayesian neural networks with fuzzy logic inferences was applied to data from five trials of Tirilazad for aneurysmal subarachnoid hemorrhage (3551 patients). Results. Bayesian meta-analyses of observational studies on aSAH prognostic factors gave generalizable posterior distributions of population mean log odd ratios (ORs). Similar trends were noted in Bayesian and linear regression ORs. Significant outcome predictors include normal motor response, cerebral infarction, history of myocardial infarction, cerebral edema, history of diabetes mellitus, fever on day 8, prior subarachnoid hemorrhage, admission angiographic vasospasm, neurological grade, intraventricular hemorrhage, ruptured aneurysm size, history of hypertension, vasospasm day, age and mean arterial pressure. Heteroscedasticity was present in the nontransformed dataset. Artificial neural networks found nonlinear relationships with 11 hidden variables in 1 layer, using the multilayer perceptron model. Fuzzy logic decision rules (centroid defuzzification technique) denoted cut-off points for poor prognosis at greater than 2.5 clusters. Discussion. This aSAH prognostic system makes use of existing knowledge, recognizes unknown areas, incorporates one's clinical reasoning, and compensates for uncertainty in prognostication. PMID:23690884

Bayesian Nonparametric Ordination for the Analysis of Microbial Communities.

PubMed

Ren, Boyu; Bacallado, Sergio; Favaro, Stefano; Holmes, Susan; Trippa, Lorenzo

2017-01-01

Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency tables with OTU counts across heterogeneous biological samples. In the microbial ecology community, ordination methods are frequently used to investigate latent factors or clusters that capture and describe variations of OTU counts across biological samples. It remains important to evaluate how uncertainty in estimates of each biological sample's microbial distribution propagates to ordination analyses, including visualization of clusters and projections of biological samples on low dimensional spaces. We propose a Bayesian analysis for dependent distributions to endow frequently used ordinations with estimates of uncertainty. A Bayesian nonparametric prior for dependent normalized random measures is constructed, which is marginally equivalent to the normalized generalized Gamma process, a well-known prior for nonparametric analyses. In our prior, the dependence and similarity between microbial distributions is represented by latent factors that concentrate in a low dimensional space. We use a shrinkage prior to tune the dimensionality of the latent factors. The resulting posterior samples of model parameters can be used to evaluate uncertainty in analyses routinely applied in microbiome studies. Specifically, by combining them with multivariate data analysis techniques we can visualize credible regions in ecological ordination plots. The characteristics of the proposed model are illustrated through a simulation study and applications in two microbiome datasets.

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.

Using Approximate Bayesian Computation to Probe Multiple Transiting Planet Systems

NASA Astrophysics Data System (ADS)

Morehead, Robert C.

2015-08-01

The large number of multiple transiting planet systems (MTPS) uncovered with Kepler suggest a population of well-aligned planetary systems. Previously, the distribution of transit duration ratios in MTPSs has been used to place constraints on the distributions of mutual orbital inclinations and orbital eccentricities in these systems. However, degeneracies with the underlying number of planets in these systems pose added challenges and make explicit likelihood functions intractable. Approximate Bayesian computation (ABC) offers an intriguing path forward. In its simplest form, ABC proposes from a prior on the population parameters to produce synthetic datasets via a physically-motivated model. Samples are accepted or rejected based on how close they come to reproducing the actual observed dataset to some tolerance. The accepted samples then form a robust and useful approximation of the true posterior distribution of the underlying population parameters. We will demonstrate the utility of ABC in exoplanet populations by presenting new constraints on the mutual inclination and eccentricity distributions in the Kepler MTPSs. We will also introduce Simple-ABC, a new open-source Python package designed for ease of use and rapid specification of general models, suitable for use in a wide variety of applications in both exoplanet science and astrophysics as a whole.

Using discharge data to reduce structural deficits in a hydrological model with a Bayesian inference approach and the implications for the prediction of critical source areas

NASA Astrophysics Data System (ADS)

Frey, M. P.; Stamm, C.; Schneider, M. K.; Reichert, P.

2011-12-01

A distributed hydrological model was used to simulate the distribution of fast runoff formation as a proxy for critical source areas for herbicide pollution in a small agricultural catchment in Switzerland. We tested to what degree predictions based on prior knowledge without local measurements could be improved upon relying on observed discharge. This learning process consisted of five steps: For the prior prediction (step 1), knowledge of the model parameters was coarse and predictions were fairly uncertain. In the second step, discharge data were used to update the prior parameter distribution. Effects of uncertainty in input data and model structure were accounted for by an autoregressive error model. This step decreased the width of the marginal distributions of parameters describing the lower boundary (percolation rates) but hardly affected soil hydraulic parameters. Residual analysis (step 3) revealed model structure deficits. We modified the model, and in the subsequent Bayesian updating (step 4) the widths of the posterior marginal distributions were reduced for most parameters compared to those of the prior. This incremental procedure led to a strong reduction in the uncertainty of the spatial prediction. Thus, despite only using spatially integrated data (discharge), the spatially distributed effect of the improved model structure can be expected to improve the spatially distributed predictions also. The fifth step consisted of a test with independent spatial data on herbicide losses and revealed ambiguous results. The comparison depended critically on the ratio of event to preevent water that was discharged. This ratio cannot be estimated from hydrological data only. The results demonstrate that the value of local data is strongly dependent on a correct model structure. An iterative procedure of Bayesian updating, model testing, and model modification is suggested.

A Bayesian Hybrid Adaptive Randomisation Design for Clinical Trials with Survival Outcomes.

PubMed

Moatti, M; Chevret, S; Zohar, S; Rosenberger, W F

2016-01-01

Response-adaptive randomisation designs have been proposed to improve the efficiency of phase III randomised clinical trials and improve the outcomes of the clinical trial population. In the setting of failure time outcomes, Zhang and Rosenberger (2007) developed a response-adaptive randomisation approach that targets an optimal allocation, based on a fixed sample size. The aim of this research is to propose a response-adaptive randomisation procedure for survival trials with an interim monitoring plan, based on the following optimal criterion: for fixed variance of the estimated log hazard ratio, what allocation minimizes the expected hazard of failure? We demonstrate the utility of the design by redesigning a clinical trial on multiple myeloma. To handle continuous monitoring of data, we propose a Bayesian response-adaptive randomisation procedure, where the log hazard ratio is the effect measure of interest. Combining the prior with the normal likelihood, the mean posterior estimate of the log hazard ratio allows derivation of the optimal target allocation. We perform a simulation study to assess and compare the performance of this proposed Bayesian hybrid adaptive design to those of fixed, sequential or adaptive - either frequentist or fully Bayesian - designs. Non informative normal priors of the log hazard ratio were used, as well as mixture of enthusiastic and skeptical priors. Stopping rules based on the posterior distribution of the log hazard ratio were computed. The method is then illustrated by redesigning a phase III randomised clinical trial of chemotherapy in patients with multiple myeloma, with mixture of normal priors elicited from experts. As expected, there was a reduction in the proportion of observed deaths in the adaptive vs. non-adaptive designs; this reduction was maximized using a Bayes mixture prior, with no clear-cut improvement by using a fully Bayesian procedure. The use of stopping rules allows a slight decrease in the observed proportion of deaths under the alternate hypothesis compared with the adaptive designs with no stopping rules. Such Bayesian hybrid adaptive survival trials may be promising alternatives to traditional designs, reducing the duration of survival trials, as well as optimizing the ethical concerns for patients enrolled in the trial.

The maximum entropy method of moments and Bayesian probability theory

NASA Astrophysics Data System (ADS)

Bretthorst, G. Larry

2013-08-01

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.

Simulation-based estimation of mean and standard deviation for meta-analysis via Approximate Bayesian Computation (ABC).

PubMed

Kwon, Deukwoo; Reis, Isildinha M

2015-08-12

When conducting a meta-analysis of a continuous outcome, estimated means and standard deviations from the selected studies are required in order to obtain an overall estimate of the mean effect and its confidence interval. If these quantities are not directly reported in the publications, they must be estimated from other reported summary statistics, such as the median, the minimum, the maximum, and quartiles. We propose a simulation-based estimation approach using the Approximate Bayesian Computation (ABC) technique for estimating mean and standard deviation based on various sets of summary statistics found in published studies. We conduct a simulation study to compare the proposed ABC method with the existing methods of Hozo et al. (2005), Bland (2015), and Wan et al. (2014). In the estimation of the standard deviation, our ABC method performs better than the other methods when data are generated from skewed or heavy-tailed distributions. The corresponding average relative error (ARE) approaches zero as sample size increases. In data generated from the normal distribution, our ABC performs well. However, the Wan et al. method is best for estimating standard deviation under normal distribution. In the estimation of the mean, our ABC method is best regardless of assumed distribution. ABC is a flexible method for estimating the study-specific mean and standard deviation for meta-analysis, especially with underlying skewed or heavy-tailed distributions. The ABC method can be applied using other reported summary statistics such as the posterior mean and 95 % credible interval when Bayesian analysis has been employed.

Development and Validation of a Lifecycle-based Prognostics Architecture with Test Bed Validation

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

Hines, J. Wesley; Upadhyaya, Belle; Sharp, Michael

On-line monitoring and tracking of nuclear plant system and component degradation is being investigated as a method for improving the safety, reliability, and maintainability of aging nuclear power plants. Accurate prediction of the current degradation state of system components and structures is important for accurate estimates of their remaining useful life (RUL). The correct quantification and propagation of both the measurement uncertainty and model uncertainty is necessary for quantifying the uncertainty of the RUL prediction. This research project developed and validated methods to perform RUL estimation throughout the lifecycle of plant components. Prognostic methods should seamlessly operate from beginning ofmore » component life (BOL) to end of component life (EOL). We term this "Lifecycle Prognostics." When a component is put into use, the only information available may be past failure times of similar components used in similar conditions, and the predicted failure distribution can be estimated with reliability methods such as Weibull Analysis (Type I Prognostics). As the component operates, it begins to degrade and consume its available life. This life consumption may be a function of system stresses, and the failure distribution should be updated to account for the system operational stress levels (Type II Prognostics). When degradation becomes apparent, this information can be used to again improve the RUL estimate (Type III Prognostics). This research focused on developing prognostics algorithms for the three types of prognostics, developing uncertainty quantification methods for each of the algorithms, and, most importantly, developing a framework using Bayesian methods to transition between prognostic model types and update failure distribution estimates as new information becomes available. The developed methods were then validated on a range of accelerated degradation test beds. The ultimate goal of prognostics is to provide an accurate assessment for RUL predictions, with as little uncertainty as possible. From a reliability and maintenance standpoint, there would be improved safety by avoiding all failures. Calculated risk would decrease, saving money by avoiding unnecessary maintenance. One major bottleneck for data-driven prognostics is the availability of run-to-failure degradation data. Without enough degradation data leading to failure, prognostic models can yield RUL distributions with large uncertainty or mathematically unsound predictions. To address these issues a "Lifecycle Prognostics" method was developed to create RUL distributions from Beginning of Life (BOL) to End of Life (EOL). This employs established Type I, II, and III prognostic methods, and Bayesian transitioning between each Type. Bayesian methods, as opposed to classical frequency statistics, show how an expected value, a priori, changes with new data to form a posterior distribution. For example, when you purchase a component you have a prior belief, or estimation, of how long it will operate before failing. As you operate it, you may collect information related to its condition that will allow you to update your estimated failure time. Bayesian methods are best used when limited data are available. The use of a prior also means that information is conserved when new data are available. The weightings of the prior belief and information contained in the sampled data are dependent on the variance (uncertainty) of the prior, the variance (uncertainty) of the data, and the amount of measured data (number of samples). If the variance of the prior is small compared to the uncertainty of the data, the prior will be weighed more heavily. However, as more data are collected, the data will be weighted more heavily and will eventually swamp out the prior in calculating the posterior distribution of model parameters. Fundamentally Bayesian analysis updates a prior belief with new data to get a posterior belief. The general approach to applying the Bayesian method to lifecycle prognostics consisted of identifying the prior, which is the RUL estimate and uncertainty from the previous prognostics type, and combining it with observational data related to the newer prognostics type. The resulting lifecycle prognostics algorithm uses all available information throughout the component lifecycle.« less

Determining X-ray source intensity and confidence bounds in crowded fields

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

Primini, F. A.; Kashyap, V. L., E-mail: fap@head.cfa.harvard.edu

We present a rigorous description of the general problem of aperture photometry in high-energy astrophysics photon-count images, in which the statistical noise model is Poisson, not Gaussian. We compute the full posterior probability density function for the expected source intensity for various cases of interest, including the important cases in which both source and background apertures contain contributions from the source, and when multiple source apertures partially overlap. A Bayesian approach offers the advantages of allowing one to (1) include explicit prior information on source intensities, (2) propagate posterior distributions as priors for future observations, and (3) use Poisson likelihoods,more » making the treatment valid in the low-counts regime. Elements of this approach have been implemented in the Chandra Source Catalog.« less

A Bayesian least squares support vector machines based framework for fault diagnosis and failure prognosis

NASA Astrophysics Data System (ADS)

Khawaja, Taimoor Saleem

A high-belief low-overhead Prognostics and Health Management (PHM) system is desired for online real-time monitoring of complex non-linear systems operating in a complex (possibly non-Gaussian) noise environment. This thesis presents a Bayesian Least Squares Support Vector Machine (LS-SVM) based framework for fault diagnosis and failure prognosis in nonlinear non-Gaussian systems. The methodology assumes the availability of real-time process measurements, definition of a set of fault indicators and the existence of empirical knowledge (or historical data) to characterize both nominal and abnormal operating conditions. An efficient yet powerful Least Squares Support Vector Machine (LS-SVM) algorithm, set within a Bayesian Inference framework, not only allows for the development of real-time algorithms for diagnosis and prognosis but also provides a solid theoretical framework to address key concepts related to classification for diagnosis and regression modeling for prognosis. SVM machines are founded on the principle of Structural Risk Minimization (SRM) which tends to find a good trade-off between low empirical risk and small capacity. The key features in SVM are the use of non-linear kernels, the absence of local minima, the sparseness of the solution and the capacity control obtained by optimizing the margin. The Bayesian Inference framework linked with LS-SVMs allows a probabilistic interpretation of the results for diagnosis and prognosis. Additional levels of inference provide the much coveted features of adaptability and tunability of the modeling parameters. The two main modules considered in this research are fault diagnosis and failure prognosis. With the goal of designing an efficient and reliable fault diagnosis scheme, a novel Anomaly Detector is suggested based on the LS-SVM machines. The proposed scheme uses only baseline data to construct a 1-class LS-SVM machine which, when presented with online data is able to distinguish between normal behavior and any abnormal or novel data during real-time operation. The results of the scheme are interpreted as a posterior probability of health (1 - probability of fault). As shown through two case studies in Chapter 3, the scheme is well suited for diagnosing imminent faults in dynamical non-linear systems. Finally, the failure prognosis scheme is based on an incremental weighted Bayesian LS-SVR machine. It is particularly suited for online deployment given the incremental nature of the algorithm and the quick optimization problem solved in the LS-SVR algorithm. By way of kernelization and a Gaussian Mixture Modeling (GMM) scheme, the algorithm can estimate "possibly" non-Gaussian posterior distributions for complex non-linear systems. An efficient regression scheme associated with the more rigorous core algorithm allows for long-term predictions, fault growth estimation with confidence bounds and remaining useful life (RUL) estimation after a fault is detected. The leading contributions of this thesis are (a) the development of a novel Bayesian Anomaly Detector for efficient and reliable Fault Detection and Identification (FDI) based on Least Squares Support Vector Machines, (b) the development of a data-driven real-time architecture for long-term Failure Prognosis using Least Squares Support Vector Machines, (c) Uncertainty representation and management using Bayesian Inference for posterior distribution estimation and hyper-parameter tuning, and finally (d) the statistical characterization of the performance of diagnosis and prognosis algorithms in order to relate the efficiency and reliability of the proposed schemes.

Bayesian inference based on stationary Fokker-Planck sampling.

PubMed

Berrones, Arturo

2010-06-01

A novel formalism for bayesian learning in the context of complex inference models is proposed. The method is based on the use of the stationary Fokker-Planck (SFP) approach to sample from the posterior density. Stationary Fokker-Planck sampling generalizes the Gibbs sampler algorithm for arbitrary and unknown conditional densities. By the SFP procedure, approximate analytical expressions for the conditionals and marginals of the posterior can be constructed. At each stage of SFP, the approximate conditionals are used to define a Gibbs sampling process, which is convergent to the full joint posterior. By the analytical marginals efficient learning methods in the context of artificial neural networks are outlined. Offline and incremental bayesian inference and maximum likelihood estimation from the posterior are performed in classification and regression examples. A comparison of SFP with other Monte Carlo strategies in the general problem of sampling from arbitrary densities is also presented. It is shown that SFP is able to jump large low-probability regions without the need of a careful tuning of any step-size parameter. In fact, the SFP method requires only a small set of meaningful parameters that can be selected following clear, problem-independent guidelines. The computation cost of SFP, measured in terms of loss function evaluations, grows linearly with the given model's dimension.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

NASA Astrophysics Data System (ADS)

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

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

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic systemmore » leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.« less

Model based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach

PubMed Central

Rasmussen, Peter M.; Smith, Amy F.; Sakadžić, Sava; Boas, David A.; Pries, Axel R.; Secomb, Timothy W.; Østergaard, Leif

2017-01-01

Objective In vivo imaging of the microcirculation and network-oriented modeling have emerged as powerful means of studying microvascular function and understanding its physiological significance. Network-oriented modeling may provide the means of summarizing vast amounts of data produced by high-throughput imaging techniques in terms of key, physiological indices. To estimate such indices with sufficient certainty, however, network-oriented analysis must be robust to the inevitable presence of uncertainty due to measurement errors as well as model errors. Methods We propose the Bayesian probabilistic data analysis framework as a means of integrating experimental measurements and network model simulations into a combined and statistically coherent analysis. The framework naturally handles noisy measurements and provides posterior distributions of model parameters as well as physiological indices associated with uncertainty. Results We applied the analysis framework to experimental data from three rat mesentery networks and one mouse brain cortex network. We inferred distributions for more than five hundred unknown pressure and hematocrit boundary conditions. Model predictions were consistent with previous analyses, and remained robust when measurements were omitted from model calibration. Conclusion Our Bayesian probabilistic approach may be suitable for optimizing data acquisition and for analyzing and reporting large datasets acquired as part of microvascular imaging studies. PMID:27987383

The pharmacokinetics of dexmedetomidine during long-term infusion in critically ill pediatric patients. A Bayesian approach with informative priors.

PubMed

Wiczling, Paweł; Bartkowska-Śniatkowska, Alicja; Szerkus, Oliwia; Siluk, Danuta; Rosada-Kurasińska, Jowita; Warzybok, Justyna; Borsuk, Agnieszka; Kaliszan, Roman; Grześkowiak, Edmund; Bienert, Agnieszka

2016-06-01

The purpose of this study was to assess the pharmacokinetics of dexmedetomidine in the ICU settings during the prolonged infusion and to compare it with the existing literature data using the Bayesian population modeling with literature-based informative priors. Thirty-eight patients were included in the analysis with concentration measurements obtained at two occasions: first from 0 to 24 h after infusion initiation and second from 0 to 8 h after infusion end. Data analysis was conducted using WinBUGS software. The prior information on dexmedetomidine pharmacokinetics was elicited from the literature study pooling results from a relatively large group of 95 children. A two compartment PK model, with allometrically scaled parameters, maturation of clearance and t-student residual distribution on a log-scale was used to describe the data. The incorporation of time-dependent (different between two occasions) PK parameters improved the model. It was observed that volume of distribution is 1.5-fold higher during the second occasion. There was also an evidence of increased (1.3-fold) clearance for the second occasion with posterior probability equal to 62 %. This work demonstrated the usefulness of Bayesian modeling with informative priors in analyzing pharmacokinetic data and comparing it with existing literature knowledge.

Assessment of CT image quality using a Bayesian approach

NASA Astrophysics Data System (ADS)

Reginatto, M.; Anton, M.; Elster, C.

2017-08-01

One of the most promising approaches for evaluating CT image quality is task-specific quality assessment. This involves a simplified version of a clinical task, e.g. deciding whether an image belongs to the class of images that contain the signature of a lesion or not. Task-specific quality assessment can be done by model observers, which are mathematical procedures that carry out the classification task. The most widely used figure of merit for CT image quality is the area under the ROC curve (AUC), a quantity which characterizes the performance of a given model observer. In order to estimate AUC from a finite sample of images, different approaches from classical statistics have been suggested. The goal of this paper is to introduce task-specific quality assessment of CT images to metrology and to propose a novel Bayesian estimation of AUC for the channelized Hotelling observer (CHO) applied to the task of detecting a lesion at a known image location. It is assumed that signal-present and signal-absent images follow multivariate normal distributions with the same covariance matrix. The Bayesian approach results in a posterior distribution for the AUC of the CHO which provides in addition a complete characterization of the uncertainty of this figure of merit. The approach is illustrated by its application to both simulated and experimental data.

A Bayesian Framework for Reliability Analysis of Spacecraft Deployments

NASA Technical Reports Server (NTRS)

Evans, John W.; Gallo, Luis; Kaminsky, Mark

2012-01-01

Deployable subsystems are essential to mission success of most spacecraft. These subsystems enable critical functions including power, communications and thermal control. The loss of any of these functions will generally result in loss of the mission. These subsystems and their components often consist of unique designs and applications for which various standardized data sources are not applicable for estimating reliability and for assessing risks. In this study, a two stage sequential Bayesian framework for reliability estimation of spacecraft deployment was developed for this purpose. This process was then applied to the James Webb Space Telescope (JWST) Sunshield subsystem, a unique design intended for thermal control of the Optical Telescope Element. Initially, detailed studies of NASA deployment history, "heritage information", were conducted, extending over 45 years of spacecraft launches. This information was then coupled to a non-informative prior and a binomial likelihood function to create a posterior distribution for deployments of various subsystems uSing Monte Carlo Markov Chain sampling. Select distributions were then coupled to a subsequent analysis, using test data and anomaly occurrences on successive ground test deployments of scale model test articles of JWST hardware, to update the NASA heritage data. This allowed for a realistic prediction for the reliability of the complex Sunshield deployment, with credibility limits, within this two stage Bayesian framework.

Efficient Posterior Probability Mapping Using Savage-Dickey Ratios

PubMed Central

Penny, William D.; Ridgway, Gerard R.

2013-01-01

Statistical Parametric Mapping (SPM) is the dominant paradigm for mass-univariate analysis of neuroimaging data. More recently, a Bayesian approach termed Posterior Probability Mapping (PPM) has been proposed as an alternative. PPM offers two advantages: (i) inferences can be made about effect size thus lending a precise physiological meaning to activated regions, (ii) regions can be declared inactive. This latter facility is most parsimoniously provided by PPMs based on Bayesian model comparisons. To date these comparisons have been implemented by an Independent Model Optimization (IMO) procedure which separately fits null and alternative models. This paper proposes a more computationally efficient procedure based on Savage-Dickey approximations to the Bayes factor, and Taylor-series approximations to the voxel-wise posterior covariance matrices. Simulations show the accuracy of this Savage-Dickey-Taylor (SDT) method to be comparable to that of IMO. Results on fMRI data show excellent agreement between SDT and IMO for second-level models, and reasonable agreement for first-level models. This Savage-Dickey test is a Bayesian analogue of the classical SPM-F and allows users to implement model comparison in a truly interactive manner. PMID:23533640

Hyperspectral Image Classification With Markov Random Fields and a Convolutional Neural Network

NASA Astrophysics Data System (ADS)

Cao, Xiangyong; Zhou, Feng; Xu, Lin; Meng, Deyu; Xu, Zongben; Paisley, John

2018-05-01

This paper presents a new supervised classification algorithm for remotely sensed hyperspectral image (HSI) which integrates spectral and spatial information in a unified Bayesian framework. First, we formulate the HSI classification problem from a Bayesian perspective. Then, we adopt a convolutional neural network (CNN) to learn the posterior class distributions using a patch-wise training strategy to better use the spatial information. Next, spatial information is further considered by placing a spatial smoothness prior on the labels. Finally, we iteratively update the CNN parameters using stochastic gradient decent (SGD) and update the class labels of all pixel vectors using an alpha-expansion min-cut-based algorithm. Compared with other state-of-the-art methods, the proposed classification method achieves better performance on one synthetic dataset and two benchmark HSI datasets in a number of experimental settings.

On the Empirical Importance of the Conditional Skewness Assumption in Modelling the Relationship between Risk and Return

NASA Astrophysics Data System (ADS)

Pipień, M.

2008-09-01

We present the results of an application of Bayesian inference in testing the relation between risk and return on the financial instruments. On the basis of the Intertemporal Capital Asset Pricing Model, proposed by Merton we built a general sampling distribution suitable in analysing this relationship. The most important feature of our assumptions is that the skewness of the conditional distribution of returns is used as an alternative source of relation between risk and return. This general specification relates to Skewed Generalized Autoregressive Conditionally Heteroscedastic-in-Mean model. In order to make conditional distribution of financial returns skewed we considered the unified approach based on the inverse probability integral transformation. In particular, we applied hidden truncation mechanism, inverse scale factors, order statistics concept, Beta and Bernstein distribution transformations and also a constructive method. Based on the daily excess returns on the Warsaw Stock Exchange Index we checked the empirical importance of the conditional skewness assumption on the relation between risk and return on the Warsaw Stock Market. We present posterior probabilities of all competing specifications as well as the posterior analysis of the positive sign of the tested relationship.

Clarifying the Hubble constant tension with a Bayesian hierarchical model of the local distance ladder

NASA Astrophysics Data System (ADS)

Feeney, Stephen M.; Mortlock, Daniel J.; Dalmasso, Niccolò

2018-05-01

Estimates of the Hubble constant, H0, from the local distance ladder and from the cosmic microwave background (CMB) are discrepant at the ˜3σ level, indicating a potential issue with the standard Λ cold dark matter (ΛCDM) cosmology. A probabilistic (i.e. Bayesian) interpretation of this tension requires a model comparison calculation, which in turn depends strongly on the tails of the H0 likelihoods. Evaluating the tails of the local H0 likelihood requires the use of non-Gaussian distributions to faithfully represent anchor likelihoods and outliers, and simultaneous fitting of the complete distance-ladder data set to ensure correct uncertainty propagation. We have hence developed a Bayesian hierarchical model of the full distance ladder that does not rely on Gaussian distributions and allows outliers to be modelled without arbitrary data cuts. Marginalizing over the full ˜3000-parameter joint posterior distribution, we find H0 = (72.72 ± 1.67) km s-1 Mpc-1 when applied to the outlier-cleaned Riess et al. data, and (73.15 ± 1.78) km s-1 Mpc-1 with supernova outliers reintroduced (the pre-cut Cepheid data set is not available). Using our precise evaluation of the tails of the H0 likelihood, we apply Bayesian model comparison to assess the evidence for deviation from ΛCDM given the distance-ladder and CMB data. The odds against ΛCDM are at worst ˜10:1 when considering the Planck 2015 XIII data, regardless of outlier treatment, considerably less dramatic than naïvely implied by the 2.8σ discrepancy. These odds become ˜60:1 when an approximation to the more-discrepant Planck Intermediate XLVI likelihood is included.

Within-herd prevalence and clinical incidence distributions of Mycobacterium avium subspecies paratuberculosis infection on dairy herds in Chile.

PubMed

Verdugo, Cristobal; Valdes, Maria Francisca; Salgado, Miguel

2018-06-01

This study aimed to estimate the distributions of the within-herd true prevalence (TP) and the annual clinical incidence proportion (CIp) of Mycobacterium avium subsp. paratuberculosis (MAP) infection in dairy cattle herds in Chile. Forty two commercial herds with antecedents of MAP infection were randomly selected to participate in the study. In small herds (≤30 cows), serum samples were collected from all animals present. Whereas, in larger herds, milk or serum samples were collected from all milking cows with 2 or more parities. Samples were analysed using the Pourquier® ELISA PARATUBERCULOSIS (Insitute Pourquier, France) test. Moreover, a questionnaire gathering information on management practices and the frequency of clinical cases, compatible with paratuberculosis (in the previous 12 months), was applied on the sampling date. A Bayesian latent class analysis was used to obtain TP and clinical incidence posterior distributions. The model adjusts for uncertainty in test sensitivity (serum or milk) and specificity, and prior TP & CIp estimates. A total of 4963 animals were tested, with an average contribution of 124 samples per herd. A mean apparent prevalence of 6.3% (95% confidence interval: 4.0-8.0%) was observed. Model outputs indicated an overall TP posterior distribution, across herds, with a median of 13.1% (95% posterior probability interval (PPI); 3.2-38.1%). A high TP variability was observed between herds. CIp presented a posterior median of 1.1% (95% PPI; 0.2-4.6%). Model results complement information missing from previously conducted epidemiological studies in the sector, and they could be used for further assessment of the disease impact and planning of control programs. Copyright © 2018 Elsevier B.V. All rights reserved.

Bayesian models for comparative analysis integrating phylogenetic uncertainty.

PubMed

de Villemereuil, Pierre; Wells, Jessie A; Edwards, Robert D; Blomberg, Simon P

2012-06-28

Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language.

Bayesian models for comparative analysis integrating phylogenetic uncertainty

PubMed Central

2012-01-01

Background Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language. PMID:22741602

Bayesian randomized clinical trials: From fixed to adaptive design.

PubMed

Yin, Guosheng; Lam, Chi Kin; Shi, Haolun

2017-08-01

Randomized controlled studies are the gold standard for phase III clinical trials. Using α-spending functions to control the overall type I error rate, group sequential methods are well established and have been dominating phase III studies. Bayesian randomized design, on the other hand, can be viewed as a complement instead of competitive approach to the frequentist methods. For the fixed Bayesian design, the hypothesis testing can be cast in the posterior probability or Bayes factor framework, which has a direct link to the frequentist type I error rate. Bayesian group sequential design relies upon Bayesian decision-theoretic approaches based on backward induction, which is often computationally intensive. Compared with the frequentist approaches, Bayesian methods have several advantages. The posterior predictive probability serves as a useful and convenient tool for trial monitoring, and can be updated at any time as the data accrue during the trial. The Bayesian decision-theoretic framework possesses a direct link to the decision making in the practical setting, and can be modeled more realistically to reflect the actual cost-benefit analysis during the drug development process. Other merits include the possibility of hierarchical modeling and the use of informative priors, which would lead to a more comprehensive utilization of information from both historical and longitudinal data. From fixed to adaptive design, we focus on Bayesian randomized controlled clinical trials and make extensive comparisons with frequentist counterparts through numerical studies. Copyright © 2017 Elsevier Inc. All rights reserved.

Phylogenetic relationships of Malaysia’s long-tailed macaques, Macaca fascicularis, based on cytochrome b sequences

PubMed Central

Abdul-Latiff, Muhammad Abu Bakar; Ruslin, Farhani; Fui, Vun Vui; Abu, Mohd-Hashim; Rovie-Ryan, Jeffrine Japning; Abdul-Patah, Pazil; Lakim, Maklarin; Roos, Christian; Yaakop, Salmah; Md-Zain, Badrul Munir

2014-01-01

Abstract Phylogenetic relationships among Malaysia’s long-tailed macaques have yet to be established, despite abundant genetic studies of the species worldwide. The aims of this study are to examine the phylogenetic relationships of Macaca fascicularis in Malaysia and to test its classification as a morphological subspecies. A total of 25 genetic samples of M. fascicularis yielding 383 bp of Cytochrome b (Cyt b) sequences were used in phylogenetic analysis along with one sample each of M. nemestrina and M. arctoides used as outgroups. Sequence character analysis reveals that Cyt b locus is a highly conserved region with only 23% parsimony informative character detected among ingroups. Further analysis indicates a clear separation between populations originating from different regions; the Malay Peninsula versus Borneo Insular, the East Coast versus West Coast of the Malay Peninsula, and the island versus mainland Malay Peninsula populations. Phylogenetic trees (NJ, MP and Bayesian) portray a consistent clustering paradigm as Borneo’s population was distinguished from Peninsula’s population (99% and 100% bootstrap value in NJ and MP respectively and 1.00 posterior probability in Bayesian trees). The East coast population was separated from other Peninsula populations (64% in NJ, 66% in MP and 0.53 posterior probability in Bayesian). West coast populations were divided into 2 clades: the North-South (47%/54% in NJ, 26/26% in MP and 1.00/0.80 posterior probability in Bayesian) and Island-Mainland (93% in NJ, 90% in MP and 1.00 posterior probability in Bayesian). The results confirm the previous morphological assignment of 2 subspecies, M. f. fascicularis and M. f. argentimembris, in the Malay Peninsula. These populations should be treated as separate genetic entities in order to conserve the genetic diversity of Malaysia’s M. fascicularis. These findings are crucial in aiding the conservation management and translocation process of M. fascicularis populations in Malaysia. PMID:24899832

Phylogenetic relationships of Malaysia's long-tailed macaques, Macaca fascicularis, based on cytochrome b sequences.

PubMed

Abdul-Latiff, Muhammad Abu Bakar; Ruslin, Farhani; Fui, Vun Vui; Abu, Mohd-Hashim; Rovie-Ryan, Jeffrine Japning; Abdul-Patah, Pazil; Lakim, Maklarin; Roos, Christian; Yaakop, Salmah; Md-Zain, Badrul Munir

2014-01-01

Phylogenetic relationships among Malaysia's long-tailed macaques have yet to be established, despite abundant genetic studies of the species worldwide. The aims of this study are to examine the phylogenetic relationships of Macaca fascicularis in Malaysia and to test its classification as a morphological subspecies. A total of 25 genetic samples of M. fascicularis yielding 383 bp of Cytochrome b (Cyt b) sequences were used in phylogenetic analysis along with one sample each of M. nemestrina and M. arctoides used as outgroups. Sequence character analysis reveals that Cyt b locus is a highly conserved region with only 23% parsimony informative character detected among ingroups. Further analysis indicates a clear separation between populations originating from different regions; the Malay Peninsula versus Borneo Insular, the East Coast versus West Coast of the Malay Peninsula, and the island versus mainland Malay Peninsula populations. Phylogenetic trees (NJ, MP and Bayesian) portray a consistent clustering paradigm as Borneo's population was distinguished from Peninsula's population (99% and 100% bootstrap value in NJ and MP respectively and 1.00 posterior probability in Bayesian trees). The East coast population was separated from other Peninsula populations (64% in NJ, 66% in MP and 0.53 posterior probability in Bayesian). West coast populations were divided into 2 clades: the North-South (47%/54% in NJ, 26/26% in MP and 1.00/0.80 posterior probability in Bayesian) and Island-Mainland (93% in NJ, 90% in MP and 1.00 posterior probability in Bayesian). The results confirm the previous morphological assignment of 2 subspecies, M. f. fascicularis and M. f. argentimembris, in the Malay Peninsula. These populations should be treated as separate genetic entities in order to conserve the genetic diversity of Malaysia's M. fascicularis. These findings are crucial in aiding the conservation management and translocation process of M. fascicularis populations in Malaysia.

A Bayesian Analysis of a Randomized Clinical Trial Comparing Antimetabolite Therapies for Non-Infectious Uveitis

PubMed Central

Browne, Erica N; Rathinam, Sivakumar R; Kanakath, Anuradha; Thundikandy, Radhika; Babu, Manohar; Lietman, Thomas M; Acharya, Nisha R

2017-01-01

Purpose To conduct a Bayesian analysis of a randomized clinical trial (RCT) for non-infectious uveitis using expert opinion as a subjective prior belief. Methods A RCT was conducted to determine which antimetabolite, methotrexate or mycophenolate mofetil, is more effective as an initial corticosteroid-sparing agent for the treatment of intermediate, posterior, and pan- uveitis. Before the release of trial results, expert opinion on the relative effectiveness of these two medications was collected via online survey. Members of the American Uveitis Society executive committee were invited to provide an estimate for the relative decrease in efficacy with a 95% credible interval (CrI). A prior probability distribution was created from experts’ estimates. A Bayesian analysis was performed using the constructed expert prior probability distribution and the trial’s primary outcome. Results 11 of 12 invited uveitis specialists provided estimates. Eight of 11 experts (73%) believed mycophenolate mofetil is more effective. The group prior belief was that the odds of treatment success for patients taking mycophenolate mofetil were 1.4-fold the odds of those taking methotrexate (95% CrI 0.03 – 45.0). The odds of treatment success with mycophenolate mofetil compared to methotrexate was 0.4 from the RCT (95% confidence interval 0.1–1.2) and 0.7 (95% CrI 0.2–1.7) from the Bayesian analysis. Conclusions A Bayesian analysis combining expert belief with the trial’s result did not indicate preference for one drug. However, the wide credible interval leaves open the possibility of a substantial treatment effect. This suggests clinical equipoise necessary to allow a larger, more definitive RCT. PMID:27982726

Minimally Informative Prior Distributions for PSA

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

Dana L. Kelly; Robert W. Youngblood; Kurt G. Vedros

2010-06-01

A salient feature of Bayesian inference is its ability to incorporate information from a variety of sources into the inference model, via the prior distribution (hereafter simply “the prior”). However, over-reliance on old information can lead to priors that dominate new data. Some analysts seek to avoid this by trying to work with a minimally informative prior distribution. Another reason for choosing a minimally informative prior is to avoid the often-voiced criticism of subjectivity in the choice of prior. Minimally informative priors fall into two broad classes: 1) so-called noninformative priors, which attempt to be completely objective, in that themore » posterior distribution is determined as completely as possible by the observed data, the most well known example in this class being the Jeffreys prior, and 2) priors that are diffuse over the region where the likelihood function is nonnegligible, but that incorporate some information about the parameters being estimated, such as a mean value. In this paper, we compare four approaches in the second class, with respect to their practical implications for Bayesian inference in Probabilistic Safety Assessment (PSA). The most commonly used such prior, the so-called constrained noninformative prior, is a special case of the maximum entropy prior. This is formulated as a conjugate distribution for the most commonly encountered aleatory models in PSA, and is correspondingly mathematically convenient; however, it has a relatively light tail and this can cause the posterior mean to be overly influenced by the prior in updates with sparse data. A more informative prior that is capable, in principle, of dealing more effectively with sparse data is a mixture of conjugate priors. A particular diffuse nonconjugate prior, the logistic-normal, is shown to behave similarly for some purposes. Finally, we review the so-called robust prior. Rather than relying on the mathematical abstraction of entropy, as does the constrained noninformative prior, the robust prior places a heavy-tailed Cauchy prior on the canonical parameter of the aleatory model.« less

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

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

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

A new prior for bayesian anomaly detection: application to biosurveillance.

PubMed

Shen, Y; Cooper, G F

2010-01-01

Bayesian anomaly detection computes posterior probabilities of anomalous events by combining prior beliefs and evidence from data. However, the specification of prior probabilities can be challenging. This paper describes a Bayesian prior in the context of disease outbreak detection. The goal is to provide a meaningful, easy-to-use prior that yields a posterior probability of an outbreak that performs at least as well as a standard frequentist approach. If this goal is achieved, the resulting posterior could be usefully incorporated into a decision analysis about how to act in light of a possible disease outbreak. This paper describes a Bayesian method for anomaly detection that combines learning from data with a semi-informative prior probability over patterns of anomalous events. A univariate version of the algorithm is presented here for ease of illustration of the essential ideas. The paper describes the algorithm in the context of disease-outbreak detection, but it is general and can be used in other anomaly detection applications. For this application, the semi-informative prior specifies that an increased count over baseline is expected for the variable being monitored, such as the number of respiratory chief complaints per day at a given emergency department. The semi-informative prior is derived based on the baseline prior, which is estimated from using historical data. The evaluation reported here used semi-synthetic data to evaluate the detection performance of the proposed Bayesian method and a control chart method, which is a standard frequentist algorithm that is closest to the Bayesian method in terms of the type of data it uses. The disease-outbreak detection performance of the Bayesian method was statistically significantly better than that of the control chart method when proper baseline periods were used to estimate the baseline behavior to avoid seasonal effects. When using longer baseline periods, the Bayesian method performed as well as the control chart method. The time complexity of the Bayesian algorithm is linear in the number of the observed events being monitored, due to a novel, closed-form derivation that is introduced in the paper. This paper introduces a novel prior probability for Bayesian outbreak detection that is expressive, easy-to-apply, computationally efficient, and performs as well or better than a standard frequentist method.

Uncertainty Analysis Based on Sparse Grid Collocation and Quasi-Monte Carlo Sampling with Application in Groundwater Modeling

NASA Astrophysics Data System (ADS)

Zhang, G.; Lu, D.; Ye, M.; Gunzburger, M.

2011-12-01

Markov Chain Monte Carlo (MCMC) methods have been widely used in many fields of uncertainty analysis to estimate the posterior distributions of parameters and credible intervals of predictions in the Bayesian framework. However, in practice, MCMC may be computationally unaffordable due to slow convergence and the excessive number of forward model executions required, especially when the forward model is expensive to compute. Both disadvantages arise from the curse of dimensionality, i.e., the posterior distribution is usually a multivariate function of parameters. Recently, sparse grid method has been demonstrated to be an effective technique for coping with high-dimensional interpolation or integration problems. Thus, in order to accelerate the forward model and avoid the slow convergence of MCMC, we propose a new method for uncertainty analysis based on sparse grid interpolation and quasi-Monte Carlo sampling. First, we construct a polynomial approximation of the forward model in the parameter space by using the sparse grid interpolation. This approximation then defines an accurate surrogate posterior distribution that can be evaluated repeatedly at minimal computational cost. Second, instead of using MCMC, a quasi-Monte Carlo method is applied to draw samples in the parameter space. Then, the desired probability density function of each prediction is approximated by accumulating the posterior density values of all the samples according to the prediction values. Our method has the following advantages: (1) the polynomial approximation of the forward model on the sparse grid provides a very efficient evaluation of the surrogate posterior distribution; (2) the quasi-Monte Carlo method retains the same accuracy in approximating the PDF of predictions but avoids all disadvantages of MCMC. The proposed method is applied to a controlled numerical experiment of groundwater flow modeling. The results show that our method attains the same accuracy much more efficiently than traditional MCMC.

A Mixtures-of-Trees Framework for Multi-Label Classification

PubMed Central

Hong, Charmgil; Batal, Iyad; Hauskrecht, Milos

2015-01-01

We propose a new probabilistic approach for multi-label classification that aims to represent the class posterior distribution P(Y|X). Our approach uses a mixture of tree-structured Bayesian networks, which can leverage the computational advantages of conditional tree-structured models and the abilities of mixtures to compensate for tree-structured restrictions. We develop algorithms for learning the model from data and for performing multi-label predictions using the learned model. Experiments on multiple datasets demonstrate that our approach outperforms several state-of-the-art multi-label classification methods. PMID:25927011

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.

Finite‐fault Bayesian inversion of teleseismic body waves

USGS Publications Warehouse

Clayton, Brandon; Hartzell, Stephen; Moschetti, Morgan P.; Minson, Sarah E.

2017-01-01

Inverting geophysical data has provided fundamental information about the behavior of earthquake rupture. However, inferring kinematic source model parameters for finite‐fault ruptures is an intrinsically underdetermined problem (the problem of nonuniqueness), because we are restricted to finite noisy observations. Although many studies use least‐squares techniques to make the finite‐fault problem tractable, these methods generally lack the ability to apply non‐Gaussian error analysis and the imposition of nonlinear constraints. However, the Bayesian approach can be employed to find a Gaussian or non‐Gaussian distribution of all probable model parameters, while utilizing nonlinear constraints. We present case studies to quantify the resolving power and associated uncertainties using only teleseismic body waves in a Bayesian framework to infer the slip history for a synthetic case and two earthquakes: the 2011 Mw 7.1 Van, east Turkey, earthquake and the 2010 Mw 7.2 El Mayor–Cucapah, Baja California, earthquake. In implementing the Bayesian method, we further present two distinct solutions to investigate the uncertainties by performing the inversion with and without velocity structure perturbations. We find that the posterior ensemble becomes broader when including velocity structure variability and introduces a spatial smearing of slip. Using the Bayesian framework solely on teleseismic body waves, we find rake is poorly constrained by the observations and rise time is poorly resolved when slip amplitude is low.

Bayesian model selection applied to artificial neural networks used for water resources modeling

NASA Astrophysics Data System (ADS)

Kingston, Greer B.; Maier, Holger R.; Lambert, Martin F.

2008-04-01

Artificial neural networks (ANNs) have proven to be extremely valuable tools in the field of water resources engineering. However, one of the most difficult tasks in developing an ANN is determining the optimum level of complexity required to model a given problem, as there is no formal systematic model selection method. This paper presents a Bayesian model selection (BMS) method for ANNs that provides an objective approach for comparing models of varying complexity in order to select the most appropriate ANN structure. The approach uses Markov Chain Monte Carlo posterior simulations to estimate the evidence in favor of competing models and, in this study, three known methods for doing this are compared in terms of their suitability for being incorporated into the proposed BMS framework for ANNs. However, it is acknowledged that it can be particularly difficult to accurately estimate the evidence of ANN models. Therefore, the proposed BMS approach for ANNs incorporates a further check of the evidence results by inspecting the marginal posterior distributions of the hidden-to-output layer weights, which unambiguously indicate any redundancies in the hidden layer nodes. The fact that this check is available is one of the greatest advantages of the proposed approach over conventional model selection methods, which do not provide such a test and instead rely on the modeler's subjective choice of selection criterion. The advantages of a total Bayesian approach to ANN development, including training and model selection, are demonstrated on two synthetic and one real world water resources case study.

Nonparametric Bayesian inference of the microcanonical stochastic block model

NASA Astrophysics Data System (ADS)

Peixoto, Tiago P.

2017-01-01

A principled approach to characterize the hidden modular structure of networks is to formulate generative models and then infer their parameters from data. When the desired structure is composed of modules or "communities," a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints, i.e., the generated networks are not allowed to violate the patterns imposed by the model. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: (1) deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, which not only remove limitations that seriously degrade the inference on large networks but also reveal structures at multiple scales; (2) a very efficient inference algorithm that scales well not only for networks with a large number of nodes and edges but also with an unlimited number of modules. We show also how this approach can be used to sample modular hierarchies from the posterior distribution, as well as to perform model selection. We discuss and analyze the differences between sampling from the posterior and simply finding the single parameter estimate that maximizes it. Furthermore, we expose a direct equivalence between our microcanonical approach and alternative derivations based on the canonical SBM.

Toward improved prediction of the bedrock depth underneath hillslopes: Bayesian inference of the bottom-up control hypothesis using high-resolution topographic data

NASA Astrophysics Data System (ADS)

Gomes, Guilherme J. C.; Vrugt, Jasper A.; Vargas, Eurípedes A.

2016-04-01

The depth to bedrock controls a myriad of processes by influencing subsurface flow paths, erosion rates, soil moisture, and water uptake by plant roots. As hillslope interiors are very difficult and costly to illuminate and access, the topography of the bedrock surface is largely unknown. This essay is concerned with the prediction of spatial patterns in the depth to bedrock (DTB) using high-resolution topographic data, numerical modeling, and Bayesian analysis. Our DTB model builds on the bottom-up control on fresh-bedrock topography hypothesis of Rempe and Dietrich (2014) and includes a mass movement and bedrock-valley morphology term to extent the usefulness and general applicability of the model. We reconcile the DTB model with field observations using Bayesian analysis with the DREAM algorithm. We investigate explicitly the benefits of using spatially distributed parameter values to account implicitly, and in a relatively simple way, for rock mass heterogeneities that are very difficult, if not impossible, to characterize adequately in the field. We illustrate our method using an artificial data set of bedrock depth observations and then evaluate our DTB model with real-world data collected at the Papagaio river basin in Rio de Janeiro, Brazil. Our results demonstrate that the DTB model predicts accurately the observed bedrock depth data. The posterior mean DTB simulation is shown to be in good agreement with the measured data. The posterior prediction uncertainty of the DTB model can be propagated forward through hydromechanical models to derive probabilistic estimates of factors of safety.

Order-Constrained Reference Priors with Implications for Bayesian Isotonic Regression, Analysis of Covariance and Spatial Models

NASA Astrophysics Data System (ADS)

Gong, Maozhen

Selecting an appropriate prior distribution is a fundamental issue in Bayesian Statistics. In this dissertation, under the framework provided by Berger and Bernardo, I derive the reference priors for several models which include: Analysis of Variance (ANOVA)/Analysis of Covariance (ANCOVA) models with a categorical variable under common ordering constraints, the conditionally autoregressive (CAR) models and the simultaneous autoregressive (SAR) models with a spatial autoregression parameter rho considered. The performances of reference priors for ANOVA/ANCOVA models are evaluated by simulation studies with comparisons to Jeffreys' prior and Least Squares Estimation (LSE). The priors are then illustrated in a Bayesian model of the "Risk of Type 2 Diabetes in New Mexico" data, where the relationship between the type 2 diabetes risk (through Hemoglobin A1c) and different smoking levels is investigated. In both simulation studies and real data set modeling, the reference priors that incorporate internal order information show good performances and can be used as default priors. The reference priors for the CAR and SAR models are also illustrated in the "1999 SAT State Average Verbal Scores" data with a comparison to a Uniform prior distribution. Due to the complexity of the reference priors for both CAR and SAR models, only a portion (12 states in the Midwest) of the original data set is considered. The reference priors can give a different marginal posterior distribution compared to a Uniform prior, which provides an alternative for prior specifications for areal data in Spatial statistics.

Bayesian modelling of uncertainties of Monte Carlo radiative-transfer simulations

NASA Astrophysics Data System (ADS)

Beaujean, Frederik; Eggers, Hans C.; Kerzendorf, Wolfgang E.

2018-04-01

One of the big challenges in astrophysics is the comparison of complex simulations to observations. As many codes do not directly generate observables (e.g. hydrodynamic simulations), the last step in the modelling process is often a radiative-transfer treatment. For this step, the community relies increasingly on Monte Carlo radiative transfer due to the ease of implementation and scalability with computing power. We show how to estimate the statistical uncertainty given the output of just a single radiative-transfer simulation in which the number of photon packets follows a Poisson distribution and the weight (e.g. energy or luminosity) of a single packet may follow an arbitrary distribution. Our Bayesian approach produces a posterior distribution that is valid for any number of packets in a bin, even zero packets, and is easy to implement in practice. Our analytic results for large number of packets show that we generalise existing methods that are valid only in limiting cases. The statistical problem considered here appears in identical form in a wide range of Monte Carlo simulations including particle physics and importance sampling. It is particularly powerful in extracting information when the available data are sparse or quantities are small.

Bayesian modelling of uncertainties of Monte Carlo radiative-transfer simulations

NASA Astrophysics Data System (ADS)

Beaujean, Frederik; Eggers, Hans C.; Kerzendorf, Wolfgang E.

2018-07-01

One of the big challenges in astrophysics is the comparison of complex simulations to observations. As many codes do not directly generate observables (e.g. hydrodynamic simulations), the last step in the modelling process is often a radiative-transfer treatment. For this step, the community relies increasingly on Monte Carlo radiative transfer due to the ease of implementation and scalability with computing power. We consider simulations in which the number of photon packets is Poisson distributed, while the weight assigned to a single photon packet follows any distribution of choice. We show how to estimate the statistical uncertainty of the sum of weights in each bin from the output of a single radiative-transfer simulation. Our Bayesian approach produces a posterior distribution that is valid for any number of packets in a bin, even zero packets, and is easy to implement in practice. Our analytic results for large number of packets show that we generalize existing methods that are valid only in limiting cases. The statistical problem considered here appears in identical form in a wide range of Monte Carlo simulations including particle physics and importance sampling. It is particularly powerful in extracting information when the available data are sparse or quantities are small.

Bayesian Estimation of Combined Accuracy for Tests with Verification Bias

PubMed Central

Broemeling, Lyle D.

2011-01-01

This presentation will emphasize the estimation of the combined accuracy of two or more tests when verification bias is present. Verification bias occurs when some of the subjects are not subject to the gold standard. The approach is Bayesian where the estimation of test accuracy is based on the posterior distribution of the relevant parameter. Accuracy of two combined binary tests is estimated employing either “believe the positive” or “believe the negative” rule, then the true and false positive fractions for each rule are computed for two tests. In order to perform the analysis, the missing at random assumption is imposed, and an interesting example is provided by estimating the combined accuracy of CT and MRI to diagnose lung cancer. The Bayesian approach is extended to two ordinal tests when verification bias is present, and the accuracy of the combined tests is based on the ROC area of the risk function. An example involving mammography with two readers with extreme verification bias illustrates the estimation of the combined test accuracy for ordinal tests. PMID:26859487

Topics in Computational Bayesian Statistics With Applications to Hierarchical Models in Astronomy and Sociology

NASA Astrophysics Data System (ADS)

Sahai, Swupnil

This thesis includes three parts. The overarching theme is how to analyze structured hierarchical data, with applications to astronomy and sociology. The first part discusses how expectation propagation can be used to parallelize the computation when fitting big hierarchical bayesian models. This methodology is then used to fit a novel, nonlinear mixture model to ultraviolet radiation from various regions of the observable universe. The second part discusses how the Stan probabilistic programming language can be used to numerically integrate terms in a hierarchical bayesian model. This technique is demonstrated on supernovae data to significantly speed up convergence to the posterior distribution compared to a previous study that used a Gibbs-type sampler. The third part builds a formal latent kernel representation for aggregate relational data as a way to more robustly estimate the mixing characteristics of agents in a network. In particular, the framework is applied to sociology surveys to estimate, as a function of ego age, the age and sex composition of the personal networks of individuals in the United States.

Bayesian Inference for Source Reconstruction: A Real-World Application

PubMed Central

Yee, Eugene; Hoffman, Ian; Ungar, Kurt

2014-01-01

This paper applies a Bayesian probabilistic inferential methodology for the reconstruction of the location and emission rate from an actual contaminant source (emission from the Chalk River Laboratories medical isotope production facility) using a small number of activity concentration measurements of a noble gas (Xenon-133) obtained from three stations that form part of the International Monitoring System radionuclide network. The sampling of the resulting posterior distribution of the source parameters is undertaken using a very efficient Markov chain Monte Carlo technique that utilizes a multiple-try differential evolution adaptive Metropolis algorithm with an archive of past states. It is shown that the principal difficulty in the reconstruction lay in the correct specification of the model errors (both scale and structure) for use in the Bayesian inferential methodology. In this context, two different measurement models for incorporation of the model error of the predicted concentrations are considered. The performance of both of these measurement models with respect to their accuracy and precision in the recovery of the source parameters is compared and contrasted. PMID:27379292

Pig Data and Bayesian Inference on Multinomial Probabilities

ERIC Educational Resources Information Center

Kern, John C.

2006-01-01

Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs[R]. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical…

Uncertainty analysis of gross primary production partitioned from net ecosystem exchange measurements

NASA Astrophysics Data System (ADS)

Raj, Rahul; Hamm, Nicholas Alexander Samuel; van der Tol, Christiaan; Stein, Alfred

2016-03-01

Gross primary production (GPP) can be separated from flux tower measurements of net ecosystem exchange (NEE) of CO2. This is used increasingly to validate process-based simulators and remote-sensing-derived estimates of simulated GPP at various time steps. Proper validation includes the uncertainty associated with this separation. In this study, uncertainty assessment was done in a Bayesian framework. It was applied to data from the Speulderbos forest site, The Netherlands. We estimated the uncertainty in GPP at half-hourly time steps, using a non-rectangular hyperbola (NRH) model for its separation from the flux tower measurements. The NRH model provides a robust empirical relationship between radiation and GPP. It includes the degree of curvature of the light response curve, radiation and temperature. Parameters of the NRH model were fitted to the measured NEE data for every 10-day period during the growing season (April to October) in 2009. We defined the prior distribution of each NRH parameter and used Markov chain Monte Carlo (MCMC) simulation to estimate the uncertainty in the separated GPP from the posterior distribution at half-hourly time steps. This time series also allowed us to estimate the uncertainty at daily time steps. We compared the informative with the non-informative prior distributions of the NRH parameters and found that both choices produced similar posterior distributions of GPP. This will provide relevant and important information for the validation of process-based simulators in the future. Furthermore, the obtained posterior distributions of NEE and the NRH parameters are of interest for a range of applications.

Ockham's razor and Bayesian analysis. [statistical theory for systems evaluation

NASA Technical Reports Server (NTRS)

Jefferys, William H.; Berger, James O.

1992-01-01

'Ockham's razor', the ad hoc principle enjoining the greatest possible simplicity in theoretical explanations, is presently shown to be justifiable as a consequence of Bayesian inference; Bayesian analysis can, moreover, clarify the nature of the 'simplest' hypothesis consistent with the given data. By choosing the prior probabilities of hypotheses, it becomes possible to quantify the scientific judgment that simpler hypotheses are more likely to be correct. Bayesian analysis also shows that a hypothesis with fewer adjustable parameters intrinsically possesses an enhanced posterior probability, due to the clarity of its predictions.

Geotechnical parameter spatial distribution stochastic analysis based on multi-precision information assimilation

NASA Astrophysics Data System (ADS)

Wang, C.; Rubin, Y.

2014-12-01

Spatial distribution of important geotechnical parameter named compression modulus Es contributes considerably to the understanding of the underlying geological processes and the adequate assessment of the Es mechanics effects for differential settlement of large continuous structure foundation. These analyses should be derived using an assimilating approach that combines in-situ static cone penetration test (CPT) with borehole experiments. To achieve such a task, the Es distribution of stratum of silty clay in region A of China Expo Center (Shanghai) is studied using the Bayesian-maximum entropy method. This method integrates rigorously and efficiently multi-precision of different geotechnical investigations and sources of uncertainty. Single CPT samplings were modeled as a rational probability density curve by maximum entropy theory. Spatial prior multivariate probability density function (PDF) and likelihood PDF of the CPT positions were built by borehole experiments and the potential value of the prediction point, then, preceding numerical integration on the CPT probability density curves, the posterior probability density curve of the prediction point would be calculated by the Bayesian reverse interpolation framework. The results were compared between Gaussian Sequential Stochastic Simulation and Bayesian methods. The differences were also discussed between single CPT samplings of normal distribution and simulated probability density curve based on maximum entropy theory. It is shown that the study of Es spatial distributions can be improved by properly incorporating CPT sampling variation into interpolation process, whereas more informative estimations are generated by considering CPT Uncertainty for the estimation points. Calculation illustrates the significance of stochastic Es characterization in a stratum, and identifies limitations associated with inadequate geostatistical interpolation techniques. This characterization results will provide a multi-precision information assimilation method of other geotechnical parameters.

Distributed Bayesian Computation and Self-Organized Learning in Sheets of Spiking Neurons with Local Lateral Inhibition

PubMed Central

Bill, Johannes; Buesing, Lars; Habenschuss, Stefan; Nessler, Bernhard; Maass, Wolfgang; Legenstein, Robert

2015-01-01

During the last decade, Bayesian probability theory has emerged as a framework in cognitive science and neuroscience for describing perception, reasoning and learning of mammals. However, our understanding of how probabilistic computations could be organized in the brain, and how the observed connectivity structure of cortical microcircuits supports these calculations, is rudimentary at best. In this study, we investigate statistical inference and self-organized learning in a spatially extended spiking network model, that accommodates both local competitive and large-scale associative aspects of neural information processing, under a unified Bayesian account. Specifically, we show how the spiking dynamics of a recurrent network with lateral excitation and local inhibition in response to distributed spiking input, can be understood as sampling from a variational posterior distribution of a well-defined implicit probabilistic model. This interpretation further permits a rigorous analytical treatment of experience-dependent plasticity on the network level. Using machine learning theory, we derive update rules for neuron and synapse parameters which equate with Hebbian synaptic and homeostatic intrinsic plasticity rules in a neural implementation. In computer simulations, we demonstrate that the interplay of these plasticity rules leads to the emergence of probabilistic local experts that form distributed assemblies of similarly tuned cells communicating through lateral excitatory connections. The resulting sparse distributed spike code of a well-adapted network carries compressed information on salient input features combined with prior experience on correlations among them. Our theory predicts that the emergence of such efficient representations benefits from network architectures in which the range of local inhibition matches the spatial extent of pyramidal cells that share common afferent input. PMID:26284370

Architectures of Kepler Planet Systems with Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Morehead, Robert C.; Ford, Eric B.

2015-12-01

The distribution of period normalized transit duration ratios among Kepler’s multiple transiting planet systems constrains the distributions of mutual orbital inclinations and orbital eccentricities. However, degeneracies in these parameters tied to the underlying number of planets in these systems complicate their interpretation. To untangle the true architecture of planet systems, the mutual inclination, eccentricity, and underlying planet number distributions must be considered simultaneously. The complexities of target selection, transit probability, detection biases, vetting, and follow-up observations make it impractical to write an explicit likelihood function. Approximate Bayesian computation (ABC) offers an intriguing path forward. In its simplest form, ABC generates a sample of trial population parameters from a prior distribution to produce synthetic datasets via a physically-motivated forward model. Samples are then accepted or rejected based on how close they come to reproducing the actual observed dataset to some tolerance. The accepted samples form a robust and useful approximation of the true posterior distribution of the underlying population parameters. We build on the considerable progress from the field of statistics to develop sequential algorithms for performing ABC in an efficient and flexible manner. We demonstrate the utility of ABC in exoplanet populations and present new constraints on the distributions of mutual orbital inclinations, eccentricities, and the relative number of short-period planets per star. We conclude with a discussion of the implications for other planet occurrence rate calculations, such as eta-Earth.

Integrating probabilistic models of perception and interactive neural networks: a historical and tutorial review

PubMed Central

McClelland, James L.

2013-01-01

This article seeks to establish a rapprochement between explicitly Bayesian models of contextual effects in perception and neural network models of such effects, particularly the connectionist interactive activation (IA) model of perception. The article is in part an historical review and in part a tutorial, reviewing the probabilistic Bayesian approach to understanding perception and how it may be shaped by context, and also reviewing ideas about how such probabilistic computations may be carried out in neural networks, focusing on the role of context in interactive neural networks, in which both bottom-up and top-down signals affect the interpretation of sensory inputs. It is pointed out that connectionist units that use the logistic or softmax activation functions can exactly compute Bayesian posterior probabilities when the bias terms and connection weights affecting such units are set to the logarithms of appropriate probabilistic quantities. Bayesian concepts such the prior, likelihood, (joint and marginal) posterior, probability matching and maximizing, and calculating vs. sampling from the posterior are all reviewed and linked to neural network computations. Probabilistic and neural network models are explicitly linked to the concept of a probabilistic generative model that describes the relationship between the underlying target of perception (e.g., the word intended by a speaker or other source of sensory stimuli) and the sensory input that reaches the perceiver for use in inferring the underlying target. It is shown how a new version of the IA model called the multinomial interactive activation (MIA) model can sample correctly from the joint posterior of a proposed generative model for perception of letters in words, indicating that interactive processing is fully consistent with principled probabilistic computation. Ways in which these computations might be realized in real neural systems are also considered. PMID:23970868

Integrating probabilistic models of perception and interactive neural networks: a historical and tutorial review.

PubMed

McClelland, James L

2013-01-01

This article seeks to establish a rapprochement between explicitly Bayesian models of contextual effects in perception and neural network models of such effects, particularly the connectionist interactive activation (IA) model of perception. The article is in part an historical review and in part a tutorial, reviewing the probabilistic Bayesian approach to understanding perception and how it may be shaped by context, and also reviewing ideas about how such probabilistic computations may be carried out in neural networks, focusing on the role of context in interactive neural networks, in which both bottom-up and top-down signals affect the interpretation of sensory inputs. It is pointed out that connectionist units that use the logistic or softmax activation functions can exactly compute Bayesian posterior probabilities when the bias terms and connection weights affecting such units are set to the logarithms of appropriate probabilistic quantities. Bayesian concepts such the prior, likelihood, (joint and marginal) posterior, probability matching and maximizing, and calculating vs. sampling from the posterior are all reviewed and linked to neural network computations. Probabilistic and neural network models are explicitly linked to the concept of a probabilistic generative model that describes the relationship between the underlying target of perception (e.g., the word intended by a speaker or other source of sensory stimuli) and the sensory input that reaches the perceiver for use in inferring the underlying target. It is shown how a new version of the IA model called the multinomial interactive activation (MIA) model can sample correctly from the joint posterior of a proposed generative model for perception of letters in words, indicating that interactive processing is fully consistent with principled probabilistic computation. Ways in which these computations might be realized in real neural systems are also considered.

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.

Influence of Averaging Preprocessing on Image Analysis with a Markov Random Field Model

NASA Astrophysics Data System (ADS)

Sakamoto, Hirotaka; Nakanishi-Ohno, Yoshinori; Okada, Masato

2018-02-01

This paper describes our investigations into the influence of averaging preprocessing on the performance of image analysis. Averaging preprocessing involves a trade-off: image averaging is often undertaken to reduce noise while the number of image data available for image analysis is decreased. We formulated a process of generating image data by using a Markov random field (MRF) model to achieve image analysis tasks such as image restoration and hyper-parameter estimation by a Bayesian approach. According to the notions of Bayesian inference, posterior distributions were analyzed to evaluate the influence of averaging. There are three main results. First, we found that the performance of image restoration with a predetermined value for hyper-parameters is invariant regardless of whether averaging is conducted. We then found that the performance of hyper-parameter estimation deteriorates due to averaging. Our analysis of the negative logarithm of the posterior probability, which is called the free energy based on an analogy with statistical mechanics, indicated that the confidence of hyper-parameter estimation remains higher without averaging. Finally, we found that when the hyper-parameters are estimated from the data, the performance of image restoration worsens as averaging is undertaken. We conclude that averaging adversely influences the performance of image analysis through hyper-parameter estimation.

Exploring the Energy Landscapes of Protein Folding Simulations with Bayesian Computation

PubMed Central

Burkoff, Nikolas S.; Várnai, Csilla; Wells, Stephen A.; Wild, David L.

2012-01-01

Nested sampling is a Bayesian sampling technique developed to explore probability distributions localized in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence (marginal likelihood) of the model. The nested sampling algorithm also provides an efficient way to calculate free energies and the expectation value of thermodynamic observables at any temperature, through a simple post processing of the output. Previous applications of the algorithm have yielded large efficiency gains over other sampling techniques, including parallel tempering. In this article, we describe a parallel implementation of the nested sampling algorithm and its application to the problem of protein folding in a Gō-like force field of empirical potentials that were designed to stabilize secondary structure elements in room-temperature simulations. We demonstrate the method by conducting folding simulations on a number of small proteins that are commonly used for testing protein-folding procedures. A topological analysis of the posterior samples is performed to produce energy landscape charts, which give a high-level description of the potential energy surface for the protein folding simulations. These charts provide qualitative insights into both the folding process and the nature of the model and force field used. PMID:22385859

Exploring the energy landscapes of protein folding simulations with Bayesian computation.

PubMed

Burkoff, Nikolas S; Várnai, Csilla; Wells, Stephen A; Wild, David L

2012-02-22

Nested sampling is a Bayesian sampling technique developed to explore probability distributions localized in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence (marginal likelihood) of the model. The nested sampling algorithm also provides an efficient way to calculate free energies and the expectation value of thermodynamic observables at any temperature, through a simple post processing of the output. Previous applications of the algorithm have yielded large efficiency gains over other sampling techniques, including parallel tempering. In this article, we describe a parallel implementation of the nested sampling algorithm and its application to the problem of protein folding in a Gō-like force field of empirical potentials that were designed to stabilize secondary structure elements in room-temperature simulations. We demonstrate the method by conducting folding simulations on a number of small proteins that are commonly used for testing protein-folding procedures. A topological analysis of the posterior samples is performed to produce energy landscape charts, which give a high-level description of the potential energy surface for the protein folding simulations. These charts provide qualitative insights into both the folding process and the nature of the model and force field used. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Asking better questions: How presentation formats influence information search.

PubMed

Wu, Charley M; Meder, Björn; Filimon, Flavia; Nelson, Jonathan D

2017-08-01

While the influence of presentation formats have been widely studied in Bayesian reasoning tasks, we present the first systematic investigation of how presentation formats influence information search decisions. Four experiments were conducted across different probabilistic environments, where subjects (N = 2,858) chose between 2 possible search queries, each with binary probabilistic outcomes, with the goal of maximizing classification accuracy. We studied 14 different numerical and visual formats for presenting information about the search environment, constructed across 6 design features that have been prominently related to improvements in Bayesian reasoning accuracy (natural frequencies, posteriors, complement, spatial extent, countability, and part-to-whole information). The posterior variants of the icon array and bar graph formats led to the highest proportion of correct responses, and were substantially better than the standard probability format. Results suggest that presenting information in terms of posterior probabilities and visualizing natural frequencies using spatial extent (a perceptual feature) were especially helpful in guiding search decisions, although environments with a mixture of probabilistic and certain outcomes were challenging across all formats. Subjects who made more accurate probability judgments did not perform better on the search task, suggesting that simple decision heuristics may be used to make search decisions without explicitly applying Bayesian inference to compute probabilities. We propose a new take-the-difference (TTD) heuristic that identifies the accuracy-maximizing query without explicit computation of posterior probabilities. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Screening for SNPs with Allele-Specific Methylation based on Next-Generation Sequencing Data.

PubMed

Hu, Bo; Ji, Yuan; Xu, Yaomin; Ting, Angela H

2013-05-01

Allele-specific methylation (ASM) has long been studied but mainly documented in the context of genomic imprinting and X chromosome inactivation. Taking advantage of the next-generation sequencing technology, we conduct a high-throughput sequencing experiment with four prostate cell lines to survey the whole genome and identify single nucleotide polymorphisms (SNPs) with ASM. A Bayesian approach is proposed to model the counts of short reads for each SNP conditional on its genotypes of multiple subjects, leading to a posterior probability of ASM. We flag SNPs with high posterior probabilities of ASM by accounting for multiple comparisons based on posterior false discovery rates. Applying the Bayesian approach to the in-house prostate cell line data, we identify 269 SNPs as candidates of ASM. A simulation study is carried out to demonstrate the quantitative performance of the proposed approach.

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 Poisson-lognormal Model for Count Data for Multiple-Trait Multiple-Environment Genomic-Enabled Prediction.

PubMed

Montesinos-López, Osval A; Montesinos-López, Abelardo; Crossa, José; Toledo, Fernando H; Montesinos-López, José C; Singh, Pawan; Juliana, Philomin; Salinas-Ruiz, Josafhat

2017-05-05

When a plant scientist wishes to make genomic-enabled predictions of multiple traits measured in multiple individuals in multiple environments, the most common strategy for performing the analysis is to use a single trait at a time taking into account genotype × environment interaction (G × E), because there is a lack of comprehensive models that simultaneously take into account the correlated counting traits and G × E. For this reason, in this study we propose a multiple-trait and multiple-environment model for count data. The proposed model was developed under the Bayesian paradigm for which we developed a Markov Chain Monte Carlo (MCMC) with noninformative priors. This allows obtaining all required full conditional distributions of the parameters leading to an exact Gibbs sampler for the posterior distribution. Our model was tested with simulated data and a real data set. Results show that the proposed multi-trait, multi-environment model is an attractive alternative for modeling multiple count traits measured in multiple environments. Copyright © 2017 Montesinos-López et al.

Meta-analysis of diagnostic test data: a bivariate Bayesian modeling approach.

PubMed

Verde, Pablo E

2010-12-30

In the last decades, the amount of published results on clinical diagnostic tests has expanded very rapidly. The counterpart to this development has been the formal evaluation and synthesis of diagnostic results. However, published results present substantial heterogeneity and they can be regarded as so far removed from the classical domain of meta-analysis, that they can provide a rather severe test of classical statistical methods. Recently, bivariate random effects meta-analytic methods, which model the pairs of sensitivities and specificities, have been presented from the classical point of view. In this work a bivariate Bayesian modeling approach is presented. This approach substantially extends the scope of classical bivariate methods by allowing the structural distribution of the random effects to depend on multiple sources of variability. Meta-analysis is summarized by the predictive posterior distributions for sensitivity and specificity. This new approach allows, also, to perform substantial model checking, model diagnostic and model selection. Statistical computations are implemented in the public domain statistical software (WinBUGS and R) and illustrated with real data examples. Copyright © 2010 John Wiley & Sons, Ltd.

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.

Selectivity curves of the capture of mangrove crab (Ucides cordatus) on the northern coast of Brazil using bayesian inference.

PubMed

Furtado-Junior, I; Abrunhosa, F A; Holanda, F C A F; Tavares, M C S

2016-06-01

Fishing selectivity of the mangrove crab Ucides cordatus in the north coast of Brazil can be defined as the fisherman's ability to capture and select individuals from a certain size or sex (or a combination of these factors) which suggests an empirical selectivity. Considering this hypothesis, we calculated the selectivity curves for males and females crabs using the logit function of the logistic model in the formulation. The Bayesian inference consisted of obtaining the posterior distribution by applying the Markov chain Monte Carlo (MCMC) method to software R using the OpenBUGS, BRugs, and R2WinBUGS libraries. The estimated results of width average carapace selection for males and females compared with previous studies reporting the average width of the carapace of sexual maturity allow us to confirm the hypothesis that most mature individuals do not suffer from fishing pressure; thus, ensuring their sustainability.

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 Design of Superiority Clinical Trials for Recurrent Events Data with Applications to Bleeding and Transfusion Events in Myelodyplastic Syndrome

PubMed Central

Chen, Ming-Hui; Zeng, Donglin; Hu, Kuolung; Jia, Catherine

2014-01-01

Summary In many biomedical studies, patients may experience the same type of recurrent event repeatedly over time, such as bleeding, multiple infections and disease. In this article, we propose a Bayesian design to a pivotal clinical trial in which lower risk myelodysplastic syndromes (MDS) patients are treated with MDS disease modifying therapies. One of the key study objectives is to demonstrate the investigational product (treatment) effect on reduction of platelet transfusion and bleeding events while receiving MDS therapies. In this context, we propose a new Bayesian approach for the design of superiority clinical trials using recurrent events frailty regression models. Historical recurrent events data from an already completed phase 2 trial are incorporated into the Bayesian design via the partial borrowing power prior of Ibrahim et al. (2012, Biometrics 68, 578–586). An efficient Gibbs sampling algorithm, a predictive data generation algorithm, and a simulation-based algorithm are developed for sampling from the fitting posterior distribution, generating the predictive recurrent events data, and computing various design quantities such as the type I error rate and power, respectively. An extensive simulation study is conducted to compare the proposed method to the existing frequentist methods and to investigate various operating characteristics of the proposed design. PMID:25041037

Stoffenmanager exposure model: company-specific exposure assessments using a Bayesian methodology.

PubMed

van de Ven, Peter; Fransman, Wouter; Schinkel, Jody; Rubingh, Carina; Warren, Nicholas; Tielemans, Erik

2010-04-01

The web-based tool "Stoffenmanager" was initially developed to assist small- and medium-sized enterprises in the Netherlands to make qualitative risk assessments and to provide advice on control at the workplace. The tool uses a mechanistic model to arrive at a "Stoffenmanager score" for exposure. In a recent study it was shown that variability in exposure measurements given a certain Stoffenmanager score is still substantial. This article discusses an extension to the tool that uses a Bayesian methodology for quantitative workplace/scenario-specific exposure assessment. This methodology allows for real exposure data observed in the company of interest to be combined with the prior estimate (based on the Stoffenmanager model). The output of the tool is a company-specific assessment of exposure levels for a scenario for which data is available. The Bayesian approach provides a transparent way of synthesizing different types of information and is especially preferred in situations where available data is sparse, as is often the case in small- and medium sized-enterprises. Real-world examples as well as simulation studies were used to assess how different parameters such as sample size, difference between prior and data, uncertainty in prior, and variance in the data affect the eventual posterior distribution of a Bayesian exposure assessment.

A Bayes linear Bayes method for estimation of correlated event rates.

PubMed

Quigley, John; Wilson, Kevin J; Walls, Lesley; Bedford, Tim

2013-12-01

Typically, full Bayesian estimation of correlated event rates can be computationally challenging since estimators are intractable. When estimation of event rates represents one activity within a larger modeling process, there is an incentive to develop more efficient inference than provided by a full Bayesian model. We develop a new subjective inference method for correlated event rates based on a Bayes linear Bayes model under the assumption that events are generated from a homogeneous Poisson process. To reduce the elicitation burden we introduce homogenization factors to the model and, as an alternative to a subjective prior, an empirical method using the method of moments is developed. Inference under the new method is compared against estimates obtained under a full Bayesian model, which takes a multivariate gamma prior, where the predictive and posterior distributions are derived in terms of well-known functions. The mathematical properties of both models are presented. A simulation study shows that the Bayes linear Bayes inference method and the full Bayesian model provide equally reliable estimates. An illustrative example, motivated by a problem of estimating correlated event rates across different users in a simple supply chain, shows how ignoring the correlation leads to biased estimation of event rates. © 2013 Society for Risk Analysis.

HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.

PubMed

Wiecki, Thomas V; Sofer, Imri; Frank, Michael J

2013-01-01

The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/

A Bayesian approach to model structural error and input variability in groundwater modeling

NASA Astrophysics Data System (ADS)

Xu, T.; Valocchi, A. J.; Lin, Y. F. F.; Liang, F.

2015-12-01

Effective water resource management typically relies on numerical models to analyze groundwater flow and solute transport processes. Model structural error (due to simplification and/or misrepresentation of the "true" environmental system) and input forcing variability (which commonly arises since some inputs are uncontrolled or estimated with high uncertainty) are ubiquitous in groundwater models. Calibration that overlooks errors in model structure and input data can lead to biased parameter estimates and compromised predictions. We present a fully Bayesian approach for a complete assessment of uncertainty for spatially distributed groundwater models. The approach explicitly recognizes stochastic input and uses data-driven error models based on nonparametric kernel methods to account for model structural error. We employ exploratory data analysis to assist in specifying informative prior for error models to improve identifiability. The inference is facilitated by an efficient sampling algorithm based on DREAM-ZS and a parameter subspace multiple-try strategy to reduce the required number of forward simulations of the groundwater model. We demonstrate the Bayesian approach through a synthetic case study of surface-ground water interaction under changing pumping conditions. It is found that explicit treatment of errors in model structure and input data (groundwater pumping rate) has substantial impact on the posterior distribution of groundwater model parameters. Using error models reduces predictive bias caused by parameter compensation. In addition, input variability increases parametric and predictive uncertainty. The Bayesian approach allows for a comparison among the contributions from various error sources, which could inform future model improvement and data collection efforts on how to best direct resources towards reducing predictive uncertainty.

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

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

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

DOE PAGES

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

2017-04-12

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

Directional data analysis under the general projected normal distribution

PubMed Central

Wang, Fangpo; Gelfand, Alan E.

2013-01-01

The projected normal distribution is an under-utilized model for explaining directional data. In particular, the general version provides flexibility, e.g., asymmetry and possible bimodality along with convenient regression specification. Here, we clarify the properties of this general class. We also develop fully Bayesian hierarchical models for analyzing circular data using this class. We show how they can be fit using MCMC methods with suitable latent variables. We show how posterior inference for distributional features such as the angular mean direction and concentration can be implemented as well as how prediction within the regression setting can be handled. With regard to model comparison, we argue for an out-of-sample approach using both a predictive likelihood scoring loss criterion and a cumulative rank probability score criterion. PMID:24046539

Linking big models to big data: efficient ecosystem model calibration through Bayesian model emulation

NASA Astrophysics Data System (ADS)

Fer, I.; Kelly, R.; Andrews, T.; Dietze, M.; Richardson, A. D.

2016-12-01

Our ability to forecast ecosystems is limited by how well we parameterize ecosystem models. Direct measurements for all model parameters are not always possible and inverse estimation of these parameters through Bayesian methods is computationally costly. A solution to computational challenges of Bayesian calibration is to approximate the posterior probability surface using a Gaussian Process that emulates the complex process-based model. Here we report the integration of this method within an ecoinformatics toolbox, Predictive Ecosystem Analyzer (PEcAn), and its application with two ecosystem models: SIPNET and ED2.1. SIPNET is a simple model, allowing application of MCMC methods both to the model itself and to its emulator. We used both approaches to assimilate flux (CO2 and latent heat), soil respiration, and soil carbon data from Bartlett Experimental Forest. This comparison showed that emulator is reliable in terms of convergence to the posterior distribution. A 10000-iteration MCMC analysis with SIPNET itself required more than two orders of magnitude greater computation time than an MCMC run of same length with its emulator. This difference would be greater for a more computationally demanding model. Validation of the emulator-calibrated SIPNET against both the assimilated data and out-of-sample data showed improved fit and reduced uncertainty around model predictions. We next applied the validated emulator method to the ED2, whose complexity precludes standard Bayesian data assimilation. We used the ED2 emulator to assimilate demographic data from a network of inventory plots. For validation of the calibrated ED2, we compared the model to results from Empirical Succession Mapping (ESM), a novel synthesis of successional patterns in Forest Inventory and Analysis data. Our results revealed that while the pre-assimilation ED2 formulation cannot capture the emergent demographic patterns from ESM analysis, constrained model parameters controlling demographic processes increased their agreement considerably.

Bayesian inference of uncertainties in precipitation-streamflow modeling in a snow affected catchment

NASA Astrophysics Data System (ADS)

Koskela, J. J.; Croke, B. W. F.; Koivusalo, H.; Jakeman, A. J.; Kokkonen, T.

2012-11-01

Bayesian inference is used to study the effect of precipitation and model structural uncertainty on estimates of model parameters and confidence limits of predictive variables in a conceptual rainfall-runoff model in the snow-fed Rudbäck catchment (142 ha) in southern Finland. The IHACRES model is coupled with a simple degree day model to account for snow accumulation and melt. The posterior probability distribution of the model parameters is sampled by using the Differential Evolution Adaptive Metropolis (DREAM(ZS)) algorithm and the generalized likelihood function. Precipitation uncertainty is taken into account by introducing additional latent variables that were used as multipliers for individual storm events. Results suggest that occasional snow water equivalent (SWE) observations together with daily streamflow observations do not contain enough information to simultaneously identify model parameters, precipitation uncertainty and model structural uncertainty in the Rudbäck catchment. The addition of an autoregressive component to account for model structure error and latent variables having uniform priors to account for input uncertainty lead to dubious posterior distributions of model parameters. Thus our hypothesis that informative priors for latent variables could be replaced by additional SWE data could not be confirmed. The model was found to work adequately in 1-day-ahead simulation mode, but the results were poor in the simulation batch mode. This was caused by the interaction of parameters that were used to describe different sources of uncertainty. The findings may have lessons for other cases where parameterizations are similarly high in relation to available prior information.

A two step Bayesian approach for genomic prediction of breeding values.

PubMed

Shariati, Mohammad M; Sørensen, Peter; Janss, Luc

2012-05-21

In genomic models that assign an individual variance to each marker, the contribution of one marker to the posterior distribution of the marker variance is only one degree of freedom (df), which introduces many variance parameters with only little information per variance parameter. A better alternative could be to form clusters of markers with similar effects where markers in a cluster have a common variance. Therefore, the influence of each marker group of size p on the posterior distribution of the marker variances will be p df. The simulated data from the 15th QTL-MAS workshop were analyzed such that SNP markers were ranked based on their effects and markers with similar estimated effects were grouped together. In step 1, all markers with minor allele frequency more than 0.01 were included in a SNP-BLUP prediction model. In step 2, markers were ranked based on their estimated variance on the trait in step 1 and each 150 markers were assigned to one group with a common variance. In further analyses, subsets of 1500 and 450 markers with largest effects in step 2 were kept in the prediction model. Grouping markers outperformed SNP-BLUP model in terms of accuracy of predicted breeding values. However, the accuracies of predicted breeding values were lower than Bayesian methods with marker specific variances. Grouping markers is less flexible than allowing each marker to have a specific marker variance but, by grouping, the power to estimate marker variances increases. A prior knowledge of the genetic architecture of the trait is necessary for clustering markers and appropriate prior parameterization.

Of bits and wows: A Bayesian theory of surprise with applications to attention.

PubMed

Baldi, Pierre; Itti, Laurent

2010-06-01

The amount of information contained in a piece of data can be measured by the effect this data has on its observer. Fundamentally, this effect is to transform the observer's prior beliefs into posterior beliefs, according to Bayes theorem. Thus the amount of information can be measured in a natural way by the distance (relative entropy) between the prior and posterior distributions of the observer over the available space of hypotheses. This facet of information, termed "surprise", is important in dynamic situations where beliefs change, in particular during learning and adaptation. Surprise can often be computed analytically, for instance in the case of distributions from the exponential family, or it can be numerically approximated. During sequential Bayesian learning, surprise decreases as the inverse of the number of training examples. Theoretical properties of surprise are discussed, in particular how it differs and complements Shannon's definition of information. A computer vision neural network architecture is then presented capable of computing surprise over images and video stimuli. Hypothesizing that surprising data ought to attract natural or artificial attention systems, the output of this architecture is used in a psychophysical experiment to analyze human eye movements in the presence of natural video stimuli. Surprise is found to yield robust performance at predicting human gaze (ROC-like ordinal dominance score approximately 0.7 compared to approximately 0.8 for human inter-observer repeatability, approximately 0.6 for simpler intensity contrast-based predictor, and 0.5 for chance). The resulting theory of surprise is applicable across different spatio-temporal scales, modalities, and levels of abstraction. Copyright 2010 Elsevier Ltd. All rights reserved.

Bayesian Model Selection in Geophysics: The evidence

NASA Astrophysics Data System (ADS)

Vrugt, J. A.

2016-12-01

Bayesian inference has found widespread application and use in science and engineering to reconcile Earth system models with data, including prediction in space (interpolation), prediction in time (forecasting), assimilation of observations and deterministic/stochastic model output, and inference of the model parameters. Per Bayes theorem, the posterior probability, , P(H|D), of a hypothesis, H, given the data D, is equivalent to the product of its prior probability, P(H), and likelihood, L(H|D), divided by a normalization constant, P(D). In geophysics, the hypothesis, H, often constitutes a description (parameterization) of the subsurface for some entity of interest (e.g. porosity, moisture content). The normalization constant, P(D), is not required for inference of the subsurface structure, yet of great value for model selection. Unfortunately, it is not particularly easy to estimate P(D) in practice. Here, I will introduce the various building blocks of a general purpose method which provides robust and unbiased estimates of the evidence, P(D). This method uses multi-dimensional numerical integration of the posterior (parameter) distribution. I will then illustrate this new estimator by application to three competing subsurface models (hypothesis) using GPR travel time data from the South Oyster Bacterial Transport Site, in Virginia, USA. The three subsurface models differ in their treatment of the porosity distribution and use (a) horizontal layering with fixed layer thicknesses, (b) vertical layering with fixed layer thicknesses and (c) a multi-Gaussian field. The results of the new estimator are compared against the brute force Monte Carlo method, and the Laplace-Metropolis method.

Using Discrete Loss Functions and Weighted Kappa for Classification: An Illustration Based on Bayesian Network Analysis

ERIC Educational Resources Information Center

Zwick, Rebecca; Lenaburg, Lubella

2009-01-01

In certain data analyses (e.g., multiple discriminant analysis and multinomial log-linear modeling), classification decisions are made based on the estimated posterior probabilities that individuals belong to each of several distinct categories. In the Bayesian network literature, this type of classification is often accomplished by assigning…

Analytic posteriors for Pearson's correlation coefficient.

PubMed

Ly, Alexander; Marsman, Maarten; Wagenmakers, Eric-Jan

2018-02-01

Pearson's correlation is one of the most common measures of linear dependence. Recently, Bernardo (11th International Workshop on Objective Bayes Methodology, 2015) introduced a flexible class of priors to study this measure in a Bayesian setting. For this large class of priors, we show that the (marginal) posterior for Pearson's correlation coefficient and all of the posterior moments are analytic. Our results are available in the open-source software package JASP.

Bayesian analysis of the flutter margin method in aeroelasticity

DOE PAGES

Khalil, Mohammad; Poirel, Dominique; Sarkar, Abhijit

2016-08-27

A Bayesian statistical framework is presented for Zimmerman and Weissenburger flutter margin method which considers the uncertainties in aeroelastic modal parameters. The proposed methodology overcomes the limitations of the previously developed least-square based estimation technique which relies on the Gaussian approximation of the flutter margin probability density function (pdf). Using the measured free-decay responses at subcritical (preflutter) airspeeds, the joint non-Gaussain posterior pdf of the modal parameters is sampled using the Metropolis–Hastings (MH) Markov chain Monte Carlo (MCMC) algorithm. The posterior MCMC samples of the modal parameters are then used to obtain the flutter margin pdfs and finally the fluttermore » speed pdf. The usefulness of the Bayesian flutter margin method is demonstrated using synthetic data generated from a two-degree-of-freedom pitch-plunge aeroelastic model. The robustness of the statistical framework is demonstrated using different sets of measurement data. In conclusion, it will be shown that the probabilistic (Bayesian) approach reduces the number of test points required in providing a flutter speed estimate for a given accuracy and precision.« less

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

Simple summation rule for optimal fixation selection in visual search.

PubMed

Najemnik, Jiri; Geisler, Wilson S

2009-06-01

When searching for a known target in a natural texture, practiced humans achieve near-optimal performance compared to a Bayesian ideal searcher constrained with the human map of target detectability across the visual field [Najemnik, J., & Geisler, W. S. (2005). Optimal eye movement strategies in visual search. Nature, 434, 387-391]. To do so, humans must be good at choosing where to fixate during the search [Najemnik, J., & Geisler, W.S. (2008). Eye movement statistics in humans are consistent with an optimal strategy. Journal of Vision, 8(3), 1-14. 4]; however, it seems unlikely that a biological nervous system would implement the computations for the Bayesian ideal fixation selection because of their complexity. Here we derive and test a simple heuristic for optimal fixation selection that appears to be a much better candidate for implementation within a biological nervous system. Specifically, we show that the near-optimal fixation location is the maximum of the current posterior probability distribution for target location after the distribution is filtered by (convolved with) the square of the retinotopic target detectability map. We term the model that uses this strategy the entropy limit minimization (ELM) searcher. We show that when constrained with human-like retinotopic map of target detectability and human search error rates, the ELM searcher performs as well as the Bayesian ideal searcher, and produces fixation statistics similar to human.

Evolution of the cerebellum as a neuronal machine for Bayesian state estimation

NASA Astrophysics Data System (ADS)

Paulin, M. G.

2005-09-01

The cerebellum evolved in association with the electric sense and vestibular sense of the earliest vertebrates. Accurate information provided by these sensory systems would have been essential for precise control of orienting behavior in predation. A simple model shows that individual spikes in electrosensory primary afferent neurons can be interpreted as measurements of prey location. Using this result, I construct a computational neural model in which the spatial distribution of spikes in a secondary electrosensory map forms a Monte Carlo approximation to the Bayesian posterior distribution of prey locations given the sense data. The neural circuit that emerges naturally to perform this task resembles the cerebellar-like hindbrain electrosensory filtering circuitry of sharks and other electrosensory vertebrates. The optimal filtering mechanism can be extended to handle dynamical targets observed from a dynamical platform; that is, to construct an optimal dynamical state estimator using spiking neurons. This may provide a generic model of cerebellar computation. Vertebrate motion-sensing neurons have specific fractional-order dynamical characteristics that allow Bayesian state estimators to be implemented elegantly and efficiently, using simple operations with asynchronous pulses, i.e. spikes. The computational neural models described in this paper represent a novel kind of particle filter, using spikes as particles. The models are specific and make testable predictions about computational mechanisms in cerebellar circuitry, while providing a plausible explanation of cerebellar contributions to aspects of motor control, perception and cognition.

A Bayesian hierarchical model for mortality data from cluster-sampling household surveys in humanitarian crises.

PubMed

Heudtlass, Peter; Guha-Sapir, Debarati; Speybroeck, Niko

2018-05-31

The crude death rate (CDR) is one of the defining indicators of humanitarian emergencies. When data from vital registration systems are not available, it is common practice to estimate the CDR from household surveys with cluster-sampling design. However, sample sizes are often too small to compare mortality estimates to emergency thresholds, at least in a frequentist framework. Several authors have proposed Bayesian methods for health surveys in humanitarian crises. Here, we develop an approach specifically for mortality data and cluster-sampling surveys. We describe a Bayesian hierarchical Poisson-Gamma mixture model with generic (weakly informative) priors that could be used as default in absence of any specific prior knowledge, and compare Bayesian and frequentist CDR estimates using five different mortality datasets. We provide an interpretation of the Bayesian estimates in the context of an emergency threshold and demonstrate how to interpret parameters at the cluster level and ways in which informative priors can be introduced. With the same set of weakly informative priors, Bayesian CDR estimates are equivalent to frequentist estimates, for all practical purposes. The probability that the CDR surpasses the emergency threshold can be derived directly from the posterior of the mean of the mixing distribution. All observation in the datasets contribute to the estimation of cluster-level estimates, through the hierarchical structure of the model. In a context of sparse data, Bayesian mortality assessments have advantages over frequentist ones already when using only weakly informative priors. More informative priors offer a formal and transparent way of combining new data with existing data and expert knowledge and can help to improve decision-making in humanitarian crises by complementing frequentist estimates.

Screening for SNPs with Allele-Specific Methylation based on Next-Generation Sequencing Data

PubMed Central

Hu, Bo; Xu, Yaomin

2013-01-01

Allele-specific methylation (ASM) has long been studied but mainly documented in the context of genomic imprinting and X chromosome inactivation. Taking advantage of the next-generation sequencing technology, we conduct a high-throughput sequencing experiment with four prostate cell lines to survey the whole genome and identify single nucleotide polymorphisms (SNPs) with ASM. A Bayesian approach is proposed to model the counts of short reads for each SNP conditional on its genotypes of multiple subjects, leading to a posterior probability of ASM. We flag SNPs with high posterior probabilities of ASM by accounting for multiple comparisons based on posterior false discovery rates. Applying the Bayesian approach to the in-house prostate cell line data, we identify 269 SNPs as candidates of ASM. A simulation study is carried out to demonstrate the quantitative performance of the proposed approach. PMID:23710259

A Bayesian Modeling Approach for Estimation of a Shape-Free Groundwater Age Distribution using Multiple Tracers

DOE PAGES

Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh; ...

2013-10-15

The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated.more » A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (Costa-Rica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.« less

A Bayesian Modeling Approach for Estimation of a Shape-Free Groundwater Age Distribution using Multiple Tracers

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

Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh

The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated.more » A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (Costa-Rica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.« less

Joint Bayesian Component Separation and CMB Power Spectrum Estimation

NASA Technical Reports Server (NTRS)

Eriksen, H. K.; Jewell, J. B.; Dickinson, C.; Banday, A. J.; Gorski, K. M.; Lawrence, C. R.

2008-01-01

We describe and implement an exact, flexible, and computationally efficient algorithm for joint component separation and CMB power spectrum estimation, building on a Gibbs sampling framework. Two essential new features are (1) conditional sampling of foreground spectral parameters and (2) joint sampling of all amplitude-type degrees of freedom (e.g., CMB, foreground pixel amplitudes, and global template amplitudes) given spectral parameters. Given a parametric model of the foreground signals, we estimate efficiently and accurately the exact joint foreground- CMB posterior distribution and, therefore, all marginal distributions such as the CMB power spectrum or foreground spectral index posteriors. The main limitation of the current implementation is the requirement of identical beam responses at all frequencies, which restricts the analysis to the lowest resolution of a given experiment. We outline a future generalization to multiresolution observations. To verify the method, we analyze simple models and compare the results to analytical predictions. We then analyze a realistic simulation with properties similar to the 3 yr WMAP data, downgraded to a common resolution of 3 deg FWHM. The results from the actual 3 yr WMAP temperature analysis are presented in a companion Letter.

Bayesian calibration of mechanistic aquatic biogeochemical models and benefits for environmental management

NASA Astrophysics Data System (ADS)

Arhonditsis, George B.; Papantou, Dimitra; Zhang, Weitao; Perhar, Gurbir; Massos, Evangelia; Shi, Molu

2008-09-01

Aquatic biogeochemical models have been an indispensable tool for addressing pressing environmental issues, e.g., understanding oceanic response to climate change, elucidation of the interplay between plankton dynamics and atmospheric CO 2 levels, and examination of alternative management schemes for eutrophication control. Their ability to form the scientific basis for environmental management decisions can be undermined by the underlying structural and parametric uncertainty. In this study, we outline how we can attain realistic predictive links between management actions and ecosystem response through a probabilistic framework that accommodates rigorous uncertainty analysis of a variety of error sources, i.e., measurement error, parameter uncertainty, discrepancy between model and natural system. Because model uncertainty analysis essentially aims to quantify the joint probability distribution of model parameters and to make inference about this distribution, we believe that the iterative nature of Bayes' Theorem is a logical means to incorporate existing knowledge and update the joint distribution as new information becomes available. The statistical methodology begins with the characterization of parameter uncertainty in the form of probability distributions, then water quality data are used to update the distributions, and yield posterior parameter estimates along with predictive uncertainty bounds. Our illustration is based on a six state variable (nitrate, ammonium, dissolved organic nitrogen, phytoplankton, zooplankton, and bacteria) ecological model developed for gaining insight into the mechanisms that drive plankton dynamics in a coastal embayment; the Gulf of Gera, Island of Lesvos, Greece. The lack of analytical expressions for the posterior parameter distributions was overcome using Markov chain Monte Carlo simulations; a convenient way to obtain representative samples of parameter values. The Bayesian calibration resulted in realistic reproduction of the key temporal patterns of the system, offered insights into the degree of information the data contain about model inputs, and also allowed the quantification of the dependence structure among the parameter estimates. Finally, our study uses two synthetic datasets to examine the ability of the updated model to provide estimates of predictive uncertainty for water quality variables of environmental management interest.

Improved parameter inference in catchment models: 1. Evaluating parameter uncertainty

NASA Astrophysics Data System (ADS)

Kuczera, George

1983-10-01

A Bayesian methodology is developed to evaluate parameter uncertainty in catchment models fitted to a hydrologic response such as runoff, the goal being to improve the chance of successful regionalization. The catchment model is posed as a nonlinear regression model with stochastic errors possibly being both autocorrelated and heteroscedastic. The end result of this methodology, which may use Box-Cox power transformations and ARMA error models, is the posterior distribution, which summarizes what is known about the catchment model parameters. This can be simplified to a multivariate normal provided a linearization in parameter space is acceptable; means of checking and improving this assumption are discussed. The posterior standard deviations give a direct measure of parameter uncertainty, and study of the posterior correlation matrix can indicate what kinds of data are required to improve the precision of poorly determined parameters. Finally, a case study involving a nine-parameter catchment model fitted to monthly runoff and soil moisture data is presented. It is shown that use of ordinary least squares when its underlying error assumptions are violated gives an erroneous description of parameter uncertainty.

Reliability analysis using an exponential power model with bathtub-shaped failure rate function: a Bayes study.

PubMed

Shehla, Romana; Khan, Athar Ali

2016-01-01

Models with bathtub-shaped hazard function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this paper, the exponential power model capable of assuming increasing as well as bathtub-shape, is studied. This article makes a Bayesian study of the same model and simultaneously shows how posterior simulations based on Markov chain Monte Carlo algorithms can be straightforward and routine in R. The study is carried out for complete as well as censored data, under the assumption of weakly-informative priors for the parameters. In addition to this, inference interest focuses on the posterior distribution of non-linear functions of the parameters. Also, the model has been extended to include continuous explanatory variables and R-codes are well illustrated. Two real data sets are considered for illustrative purposes.

Log-Linear Models for Gene Association

PubMed Central

Hu, Jianhua; Joshi, Adarsh; Johnson, Valen E.

2009-01-01

We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data that have been reduced to contingency tables using ranks of observations within subjects, and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on Ewens’ sampling distribution is used to restrict the number of interacting components assigned high posterior probability, and the calculation of posterior model probabilities is expedited by approximations based on the likelihood ratio statistic. Simulation studies are used to evaluate the efficiency of the resulting algorithm for known interaction structures. Finally, the algorithm is validated in a microarray study for which it was possible to obtain biological confirmation of detected interactions. PMID:19655032

Bayesian Factor Analysis When Only a Sample Covariance Matrix Is Available

ERIC Educational Resources Information Center

Hayashi, Kentaro; Arav, Marina

2006-01-01

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing…

Little Bayesians or Little Einsteins? Probability and Explanatory Virtue in Children's Inferences

ERIC Educational Resources Information Center

Johnston, Angie M.; Johnson, Samuel G. B.; Koven, Marissa L.; Keil, Frank C.

2017-01-01

Like scientists, children seek ways to explain causal systems in the world. But are children scientists in the strict Bayesian tradition of maximizing posterior probability? Or do they attend to other explanatory considerations, as laypeople and scientists--such as Einstein--do? Four experiments support the latter possibility. In particular, we…

Three Insights from a Bayesian Interpretation of the One-Sided "P" Value

ERIC Educational Resources Information Center

Marsman, Maarten; Wagenmakers, Eric-Jan

2017-01-01

P values have been critiqued on several grounds but remain entrenched as the dominant inferential method in the empirical sciences. In this article, we elaborate on the fact that in many statistical models, the one-sided "P" value has a direct Bayesian interpretation as the approximate posterior mass for values lower than zero. The…

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Köpke, Corinna; Irving, James; Elsheikh, Ahmed H.

2018-06-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward model linking subsurface physical properties to measured data, which is typically assumed to be perfectly known in the inversion procedure. However, to make the stochastic solution of the inverse problem computationally tractable using methods such as Markov-chain-Monte-Carlo (MCMC), fast approximations of the forward model are commonly employed. This gives rise to model error, which has the potential to significantly bias posterior statistics if not properly accounted for. Here, we present a new methodology for dealing with the model error arising from the use of approximate forward solvers in Bayesian solutions to hydrogeophysical inverse problems. Our approach is geared towards the common case where this error cannot be (i) effectively characterized through some parametric statistical distribution; or (ii) estimated by interpolating between a small number of computed model-error realizations. To this end, we focus on identification and removal of the model-error component of the residual during MCMC using a projection-based approach, whereby the orthogonal basis employed for the projection is derived in each iteration from the K-nearest-neighboring entries in a model-error dictionary. The latter is constructed during the inversion and grows at a specified rate as the iterations proceed. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar travel-time data considering three different subsurface parameterizations of varying complexity. Synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed for their inversion. In each case, our developed approach enables us to remove posterior bias and obtain a more realistic characterization of uncertainty.

MC3: Multi-core Markov-chain Monte Carlo code

NASA Astrophysics Data System (ADS)

Cubillos, Patricio; Harrington, Joseph; Lust, Nate; Foster, AJ; Stemm, Madison; Loredo, Tom; Stevenson, Kevin; Campo, Chris; Hardin, Matt; Hardy, Ryan

2016-10-01

MC3 (Multi-core Markov-chain Monte Carlo) is a Bayesian statistics tool that can be executed from the shell prompt or interactively through the Python interpreter with single- or multiple-CPU parallel computing. It offers Markov-chain Monte Carlo (MCMC) posterior-distribution sampling for several algorithms, Levenberg-Marquardt least-squares optimization, and uniform non-informative, Jeffreys non-informative, or Gaussian-informative priors. MC3 can share the same value among multiple parameters and fix the value of parameters to constant values, and offers Gelman-Rubin convergence testing and correlated-noise estimation with time-averaging or wavelet-based likelihood estimation methods.

An Efficient Independence Sampler for Updating Branches in Bayesian Markov chain Monte Carlo Sampling of Phylogenetic Trees.

PubMed

Aberer, Andre J; Stamatakis, Alexandros; Ronquist, Fredrik

2016-01-01

Sampling tree space is the most challenging aspect of Bayesian phylogenetic inference. The sheer number of alternative topologies is problematic by itself. In addition, the complex dependency between branch lengths and topology increases the difficulty of moving efficiently among topologies. Current tree proposals are fast but sample new trees using primitive transformations or re-mappings of old branch lengths. This reduces acceptance rates and presumably slows down convergence and mixing. Here, we explore branch proposals that do not rely on old branch lengths but instead are based on approximations of the conditional posterior. Using a diverse set of empirical data sets, we show that most conditional branch posteriors can be accurately approximated via a [Formula: see text] distribution. We empirically determine the relationship between the logarithmic conditional posterior density, its derivatives, and the characteristics of the branch posterior. We use these relationships to derive an independence sampler for proposing branches with an acceptance ratio of ~90% on most data sets. This proposal samples branches between 2× and 3× more efficiently than traditional proposals with respect to the effective sample size per unit of runtime. We also compare the performance of standard topology proposals with hybrid proposals that use the new independence sampler to update those branches that are most affected by the topological change. Our results show that hybrid proposals can sometimes noticeably decrease the number of generations necessary for topological convergence. Inconsistent performance gains indicate that branch updates are not the limiting factor in improving topological convergence for the currently employed set of proposals. However, our independence sampler might be essential for the construction of novel tree proposals that apply more radical topology changes. © The Author(s) 2015. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

PubMed Central

Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William

2014-01-01

Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127

Multinomial mixture model with heterogeneous classification probabilities

USGS Publications Warehouse

Holland, M.D.; Gray, B.R.

2011-01-01

Royle and Link (Ecology 86(9):2505-2512, 2005) proposed an analytical method that allowed estimation of multinomial distribution parameters and classification probabilities from categorical data measured with error. While useful, we demonstrate algebraically and by simulations that this method yields biased multinomial parameter estimates when the probabilities of correct category classifications vary among sampling units. We address this shortcoming by treating these probabilities as logit-normal random variables within a Bayesian framework. We use Markov chain Monte Carlo to compute Bayes estimates from a simulated sample from the posterior distribution. Based on simulations, this elaborated Royle-Link model yields nearly unbiased estimates of multinomial and correct classification probability estimates when classification probabilities are allowed to vary according to the normal distribution on the logit scale or according to the Beta distribution. The method is illustrated using categorical submersed aquatic vegetation data. ?? 2010 Springer Science+Business Media, LLC.

An improved approximate-Bayesian model-choice method for estimating shared evolutionary history

PubMed Central

2014-01-01

Background To understand biological diversification, it is important to account for large-scale processes that affect the evolutionary history of groups of co-distributed populations of organisms. Such events predict temporally clustered divergences times, a pattern that can be estimated using genetic data from co-distributed species. I introduce a new approximate-Bayesian method for comparative phylogeographical model-choice that estimates the temporal distribution of divergences across taxa from multi-locus DNA sequence data. The model is an extension of that implemented in msBayes. Results By reparameterizing the model, introducing more flexible priors on demographic and divergence-time parameters, and implementing a non-parametric Dirichlet-process prior over divergence models, I improved the robustness, accuracy, and power of the method for estimating shared evolutionary history across taxa. Conclusions The results demonstrate the improved performance of the new method is due to (1) more appropriate priors on divergence-time and demographic parameters that avoid prohibitively small marginal likelihoods for models with more divergence events, and (2) the Dirichlet-process providing a flexible prior on divergence histories that does not strongly disfavor models with intermediate numbers of divergence events. The new method yields more robust estimates of posterior uncertainty, and thus greatly reduces the tendency to incorrectly estimate models of shared evolutionary history with strong support. PMID:24992937

BATMAN--an R package for the automated quantification of metabolites from nuclear magnetic resonance spectra using a Bayesian model.

PubMed

Hao, Jie; Astle, William; De Iorio, Maria; Ebbels, Timothy M D

2012-08-01

Nuclear Magnetic Resonance (NMR) spectra are widely used in metabolomics to obtain metabolite profiles in complex biological mixtures. Common methods used to assign and estimate concentrations of metabolites involve either an expert manual peak fitting or extra pre-processing steps, such as peak alignment and binning. Peak fitting is very time consuming and is subject to human error. Conversely, alignment and binning can introduce artefacts and limit immediate biological interpretation of models. We present the Bayesian automated metabolite analyser for NMR spectra (BATMAN), an R package that deconvolutes peaks from one-dimensional NMR spectra, automatically assigns them to specific metabolites from a target list and obtains concentration estimates. The Bayesian model incorporates information on characteristic peak patterns of metabolites and is able to account for shifts in the position of peaks commonly seen in NMR spectra of biological samples. It applies a Markov chain Monte Carlo algorithm to sample from a joint posterior distribution of the model parameters and obtains concentration estimates with reduced error compared with conventional numerical integration and comparable to manual deconvolution by experienced spectroscopists. http://www1.imperial.ac.uk/medicine/people/t.ebbels/ t.ebbels@imperial.ac.uk.

A Bayesian state-space approach for damage detection and classification

NASA Astrophysics Data System (ADS)

Dzunic, Zoran; Chen, Justin G.; Mobahi, Hossein; Büyüköztürk, Oral; Fisher, John W.

2017-11-01

The problem of automatic damage detection in civil structures is complex and requires a system that can interpret collected sensor data into meaningful information. We apply our recently developed switching Bayesian model for dependency analysis to the problems of damage detection and classification. The model relies on a state-space approach that accounts for noisy measurement processes and missing data, which also infers the statistical temporal dependency between measurement locations signifying the potential flow of information within the structure. A Gibbs sampling algorithm is used to simultaneously infer the latent states, parameters of the state dynamics, the dependence graph, and any changes in behavior. By employing a fully Bayesian approach, we are able to characterize uncertainty in these variables via their posterior distribution and provide probabilistic estimates of the occurrence of damage or a specific damage scenario. We also implement a single class classification method which is more realistic for most real world situations where training data for a damaged structure is not available. We demonstrate the methodology with experimental test data from a laboratory model structure and accelerometer data from a real world structure during different environmental and excitation conditions.

A Bayesian framework to estimate diversification rates and their variation through time and space

PubMed Central

2011-01-01

Background Patterns of species diversity are the result of speciation and extinction processes, and molecular phylogenetic data can provide valuable information to derive their variability through time and across clades. Bayesian Markov chain Monte Carlo methods offer a promising framework to incorporate phylogenetic uncertainty when estimating rates of diversification. Results We introduce a new approach to estimate diversification rates in a Bayesian framework over a distribution of trees under various constant and variable rate birth-death and pure-birth models, and test it on simulated phylogenies. Furthermore, speciation and extinction rates and their posterior credibility intervals can be estimated while accounting for non-random taxon sampling. The framework is particularly suitable for hypothesis testing using Bayes factors, as we demonstrate analyzing dated phylogenies of Chondrostoma (Cyprinidae) and Lupinus (Fabaceae). In addition, we develop a model that extends the rate estimation to a meta-analysis framework in which different data sets are combined in a single analysis to detect general temporal and spatial trends in diversification. Conclusions Our approach provides a flexible framework for the estimation of diversification parameters and hypothesis testing while simultaneously accounting for uncertainties in the divergence times and incomplete taxon sampling. PMID:22013891

A novel Pareto-based Bayesian approach on extension of the infogram for extracting repetitive transients

NASA Astrophysics Data System (ADS)

Gu, Xiaohui; Yang, Shaopu; Liu, Yongqiang; Hao, Rujiang

2018-06-01

Two most important signatures of repetitive transients in the vibration signals of a faulty rotating machine are impulsiveness and cyclostationarity. In the newly proposed infogram, the time-domain and frequency-domain spectral negentropy were put forward to characterize these two aspects, respectively. However, in extension of the infogram to Bayesian inference based optimal wavelet filtering, only one spectral negentropy was employed in identifying the informative frequency band. To overcome its drawback, a novel Pareto-based Bayesian approach was proposed in this paper. The Pareto optimal solutions which can simultaneously maximize the time-domain and frequency-domain spectral negentropy were utilized in estimating the posterior wavelet parameters distributions. Moreover, the relationship between the impulsive and cyclostationary signatures was established by the domination. It can help balance the contributions due to these two aspects other than simply synthesize by the average weight in the infogram. Three instance studies including simulated and experimental signals were investigated to illustrate the effectiveness of the proposed method by challenging different noises and interferences. In addition, some comparisons with the aforementioned peer methods were also conducted to show its superiority and robustness in extracting the repetitive transients.

Statistical Bayesian method for reliability evaluation based on ADT data

NASA Astrophysics Data System (ADS)

Lu, Dawei; Wang, Lizhi; Sun, Yusheng; Wang, Xiaohong

2018-05-01

Accelerated degradation testing (ADT) is frequently conducted in the laboratory to predict the products’ reliability under normal operating conditions. Two kinds of methods, degradation path models and stochastic process models, are utilized to analyze degradation data and the latter one is the most popular method. However, some limitations like imprecise solution process and estimation result of degradation ratio still exist, which may affect the accuracy of the acceleration model and the extrapolation value. Moreover, the conducted solution of this problem, Bayesian method, lose key information when unifying the degradation data. In this paper, a new data processing and parameter inference method based on Bayesian method is proposed to handle degradation data and solve the problems above. First, Wiener process and acceleration model is chosen; Second, the initial values of degradation model and parameters of prior and posterior distribution under each level is calculated with updating and iteration of estimation values; Third, the lifetime and reliability values are estimated on the basis of the estimation parameters; Finally, a case study is provided to demonstrate the validity of the proposed method. The results illustrate that the proposed method is quite effective and accuracy in estimating the lifetime and reliability of a product.

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.

A Bayesian Surrogate for Regional Skew in Flood Frequency Analysis

NASA Astrophysics Data System (ADS)

Kuczera, George

1983-06-01

The problem of how to best utilize site and regional flood data to infer the shape parameter of a flood distribution is considered. One approach to this problem is given in Bulletin 17B of the U.S. Water Resources Council (1981) for the log-Pearson distribution. Here a lesser known distribution is considered, namely, the power normal which fits flood data as well as the log-Pearson and has a shape parameter denoted by λ derived from a Box-Cox power transformation. The problem of regionalizing λ is considered from an empirical Bayes perspective where site and regional flood data are used to infer λ. The distortive effects of spatial correlation and heterogeneity of site sampling variance of λ are explicitly studied with spatial correlation being found to be of secondary importance. The end product of this analysis is the posterior distribution of the power normal parameters expressing, in probabilistic terms, what is known about the parameters given site flood data and regional information on λ. This distribution can be used to provide the designer with several types of information. The posterior distribution of the T-year flood is derived. The effect of nonlinearity in λ on inference is illustrated. Because uncertainty in λ is explicitly allowed for, the understatement in confidence limits due to fixing λ (analogous to fixing log skew) is avoided. Finally, it is shown how to obtain the marginal flood distribution which can be used to select a design flood with specified exceedance probability.

Bayesian hierarchical models for regional climate reconstructions of the last glacial maximum

NASA Astrophysics Data System (ADS)

Weitzel, Nils; Hense, Andreas; Ohlwein, Christian

2017-04-01

Spatio-temporal reconstructions of past climate are important for the understanding of the long term behavior of the climate system and the sensitivity to forcing changes. Unfortunately, they are subject to large uncertainties, have to deal with a complex proxy-climate structure, and a physically reasonable interpolation between the sparse proxy observations is difficult. Bayesian Hierarchical Models (BHMs) are a class of statistical models that is well suited for spatio-temporal reconstructions of past climate because they permit the inclusion of multiple sources of information (e.g. records from different proxy types, uncertain age information, output from climate simulations) and quantify uncertainties in a statistically rigorous way. BHMs in paleoclimatology typically consist of three stages which are modeled individually and are combined using Bayesian inference techniques. The data stage models the proxy-climate relation (often named transfer function), the process stage models the spatio-temporal distribution of the climate variables of interest, and the prior stage consists of prior distributions of the model parameters. For our BHMs, we translate well-known proxy-climate transfer functions for pollen to a Bayesian framework. In addition, we can include Gaussian distributed local climate information from preprocessed proxy records. The process stage combines physically reasonable spatial structures from prior distributions with proxy records which leads to a multivariate posterior probability distribution for the reconstructed climate variables. The prior distributions that constrain the possible spatial structure of the climate variables are calculated from climate simulation output. We present results from pseudoproxy tests as well as new regional reconstructions of temperatures for the last glacial maximum (LGM, ˜ 21,000 years BP). These reconstructions combine proxy data syntheses with information from climate simulations for the LGM that were performed in the PMIP3 project. The proxy data syntheses consist either of raw pollen data or of normally distributed climate data from preprocessed proxy records. Future extensions of our method contain the inclusion of other proxy types (transfer functions), the implementation of other spatial interpolation techniques, the use of age uncertainties, and the extension to spatio-temporal reconstructions of the last deglaciation. Our work is part of the PalMod project funded by the German Federal Ministry of Education and Science (BMBF).

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.

Stochastic Modeling of the Environmental Impacts of the Mingtang Tunneling Project

NASA Astrophysics Data System (ADS)

Li, Xiaojun; Li, Yandong; Chang, Ching-Fu; Chen, Ziyang; Tan, Benjamin Zhi Wen; Sege, Jon; Wang, Changhong; Rubin, Yoram

2017-04-01

This paper investigates the environmental impacts of a major tunneling project in China. Of particular interest is the drawdown of the water table, due to its potential impacts on ecosystem health and on agricultural activity. Due to scarcity of data, the study pursues a Bayesian stochastic approach, which is built around a numerical model. We adopted the Bayesian approach with the goal of deriving the posterior distributions of the dependent variables conditional on local data. The choice of the Bayesian approach for this study is somewhat non-trivial because of the scarcity of in-situ measurements. The thought guiding this selection is that prior distributions for the model input variables are valuable tools even if that all inputs are available, the Bayesian approach could provide a good starting point for further updates as and if additional data becomes available. To construct effective priors, a systematic approach was developed and implemented for constructing informative priors based on other, well-documented sites which bear geological and hydrological similarity to the target site (the Mingtang tunneling project). The approach is built around two classes of similarity criteria: a physically-based set of criteria and an additional set covering epistemic criteria. The prior construction strategy was implemented for the hydraulic conductivity of various types of rocks at the site (Granite and Gneiss) and for modeling the geometry and conductivity of the fault zones. Additional elements of our strategy include (1) modeling the water table through bounding surfaces representing upper and lower limits, and (2) modeling the effective conductivity as a random variable (varying between realizations, not in space). The approach was tested successfully against its ability to predict the tunnel infiltration fluxes and against observations of drying soils.

Three-Dimensional Bayesian Geostatistical Aquifer Characterization at the Hanford 300 Area using Tracer Test Data

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

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

2012-06-01

Tracer testing under natural or forced gradient flow holds the potential to provide useful information for characterizing subsurface properties, through monitoring, modeling and interpretation of the tracer plume migration in an aquifer. Non-reactive tracer experiments were conducted at the Hanford 300 Area, along with constant-rate injection tests and electromagnetic borehole flowmeter (EBF) profiling. A Bayesian data assimilation technique, the method of anchored distributions (MAD) [Rubin et al., 2010], was applied to assimilate the experimental tracer test data with the other types of data and to infer the three-dimensional heterogeneous structure of the hydraulic conductivity in the saturated zone of themore » Hanford formation. In this study, the Bayesian prior information on the underlying random hydraulic conductivity field was obtained from previous field characterization efforts using the constant-rate injection tests and the EBF data. The posterior distribution of the conductivity field was obtained by further conditioning the field on the temporal moments of tracer breakthrough curves at various observation wells. MAD was implemented with the massively-parallel three-dimensional flow and transport code PFLOTRAN to cope with the highly transient flow boundary conditions at the site and to meet the computational demands of MAD. A synthetic study proved that the proposed method could effectively invert tracer test data to capture the essential spatial heterogeneity of the three-dimensional hydraulic conductivity field. Application of MAD to actual field data shows that the hydrogeological model, when conditioned on the tracer test data, can reproduce the tracer transport behavior better than the field characterized without the tracer test data. This study successfully demonstrates that MAD can sequentially assimilate multi-scale multi-type field data through a consistent Bayesian framework.« less

Bayesian methods for outliers detection in GNSS time series

NASA Astrophysics Data System (ADS)

Qianqian, Zhang; Qingming, Gui

2013-07-01

This article is concerned with the problem of detecting outliers in GNSS time series based on Bayesian statistical theory. Firstly, a new model is proposed to simultaneously detect different types of outliers based on the conception of introducing different types of classification variables corresponding to the different types of outliers; the problem of outlier detection is converted into the computation of the corresponding posterior probabilities, and the algorithm for computing the posterior probabilities based on standard Gibbs sampler is designed. Secondly, we analyze the reasons of masking and swamping about detecting patches of additive outliers intensively; an unmasking Bayesian method for detecting additive outlier patches is proposed based on an adaptive Gibbs sampler. Thirdly, the correctness of the theories and methods proposed above is illustrated by simulated data and then by analyzing real GNSS observations, such as cycle slips detection in carrier phase data. Examples illustrate that the Bayesian methods for outliers detection in GNSS time series proposed by this paper are not only capable of detecting isolated outliers but also capable of detecting additive outlier patches. Furthermore, it can be successfully used to process cycle slips in phase data, which solves the problem of small cycle slips.

A Bayesian Method for Evaluating and Discovering Disease Loci Associations

PubMed Central

Jiang, Xia; Barmada, M. Michael; Cooper, Gregory F.; Becich, Michael J.

2011-01-01

Background A genome-wide association study (GWAS) typically involves examining representative SNPs in individuals from some population. A GWAS data set can concern a million SNPs and may soon concern billions. Researchers investigate the association of each SNP individually with a disease, and it is becoming increasingly commonplace to also analyze multi-SNP associations. Techniques for handling so many hypotheses include the Bonferroni correction and recently developed Bayesian methods. These methods can encounter problems. Most importantly, they are not applicable to a complex multi-locus hypothesis which has several competing hypotheses rather than only a null hypothesis. A method that computes the posterior probability of complex hypotheses is a pressing need. Methodology/Findings We introduce the Bayesian network posterior probability (BNPP) method which addresses the difficulties. The method represents the relationship between a disease and SNPs using a directed acyclic graph (DAG) model, and computes the likelihood of such models using a Bayesian network scoring criterion. The posterior probability of a hypothesis is computed based on the likelihoods of all competing hypotheses. The BNPP can not only be used to evaluate a hypothesis that has previously been discovered or suspected, but also to discover new disease loci associations. The results of experiments using simulated and real data sets are presented. Our results concerning simulated data sets indicate that the BNPP exhibits both better evaluation and discovery performance than does a p-value based method. For the real data sets, previous findings in the literature are confirmed and additional findings are found. Conclusions/Significance We conclude that the BNPP resolves a pressing problem by providing a way to compute the posterior probability of complex multi-locus hypotheses. A researcher can use the BNPP to determine the expected utility of investigating a hypothesis further. Furthermore, we conclude that the BNPP is a promising method for discovering disease loci associations. PMID:21853025

Investigating genotype specific response in photosynthetic behavior under drought stress and nitrogen limitation in Brassica rapa.

NASA Astrophysics Data System (ADS)

Pleban, J. R.; Mackay, D. S.; Ewers, B. E.; Weinig, C.; Aston, T.

2015-12-01

Challenges in terrestrial ecosystem modeling include characterizing the impact of stress on vegetation and the heterogeneous behavior of different species within the environment. In an effort to address these challenges the impacts of drought and nutrient limitation on the CO2 assimilation of multiple genotypes of Brassica rapa was investigated using the Farquhar Model (FM) of photosynthesis following a Bayesian parameterization and updating scheme. Leaf gas exchange and chlorophyll fluorescence measurements from an unstressed group (well-watered/well-fertilized) and two stressed groups (drought/well-fertilized and well-watered/nutrient limited) were used to estimate FM model parameters. Unstressed individuals were used to initialize Bayesian parameter estimation. Posterior mean estimates yielded a close fit with data as observed assimilation (An) closely matched predicted (Ap) with mean standard error for all individuals ranging from 0.8 to 3.1 μmol CO2 m-2 s-1. Posterior parameter distributions of the unstressed individuals were combined and fit to distributions to establish species level Bayesian priors of FM parameters for testing stress responses. Species level distributions of unstressed group identified mean maximum rates of carboxylation standardized to 25° (Vcmax25) as 101.8 μmol m-2 s-1 (± 29.0) and mean maximum rates of electron transport standardized to 25° (Jmax25) as 319.7 μmol m-2 s-1 (± 64.4). These updated priors were used to test the response of drought and nutrient limitations on assimilation. In the well-watered/nutrient limited group a decrease of 28.0 μmol m-2 s-1 was observed in mean estimate of Vcmax25, a decrease of 27.9 μmol m-2 s-1 in Jmax25 and a decrease in quantum yield from 0.40 mol photon/mol e- in unstressed individuals to 0.14 in the nutrient limited group. In the drought/well-fertilized group a decrease was also observed in Vcmax25 and Jmax25. The genotype specific unstressed and stressed responses were then used to parameterize an ecosystem process model with application at the field scale to investigate mechanisms of stress response in B. rapa by testing a variety of functional forms to limit assimilation in hydraulic or nutrient limited conditions.

Quantifying model-structure- and parameter-driven uncertainties in spring wheat phenology prediction with Bayesian analysis

DOE PAGES

Alderman, Phillip D.; Stanfill, Bryan

2016-10-06

Recent international efforts have brought renewed emphasis on the comparison of different agricultural systems models. Thus far, analysis of model-ensemble simulated results has not clearly differentiated between ensemble prediction uncertainties due to model structural differences per se and those due to parameter value uncertainties. Additionally, despite increasing use of Bayesian parameter estimation approaches with field-scale crop models, inadequate attention has been given to the full posterior distributions for estimated parameters. The objectives of this study were to quantify the impact of parameter value uncertainty on prediction uncertainty for modeling spring wheat phenology using Bayesian analysis and to assess the relativemore » contributions of model-structure-driven and parameter-value-driven uncertainty to overall prediction uncertainty. This study used a random walk Metropolis algorithm to estimate parameters for 30 spring wheat genotypes using nine phenology models based on multi-location trial data for days to heading and days to maturity. Across all cases, parameter-driven uncertainty accounted for between 19 and 52% of predictive uncertainty, while model-structure-driven uncertainty accounted for between 12 and 64%. Here, this study demonstrated the importance of quantifying both model-structure- and parameter-value-driven uncertainty when assessing overall prediction uncertainty in modeling spring wheat phenology. More generally, Bayesian parameter estimation provided a useful framework for quantifying and analyzing sources of prediction uncertainty.« less

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

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

Sub-seasonal-to-seasonal Reservoir Inflow Forecast using Bayesian Hierarchical Hidden Markov Model

NASA Astrophysics Data System (ADS)

Mukhopadhyay, S.; Arumugam, S.

2017-12-01

Sub-seasonal-to-seasonal (S2S) (15-90 days) streamflow forecasting is an emerging area of research that provides seamless information for reservoir operation from weather time scales to seasonal time scales. From an operational perspective, sub-seasonal inflow forecasts are highly valuable as these enable water managers to decide short-term releases (15-30 days), while holding water for seasonal needs (e.g., irrigation and municipal supply) and to meet end-of-the-season target storage at a desired level. We propose a Bayesian Hierarchical Hidden Markov Model (BHHMM) to develop S2S inflow forecasts for the Tennessee Valley Area (TVA) reservoir system. Here, the hidden states are predicted by relevant indices that influence the inflows at S2S time scale. The hidden Markov model also captures the both spatial and temporal hierarchy in predictors that operate at S2S time scale with model parameters being estimated as a posterior distribution using a Bayesian framework. We present our work in two steps, namely single site model and multi-site model. For proof of concept, we consider inflows to Douglas Dam, Tennessee, in the single site model. For multisite model we consider reservoirs in the upper Tennessee valley. Streamflow forecasts are issued and updated continuously every day at S2S time scale. We considered precipitation forecasts obtained from NOAA Climate Forecast System (CFSv2) GCM as predictors for developing S2S streamflow forecasts along with relevant indices for predicting hidden states. Spatial dependence of the inflow series of reservoirs are also preserved in the multi-site model. To circumvent the non-normality of the data, we consider the HMM in a Generalized Linear Model setting. Skill of the proposed approach is tested using split sample validation against a traditional multi-site canonical correlation model developed using the same set of predictors. From the posterior distribution of the inflow forecasts, we also highlight different system behavior under varied global and local scale climatic influences from the developed BHMM.

Propagation of the velocity model uncertainties to the seismic event location

NASA Astrophysics Data System (ADS)

Gesret, A.; Desassis, N.; Noble, M.; Romary, T.; Maisons, C.

2015-01-01

Earthquake hypocentre locations are crucial in many domains of application (academic and industrial) as seismic event location maps are commonly used to delineate faults or fractures. The interpretation of these maps depends on location accuracy and on the reliability of the associated uncertainties. The largest contribution to location and uncertainty errors is due to the fact that the velocity model errors are usually not correctly taken into account. We propose a new Bayesian formulation that integrates properly the knowledge on the velocity model into the formulation of the probabilistic earthquake location. In this work, the velocity model uncertainties are first estimated with a Bayesian tomography of active shot data. We implement a sampling Monte Carlo type algorithm to generate velocity models distributed according to the posterior distribution. In a second step, we propagate the velocity model uncertainties to the seismic event location in a probabilistic framework. This enables to obtain more reliable hypocentre locations as well as their associated uncertainties accounting for picking and velocity model uncertainties. We illustrate the tomography results and the gain in accuracy of earthquake location for two synthetic examples and one real data case study in the context of induced microseismicity.

Diagnostic accuracy of enzyme-linked immunosorbent assay (ELISA) and immunoblot (IB) for the detection of antibodies against Neospora caninum in milk from dairy cows.

PubMed

Chatziprodromidou, I P; Apostolou, T

2018-04-01

The aim of the study was to estimate the sensitivity and specificity of enzyme-linked immunosorbent assay (ELISA) and immunoblot (IB) for detecting antibodies of Neospora caninum in dairy cows, in the absence of a gold standard. The study complies with STRADAS-paratuberculosis guidelines for reporting the accuracy of the test. We tried to apply Bayesian models that do not require conditional independence of the tests under evaluation, but as convergence problems appeared, we used Bayesian methodology, that does not assume conditional dependence of the tests. Informative prior probability distributions were constructed, based on scientific inputs regarding sensitivity and specificity of the IB test and the prevalence of disease in the studied populations. IB sensitivity and specificity were estimated to be 98.8% and 91.3%, respectively, while the respective estimates for ELISA were 60% and 96.7%. A sensitivity analysis, where modified prior probability distributions concerning IB diagnostic accuracy applied, showed a limited effect in posterior assessments. We concluded that ELISA can be used to screen the bulk milk and secondly, IB can be used whenever needed.

Bayesian Inference in the Modern Design of Experiments

NASA Technical Reports Server (NTRS)

DeLoach, Richard

2008-01-01

This paper provides an elementary tutorial overview of Bayesian inference and its potential for application in aerospace experimentation in general and wind tunnel testing in particular. Bayes Theorem is reviewed and examples are provided to illustrate how it can be applied to objectively revise prior knowledge by incorporating insights subsequently obtained from additional observations, resulting in new (posterior) knowledge that combines information from both sources. A logical merger of Bayesian methods and certain aspects of Response Surface Modeling is explored. Specific applications to wind tunnel testing, computational code validation, and instrumentation calibration are discussed.

Wave-height hazard analysis in Eastern Coast of Spain - Bayesian approach using generalized Pareto distribution

NASA Astrophysics Data System (ADS)

Egozcue, J. J.; Pawlowsky-Glahn, V.; Ortego, M. I.

2005-03-01

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0.

Sex differences in the development of neuroanatomical functional connectivity underlying intelligence found using Bayesian connectivity analysis.

PubMed

Schmithorst, Vincent J; Holland, Scott K

2007-03-01

A Bayesian method for functional connectivity analysis was adapted to investigate between-group differences. This method was applied in a large cohort of almost 300 children to investigate differences in boys and girls in the relationship between intelligence and functional connectivity for the task of narrative comprehension. For boys, a greater association was shown between intelligence and the functional connectivity linking Broca's area to auditory processing areas, including Wernicke's areas and the right posterior superior temporal gyrus. For girls, a greater association was shown between intelligence and the functional connectivity linking the left posterior superior temporal gyrus to Wernicke's areas bilaterally. A developmental effect was also seen, with girls displaying a positive correlation with age in the association between intelligence and the functional connectivity linking the right posterior superior temporal gyrus to Wernicke's areas bilaterally. Our results demonstrate a sexual dimorphism in the relationship of functional connectivity to intelligence in children and an increasing reliance on inter-hemispheric connectivity in girls with age.

Information and Entropy

NASA Astrophysics Data System (ADS)

Caticha, Ariel

2007-11-01

What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds. This problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), which is designed for updating from arbitrary priors given information in the form of arbitrary constraints, includes as special cases both MaxEnt (which allows arbitrary constraints) and Bayes' rule (which allows arbitrary priors). Thus, ME unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme that allows us to handle problems that lie beyond the reach of either of the two methods separately. I conclude with a couple of simple illustrative examples.

Statistical properties of four effect-size measures for mediation models.

PubMed

Miočević, Milica; O'Rourke, Holly P; MacKinnon, David P; Brown, Hendricks C

2018-02-01

This project examined the performance of classical and Bayesian estimators of four effect size measures for the indirect effect in a single-mediator model and a two-mediator model. Compared to the proportion and ratio mediation effect sizes, standardized mediation effect-size measures were relatively unbiased and efficient in the single-mediator model and the two-mediator model. Percentile and bias-corrected bootstrap interval estimates of ab/s Y , and ab(s X )/s Y in the single-mediator model outperformed interval estimates of the proportion and ratio effect sizes in terms of power, Type I error rate, coverage, imbalance, and interval width. For the two-mediator model, standardized effect-size measures were superior to the proportion and ratio effect-size measures. Furthermore, it was found that Bayesian point and interval summaries of posterior distributions of standardized effect-size measures reduced excessive relative bias for certain parameter combinations. The standardized effect-size measures are the best effect-size measures for quantifying mediated effects.

Bayesian estimation of optical properties of the human head via 3D structural MRI

NASA Astrophysics Data System (ADS)

Barnett, Alexander H.; Culver, Joseph P.; Sorensen, A. Gregory; Dale, Anders M.; Boas, David A.

2003-10-01

Knowledge of the baseline optical properties of the tissues of the human head is essential for absolute cerebral oximetry, and for quantitative studies of brain activation. In this work we numerically model the utility of signals from a small 6-optode time-resolved diffuse optical tomographic apparatus for inferring baseline scattering and absorption coefficients of the scalp, skull and brain, when complete geometric information is available from magnetic resonance imaging (MRI). We use an optical model where MRI-segmented tissues are assumed homogeneous. We introduce a noise model capturing both photon shot noise and forward model numerical accuracy, and use Bayesian inference to predict errorbars and correlations on the measurments. We also sample from the full posterior distribution using Markov chain Monte Carlo. We conclude that ~ 106 detected photons are sufficient to measure the brain"s scattering and absorption to a few percent. We present preliminary results using a fast multi-layer slab model, comparing the case when layer thicknesses are known versus unknown.

COSMOABC: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Ishida, E. E. O.; Vitenti, S. D. P.; Penna-Lima, M.; Cisewski, J.; de Souza, R. S.; Trindade, A. M. M.; Cameron, E.; Busti, V. C.; COIN Collaboration

2015-11-01

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogues. Here we present COSMOABC, a Python ABC sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code is very flexible and can be easily coupled to an external simulator, while allowing to incorporate arbitrary distance and prior functions. As an example of practical application, we coupled COSMOABC with the NUMCOSMO library and demonstrate how it can be used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function. COSMOABC is published under the GPLv3 license on PyPI and GitHub and documentation is available at http://goo.gl/SmB8EX.

MultiNest: Efficient and Robust Bayesian Inference

NASA Astrophysics Data System (ADS)

Feroz, F.; Hobson, M. P.; Bridges, M.

2011-09-01

We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson (2008), which itself significantly outperformed existing MCMC techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm is demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla LambdaCDM model to include spatial curvature and a varying equation of state for dark energy. The MultiNest software is fully parallelized using MPI and includes an interface to CosmoMC. It will also be released as part of the SuperBayeS package, for the analysis of supersymmetric theories of particle physics, at this http URL.

A taxonomic monograph of Nearctic Scolytus Geoffroy (Coleoptera, Curculionidae, Scolytinae).

PubMed

Smith, Sarah M; Cognato, Anthony I

2014-01-01

The Nearctic bark beetle genus Scolytus Geoffroy was revised based in part on a molecular and morphological phylogeny. Monophyly of the native species was tested using mitochondrial (COI) and nuclear (28S, CAD, ArgK) genes and 43 morphological characters in parsimony and Bayesian phylogenetic analyses. Parsimony analyses of molecular and combined datasets provided mixed results while Bayesian analysis recovered most nodes with posterior probabilities >90%. Native hardwood- and conifer-feeding Scolytus species were recovered as paraphyletic. Native Nearctic species were recovered as paraphyletic with hardwood-feeding species sister to Palearctic hardwood-feeding species rather than to native conifer-feeding species. The Nearctic conifer-feeding species were monophyletic. Twenty-five species were recognized. Four new synonyms were discovered: Scolytuspraeceps LeConte, 1868 (= Scolytusabietis Blackman, 1934; = Scolytusopacus Blackman, 1934), Scolytusreflexus Blackman, 1934 (= Scolytusvirgatus Bright, 1972; = Scolytuswickhami Blackman, 1934). Two species were reinstated: Scolytusfiskei Blackman, 1934 and Scolytussilvaticus Bright, 1972. A diagnosis, description, distribution, host records and images were provided for each species and a key is presented to all species.

Bayesian assurance and sample size determination in the process validation life-cycle.

PubMed

Faya, Paul; Seaman, John W; Stamey, James D

2017-01-01

Validation of pharmaceutical manufacturing processes is a regulatory requirement and plays a key role in the assurance of drug quality, safety, and efficacy. The FDA guidance on process validation recommends a life-cycle approach which involves process design, qualification, and verification. The European Medicines Agency makes similar recommendations. The main purpose of process validation is to establish scientific evidence that a process is capable of consistently delivering a quality product. A major challenge faced by manufacturers is the determination of the number of batches to be used for the qualification stage. In this article, we present a Bayesian assurance and sample size determination approach where prior process knowledge and data are used to determine the number of batches. An example is presented in which potency uniformity data is evaluated using a process capability metric. By using the posterior predictive distribution, we simulate qualification data and make a decision on the number of batches required for a desired level of assurance.

Planck intermediate results. XVI. Profile likelihoods for cosmological parameters

NASA Astrophysics Data System (ADS)

Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartlett, J. G.; Battaner, E.; Benabed, K.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bonaldi, A.; Bond, J. R.; Bouchet, F. R.; Burigana, C.; Cardoso, J.-F.; Catalano, A.; Chamballu, A.; Chiang, H. C.; Christensen, P. R.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Couchot, F.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Dickinson, C.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Dupac, X.; Enßlin, T. A.; Eriksen, H. K.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; González-Nuevo, J.; Górski, K. M.; Gregorio, A.; Gruppuso, A.; Hansen, F. K.; Harrison, D. L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T. S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lawrence, C. R.; Leonardi, R.; Liddle, A.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Martin, P. G.; Martínez-González, E.; Masi, S.; Massardi, M.; Matarrese, S.; Mazzotta, P.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C. A.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski∗, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G. W.; Puget, J.-L.; Rachen, J. P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rouillé d'Orfeuil, B.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Savelainen, M.; Savini, G.; Spencer, L. D.; Spinelli, M.; Starck, J.-L.; Sureau, F.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; White, M.; Yvon, D.; Zacchei, A.; Zonca, A.

2014-06-01

We explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the ΛCDM best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman-Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the cosmic microwave background (CMB) combination (Planck+WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit ∑ mν ≤ 0.26 eV (95% confidence) from the CMB+lensing+BAO data combination.

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.

Bayesian sensitivity analysis methods to evaluate bias due to misclassification and missing data using informative priors and external validation data.

PubMed

Luta, George; Ford, Melissa B; Bondy, Melissa; Shields, Peter G; Stamey, James D

2013-04-01

Recent research suggests that the Bayesian paradigm may be useful for modeling biases in epidemiological studies, such as those due to misclassification and missing data. We used Bayesian methods to perform sensitivity analyses for assessing the robustness of study findings to the potential effect of these two important sources of bias. We used data from a study of the joint associations of radiotherapy and smoking with primary lung cancer among breast cancer survivors. We used Bayesian methods to provide an operational way to combine both validation data and expert opinion to account for misclassification of the two risk factors and missing data. For comparative purposes we considered a "full model" that allowed for both misclassification and missing data, along with alternative models that considered only misclassification or missing data, and the naïve model that ignored both sources of bias. We identified noticeable differences between the four models with respect to the posterior distributions of the odds ratios that described the joint associations of radiotherapy and smoking with primary lung cancer. Despite those differences we found that the general conclusions regarding the pattern of associations were the same regardless of the model used. Overall our results indicate a nonsignificantly decreased lung cancer risk due to radiotherapy among nonsmokers, and a mildly increased risk among smokers. We described easy to implement Bayesian methods to perform sensitivity analyses for assessing the robustness of study findings to misclassification and missing data. Copyright © 2012 Elsevier Ltd. All rights reserved.

Bayesian Estimation of Small Effects in Exercise and Sports Science.

PubMed

Mengersen, Kerrie L; Drovandi, Christopher C; Robert, Christian P; Pyne, David B; Gore, Christopher J

2016-01-01

The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a 'magnitude-based inference' approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements.

Geographic analysis of shigellosis in Vietnam.

PubMed

Kim, Deok Ryun; Ali, Mohammad; Thiem, Vu Dinh; Park, Jin-Kyung; von Seidlein, Lorenz; Clemens, John

2008-12-01

Geographic and ecological analysis may provide investigators useful ecological information for the control of shigellosis. This paper provides distribution of individual Shigella species in space, and ecological covariates for shigellosis in Nha Trang, Vietnam. Data on shigellosis in neighborhoods were used to identify ecological covariates. A Bayesian hierarchical model was used to obtain joint posterior distribution of model parameters and to construct smoothed risk maps for shigellosis. Neighborhoods with a high proportion of worshippers of traditional religion, close proximity to hospital, or close proximity to the river had increased risk for shigellosis. The ecological covariates associated with Shigella flexneri differed from the covariates for Shigella sonnei. In contrast the spatial distribution of the two species was similar. The disease maps can help identify high-risk areas of shigellosis that can be targeted for interventions. This approach may be useful for the selection of populations and the analysis of vaccine trials.

On the statistical properties of viral misinformation in online social media

NASA Astrophysics Data System (ADS)

Bessi, Alessandro

2017-03-01

The massive diffusion of online social media allows for the rapid and uncontrolled spreading of conspiracy theories, hoaxes, unsubstantiated claims, and false news. Such an impressive amount of misinformation can influence policy preferences and encourage behaviors strongly divergent from recommended practices. In this paper, we study the statistical properties of viral misinformation in online social media. By means of methods belonging to Extreme Value Theory, we show that the number of extremely viral posts over time follows a homogeneous Poisson process, and that the interarrival times between such posts are independent and identically distributed, following an exponential distribution. Moreover, we characterize the uncertainty around the rate parameter of the Poisson process through Bayesian methods. Finally, we are able to derive the predictive posterior probability distribution of the number of posts exceeding a certain threshold of shares over a finite interval of time.

Ancestral sequence reconstruction in primate mitochondrial DNA: compositional bias and effect on functional inference.

PubMed

Krishnan, Neeraja M; Seligmann, Hervé; Stewart, Caro-Beth; De Koning, A P Jason; Pollock, David D

2004-10-01

Reconstruction of ancestral DNA and amino acid sequences is an important means of inferring information about past evolutionary events. Such reconstructions suggest changes in molecular function and evolutionary processes over the course of evolution and are used to infer adaptation and convergence. Maximum likelihood (ML) is generally thought to provide relatively accurate reconstructed sequences compared to parsimony, but both methods lead to the inference of multiple directional changes in nucleotide frequencies in primate mitochondrial DNA (mtDNA). To better understand this surprising result, as well as to better understand how parsimony and ML differ, we constructed a series of computationally simple "conditional pathway" methods that differed in the number of substitutions allowed per site along each branch, and we also evaluated the entire Bayesian posterior frequency distribution of reconstructed ancestral states. We analyzed primate mitochondrial cytochrome b (Cyt-b) and cytochrome oxidase subunit I (COI) genes and found that ML reconstructs ancestral frequencies that are often more different from tip sequences than are parsimony reconstructions. In contrast, frequency reconstructions based on the posterior ensemble more closely resemble extant nucleotide frequencies. Simulations indicate that these differences in ancestral sequence inference are probably due to deterministic bias caused by high uncertainty in the optimization-based ancestral reconstruction methods (parsimony, ML, Bayesian maximum a posteriori). In contrast, ancestral nucleotide frequencies based on an average of the Bayesian set of credible ancestral sequences are much less biased. The methods involving simpler conditional pathway calculations have slightly reduced likelihood values compared to full likelihood calculations, but they can provide fairly unbiased nucleotide reconstructions and may be useful in more complex phylogenetic analyses than considered here due to their speed and flexibility. To determine whether biased reconstructions using optimization methods might affect inferences of functional properties, ancestral primate mitochondrial tRNA sequences were inferred and helix-forming propensities for conserved pairs were evaluated in silico. For ambiguously reconstructed nucleotides at sites with high base composition variability, ancestral tRNA sequences from Bayesian analyses were more compatible with canonical base pairing than were those inferred by other methods. Thus, nucleotide bias in reconstructed sequences apparently can lead to serious bias and inaccuracies in functional predictions.

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.

Uncertainty estimation of Intensity-Duration-Frequency relationships: A regional analysis

NASA Astrophysics Data System (ADS)

Mélèse, Victor; Blanchet, Juliette; Molinié, Gilles

2018-03-01

We propose in this article a regional study of uncertainties in IDF curves derived from point-rainfall maxima. We develop two generalized extreme value models based on the simple scaling assumption, first in the frequentist framework and second in the Bayesian framework. Within the frequentist framework, uncertainties are obtained i) from the Gaussian density stemming from the asymptotic normality theorem of the maximum likelihood and ii) with a bootstrap procedure. Within the Bayesian framework, uncertainties are obtained from the posterior densities. We confront these two frameworks on the same database covering a large region of 100, 000 km2 in southern France with contrasted rainfall regime, in order to be able to draw conclusion that are not specific to the data. The two frameworks are applied to 405 hourly stations with data back to the 1980's, accumulated in the range 3 h-120 h. We show that i) the Bayesian framework is more robust than the frequentist one to the starting point of the estimation procedure, ii) the posterior and the bootstrap densities are able to better adjust uncertainty estimation to the data than the Gaussian density, and iii) the bootstrap density give unreasonable confidence intervals, in particular for return levels associated to large return period. Therefore our recommendation goes towards the use of the Bayesian framework to compute uncertainty.

Incorporating external evidence in trial-based cost-effectiveness analyses: the use of resampling methods

PubMed Central

2014-01-01

Background Cost-effectiveness analyses (CEAs) that use patient-specific data from a randomized controlled trial (RCT) are popular, yet such CEAs are criticized because they neglect to incorporate evidence external to the trial. A popular method for quantifying uncertainty in a RCT-based CEA is the bootstrap. The objective of the present study was to further expand the bootstrap method of RCT-based CEA for the incorporation of external evidence. Methods We utilize the Bayesian interpretation of the bootstrap and derive the distribution for the cost and effectiveness outcomes after observing the current RCT data and the external evidence. We propose simple modifications of the bootstrap for sampling from such posterior distributions. Results In a proof-of-concept case study, we use data from a clinical trial and incorporate external evidence on the effect size of treatments to illustrate the method in action. Compared to the parametric models of evidence synthesis, the proposed approach requires fewer distributional assumptions, does not require explicit modeling of the relation between external evidence and outcomes of interest, and is generally easier to implement. A drawback of this approach is potential computational inefficiency compared to the parametric Bayesian methods. Conclusions The bootstrap method of RCT-based CEA can be extended to incorporate external evidence, while preserving its appealing features such as no requirement for parametric modeling of cost and effectiveness outcomes. PMID:24888356

Incorporating external evidence in trial-based cost-effectiveness analyses: the use of resampling methods.

PubMed

Sadatsafavi, Mohsen; Marra, Carlo; Aaron, Shawn; Bryan, Stirling

2014-06-03

Cost-effectiveness analyses (CEAs) that use patient-specific data from a randomized controlled trial (RCT) are popular, yet such CEAs are criticized because they neglect to incorporate evidence external to the trial. A popular method for quantifying uncertainty in a RCT-based CEA is the bootstrap. The objective of the present study was to further expand the bootstrap method of RCT-based CEA for the incorporation of external evidence. We utilize the Bayesian interpretation of the bootstrap and derive the distribution for the cost and effectiveness outcomes after observing the current RCT data and the external evidence. We propose simple modifications of the bootstrap for sampling from such posterior distributions. In a proof-of-concept case study, we use data from a clinical trial and incorporate external evidence on the effect size of treatments to illustrate the method in action. Compared to the parametric models of evidence synthesis, the proposed approach requires fewer distributional assumptions, does not require explicit modeling of the relation between external evidence and outcomes of interest, and is generally easier to implement. A drawback of this approach is potential computational inefficiency compared to the parametric Bayesian methods. The bootstrap method of RCT-based CEA can be extended to incorporate external evidence, while preserving its appealing features such as no requirement for parametric modeling of cost and effectiveness outcomes.

Observing Inflationary Reheating

NASA Astrophysics Data System (ADS)

Martin, Jérôme; Ringeval, Christophe; Vennin, Vincent

2015-02-01

Reheating is the epoch which connects inflation to the subsequent hot big-bang phase. Conceptually very important, this era is, however, observationally poorly known. We show that the current Planck satellite measurements of the cosmic microwave background (CMB) anisotropies constrain the kinematic properties of the reheating era for most of the inflationary models. This result is obtained by deriving the marginalized posterior distributions of the reheating parameter for about 200 models of slow-roll inflation. Weighted by the statistical evidence of each model to explain the data, we show that the Planck 2013 measurements induce an average reduction of the posterior-to-prior volume by 40%. Making some additional assumptions on reheating, such as specifying a mean equation of state parameter, or focusing the analysis on peculiar scenarios, can enhance or reduce this constraint. Our study also indicates that the Bayesian evidence of a model can substantially be affected by the reheating properties. The precision of the current CMB data is therefore such that estimating the observational performance of a model now requires incorporating information about its reheating history.

Systematic influences of gamma-ray spectrometry data near the decision threshold for radioactivity measurements in the environment.

PubMed

Zorko, Benjamin; Korun, Matjaž; Mora Canadas, Juan Carlos; Nicoulaud-Gouin, Valerie; Chyly, Pavol; Blixt Buhr, Anna Maria; Lager, Charlotte; Aquilonius, Karin; Krajewski, Pawel

2016-07-01

Several methods for reporting outcomes of gamma-ray spectrometric measurements of environmental samples for dose calculations are presented and discussed. The measurement outcomes can be reported as primary measurement results, primary measurement results modified according to the quantification limit, best estimates obtained by the Bayesian posterior (ISO 11929), best estimates obtained by the probability density distribution resembling shifting, and the procedure recommended by the European Commission (EC). The annual dose is calculated from the arithmetic average using any of these five procedures. It was shown that the primary measurement results modified according to the quantification limit could lead to an underestimation of the annual dose. On the other hand the best estimates lead to an overestimation of the annual dose. The annual doses calculated from the measurement outcomes obtained according to the EC's recommended procedure, which does not cope with the uncertainties, fluctuate between an under- and overestimation, depending on the frequency of the measurement results that are larger than the limit of detection. In the extreme case, when no measurement results above the detection limit occur, the average over primary measurement results modified according to the quantification limit underestimates the average over primary measurement results for about 80%. The average over best estimates calculated according the procedure resembling shifting overestimates the average over primary measurement results for 35%, the average obtained by the Bayesian posterior for 85% and the treatment according to the EC recommendation for 89%. Copyright © 2016 Elsevier Ltd. All rights reserved.

The comparative evidence basis for the efficacy of second-generation antidepressants in the treatment of depression in the US: A Bayesian meta-analysis of Food and Drug Administration reviews.

PubMed

Monden, Rei; Roest, Annelieke M; van Ravenzwaaij, Don; Wagenmakers, Eric-Jan; Morey, Richard; Wardenaar, Klaas J; de Jonge, Peter

2018-08-01

Studies have shown similar efficacy of different antidepressants in the treatment of depression. Data of phase-2 and -3 clinical-trials for 16 antidepressants (levomilnacipran, desvenlafaxine, duloxetine, venlafaxine, paroxetine, escitalopram, vortioxetine, mirtazapine, venlafaxine XR, sertraline, fluoxetine, citalopram, paroxetine CR, nefazodone, bupropion, vilazodone), approved by the FDA for the treatment of depression between 1987 and 2016, were extracted from the FDA reviews that were used to evaluate efficacy prior to marketing approval, which are less liable to reporting biases. Meta-analytic Bayes factors, which quantify the strength of evidence for efficacy, were calculated. In addition, posterior pooled effect-sizes were calculated and compared with classical estimations. The resulted Bayes factors showed that the evidence load for efficacy varied strongly across antidepressants. However, all tested drugs except for bupropion and vilazodone showed strong evidence for their efficacy. The posterior effect-size distributions showed variation across antidepressants, with the highest pooled estimated effect size for venlafaxine followed by paroxetine, and the lowest for bupropion and vilazodone. Not all published trials were included in the study. The results illustrate the importance of considering both the effect size and the evidence-load when judging the efficacy of a treatment. In doing so, the currently employed Bayesian approach provided clear insights on top of those gained with traditional approaches. Copyright © 2018 Elsevier B.V. All rights reserved.

Bayesian Analysis of Evolutionary Divergence with Genomic Data under Diverse Demographic Models.

PubMed

Chung, Yujin; Hey, Jody

2017-06-01

We present a new Bayesian method for estimating demographic and phylogenetic history using population genomic data. Several key innovations are introduced that allow the study of diverse models within an Isolation-with-Migration framework. The new method implements a 2-step analysis, with an initial Markov chain Monte Carlo (MCMC) phase that samples simple coalescent trees, followed by the calculation of the joint posterior density for the parameters of a demographic model. In step 1, the MCMC sampling phase, the method uses a reduced state space, consisting of coalescent trees without migration paths, and a simple importance sampling distribution without the demography of interest. Once obtained, a single sample of trees can be used in step 2 to calculate the joint posterior density for model parameters under multiple diverse demographic models, without having to repeat MCMC runs. Because migration paths are not included in the state space of the MCMC phase, but rather are handled by analytic integration in step 2 of the analysis, the method is scalable to a large number of loci with excellent MCMC mixing properties. With an implementation of the new method in the computer program MIST, we demonstrate the method's accuracy, scalability, and other advantages using simulated data and DNA sequences of two common chimpanzee subspecies: Pan troglodytes (P. t.) troglodytes and P. t. verus. © The Author 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

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.

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.

Quantifying temporal trends in fisheries abundance using Bayesian dynamic linear models: A case study of riverine Smallmouth Bass populations

USGS Publications Warehouse

Schall, Megan K.; Blazer, Vicki S.; Lorantas, Robert M.; Smith, Geoffrey; Mullican, John E.; Keplinger, Brandon J.; Wagner, Tyler

2018-01-01

Detecting temporal changes in fish abundance is an essential component of fisheries management. Because of the need to understand short‐term and nonlinear changes in fish abundance, traditional linear models may not provide adequate information for management decisions. This study highlights the utility of Bayesian dynamic linear models (DLMs) as a tool for quantifying temporal dynamics in fish abundance. To achieve this goal, we quantified temporal trends of Smallmouth Bass Micropterus dolomieu catch per effort (CPE) from rivers in the mid‐Atlantic states, and we calculated annual probabilities of decline from the posterior distributions of annual rates of change in CPE. We were interested in annual declines because of recent concerns about fish health in portions of the study area. In general, periods of decline were greatest within the Susquehanna River basin, Pennsylvania. The declines in CPE began in the late 1990s—prior to observations of fish health problems—and began to stabilize toward the end of the time series (2011). In contrast, many of the other rivers investigated did not have the same magnitude or duration of decline in CPE. Bayesian DLMs provide information about annual changes in abundance that can inform management and are easily communicated with managers and stakeholders.

Profile-Based LC-MS Data Alignment—A Bayesian Approach

PubMed Central

Tsai, Tsung-Heng; Tadesse, Mahlet G.; Wang, Yue; Ressom, Habtom W.

2014-01-01

A Bayesian alignment model (BAM) is proposed for alignment of liquid chromatography-mass spectrometry (LC-MS) data. BAM belongs to the category of profile-based approaches, which are composed of two major components: a prototype function and a set of mapping functions. Appropriate estimation of these functions is crucial for good alignment results. BAM uses Markov chain Monte Carlo (MCMC) methods to draw inference on the model parameters and improves on existing MCMC-based alignment methods through 1) the implementation of an efficient MCMC sampler and 2) an adaptive selection of knots. A block Metropolis-Hastings algorithm that mitigates the problem of the MCMC sampler getting stuck at local modes of the posterior distribution is used for the update of the mapping function coefficients. In addition, a stochastic search variable selection (SSVS) methodology is used to determine the number and positions of knots. We applied BAM to a simulated data set, an LC-MS proteomic data set, and two LC-MS metabolomic data sets, and compared its performance with the Bayesian hierarchical curve registration (BHCR) model, the dynamic time-warping (DTW) model, and the continuous profile model (CPM). The advantage of applying appropriate profile-based retention time correction prior to performing a feature-based approach is also demonstrated through the metabolomic data sets. PMID:23929872

A Bayesian framework based on a Gaussian mixture model and radial-basis-function Fisher discriminant analysis (BayGmmKda V1.1) for spatial prediction of floods

NASA Astrophysics Data System (ADS)

Tien Bui, Dieu; Hoang, Nhat-Duc

2017-09-01

In this study, a probabilistic model, named as BayGmmKda, is proposed for flood susceptibility assessment in a study area in central Vietnam. The new model is a Bayesian framework constructed by a combination of a Gaussian mixture model (GMM), radial-basis-function Fisher discriminant analysis (RBFDA), and a geographic information system (GIS) database. In the Bayesian framework, GMM is used for modeling the data distribution of flood-influencing factors in the GIS database, whereas RBFDA is utilized to construct a latent variable that aims at enhancing the model performance. As a result, the posterior probabilistic output of the BayGmmKda model is used as flood susceptibility index. Experiment results showed that the proposed hybrid framework is superior to other benchmark models, including the adaptive neuro-fuzzy inference system and the support vector machine. To facilitate the model implementation, a software program of BayGmmKda has been developed in MATLAB. The BayGmmKda program can accurately establish a flood susceptibility map for the study region. Accordingly, local authorities can overlay this susceptibility map onto various land-use maps for the purpose of land-use planning or management.

Predictive coarse-graining

NASA Astrophysics Data System (ADS)

Schöberl, Markus; Zabaras, Nicholas; Koutsourelakis, Phaedon-Stelios

2017-03-01

We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a probabilistic coarse-to-fine map. This corresponds to a directed probabilistic model where the coarse variables play the role of latent generators of the fine scale (all-atom) data. From an information-theoretic perspective, the framework proposed provides an improvement upon the relative entropy method [1] and is capable of quantifying the uncertainty due to the information loss that unavoidably takes place during the coarse-graining process. Furthermore, it can be readily extended to a fully Bayesian model where various sources of uncertainties are reflected in the posterior of the model parameters. The latter can be used to produce not only point estimates of fine-scale reconstructions or macroscopic observables, but more importantly, predictive posterior distributions on these quantities. Predictive posterior distributions reflect the confidence of the model as a function of the amount of data and the level of coarse-graining. The issues of model complexity and model selection are seamlessly addressed by employing a hierarchical prior that favors the discovery of sparse solutions, revealing the most prominent features in the coarse-grained model. A flexible and parallelizable Monte Carlo - Expectation-Maximization (MC-EM) scheme is proposed for carrying out inference and learning tasks. A comparative assessment of the proposed methodology is presented for a lattice spin system and the SPC/E water model.

Predictive coarse-graining

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

Schöberl, Markus, E-mail: m.schoeberl@tum.de; Zabaras, Nicholas; Department of Aerospace and Mechanical Engineering, University of Notre Dame, 365 Fitzpatrick Hall, Notre Dame, IN 46556

We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a probabilistic coarse-to-fine map. This corresponds to a directed probabilistic model where the coarse variables play the role of latent generators of the fine scale (all-atom) data. From an information-theoretic perspective, the framework proposed provides an improvement upon the relative entropy method and is capable of quantifying the uncertainty due to the information loss that unavoidably takes place during the coarse-graining process. Furthermore, it can be readily extendedmore » to a fully Bayesian model where various sources of uncertainties are reflected in the posterior of the model parameters. The latter can be used to produce not only point estimates of fine-scale reconstructions or macroscopic observables, but more importantly, predictive posterior distributions on these quantities. Predictive posterior distributions reflect the confidence of the model as a function of the amount of data and the level of coarse-graining. The issues of model complexity and model selection are seamlessly addressed by employing a hierarchical prior that favors the discovery of sparse solutions, revealing the most prominent features in the coarse-grained model. A flexible and parallelizable Monte Carlo – Expectation–Maximization (MC-EM) scheme is proposed for carrying out inference and learning tasks. A comparative assessment of the proposed methodology is presented for a lattice spin system and the SPC/E water model.« less

Characterization of the uncertainty of divergence time estimation under relaxed molecular clock models using multiple loci.

PubMed

Zhu, Tianqi; Dos Reis, Mario; Yang, Ziheng

2015-03-01

Genetic sequence data provide information about the distances between species or branch lengths in a phylogeny, but not about the absolute divergence times or the evolutionary rates directly. Bayesian methods for dating species divergences estimate times and rates by assigning priors on them. In particular, the prior on times (node ages on the phylogeny) incorporates information in the fossil record to calibrate the molecular tree. Because times and rates are confounded, our posterior time estimates will not approach point values even if an infinite amount of sequence data are used in the analysis. In a previous study we developed a finite-sites theory to characterize the uncertainty in Bayesian divergence time estimation in analysis of large but finite sequence data sets under a strict molecular clock. As most modern clock dating analyses use more than one locus and are conducted under relaxed clock models, here we extend the theory to the case of relaxed clock analysis of data from multiple loci (site partitions). Uncertainty in posterior time estimates is partitioned into three sources: Sampling errors in the estimates of branch lengths in the tree for each locus due to limited sequence length, variation of substitution rates among lineages and among loci, and uncertainty in fossil calibrations. Using a simple but analogous estimation problem involving the multivariate normal distribution, we predict that as the number of loci ([Formula: see text]) goes to infinity, the variance in posterior time estimates decreases and approaches the infinite-data limit at the rate of 1/[Formula: see text], and the limit is independent of the number of sites in the sequence alignment. We then confirmed the predictions by using computer simulation on phylogenies of two or three species, and by analyzing a real genomic data set for six primate species. Our results suggest that with the fossil calibrations fixed, analyzing multiple loci or site partitions is the most effective way for improving the precision of posterior time estimation. However, even if a huge amount of sequence data is analyzed, considerable uncertainty will persist in time estimates. © The Author(s) 2014. Published by Oxford University Press on behalf of the Society of Systematic Biologists.

Three-dimensional Bayesian geostatistical aquifer characterization at the Hanford 300 Area using tracer test data

NASA Astrophysics Data System (ADS)

Chen, Xingyuan; Murakami, Haruko; Hahn, Melanie S.; Hammond, Glenn E.; Rockhold, Mark L.; Zachara, John M.; Rubin, Yoram

2012-06-01

Tracer tests performed under natural or forced gradient flow conditions can provide useful information for characterizing subsurface properties, through monitoring, modeling, and interpretation of the tracer plume migration in an aquifer. Nonreactive tracer experiments were conducted at the Hanford 300 Area, along with constant-rate injection tests and electromagnetic borehole flowmeter tests. A Bayesian data assimilation technique, the method of anchored distributions (MAD) (Rubin et al., 2010), was applied to assimilate the experimental tracer test data with the other types of data and to infer the three-dimensional heterogeneous structure of the hydraulic conductivity in the saturated zone of the Hanford formation.In this study, the Bayesian prior information on the underlying random hydraulic conductivity field was obtained from previous field characterization efforts using constant-rate injection and borehole flowmeter test data. The posterior distribution of the conductivity field was obtained by further conditioning the field on the temporal moments of tracer breakthrough curves at various observation wells. MAD was implemented with the massively parallel three-dimensional flow and transport code PFLOTRAN to cope with the highly transient flow boundary conditions at the site and to meet the computational demands of MAD. A synthetic study proved that the proposed method could effectively invert tracer test data to capture the essential spatial heterogeneity of the three-dimensional hydraulic conductivity field. Application of MAD to actual field tracer data at the Hanford 300 Area demonstrates that inverting for spatial heterogeneity of hydraulic conductivity under transient flow conditions is challenging and more work is needed.

Bayesian Hypothesis Testing

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

Andrews, Stephen A.; Sigeti, David E.

These are a set of slides about Bayesian hypothesis testing, where many hypotheses are tested. The conclusions are the following: The value of the Bayes factor obtained when using the median of the posterior marginal is almost the minimum value of the Bayes factor. The value of τ 2 which minimizes the Bayes factor is a reasonable choice for this parameter. This allows a likelihood ratio to be computed with is the least favorable to H 0.

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

SOMBI: Bayesian identification of parameter relations in unstructured cosmological data

NASA Astrophysics Data System (ADS)

Frank, Philipp; Jasche, Jens; Enßlin, Torsten A.

2016-11-01

This work describes the implementation and application of a correlation determination method based on self organizing maps and Bayesian inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters in unstructured cosmological or astrophysical surveys by automatically identifying data clusters in high-dimensional datasets via the self organizing map neural network algorithm. Parameter relations are then revealed by means of a Bayesian inference within respective identified data clusters. Specifically such relations are assumed to be parametrized as a polynomial of unknown order. The Bayesian approach results in a posterior probability distribution function for respective polynomial coefficients. To decide which polynomial order suffices to describe correlation structures in data, we include a method for model selection, the Bayesian information criterion, to the analysis. The performance of the SOMBI algorithm is tested with mock data. As illustration we also provide applications of our method to cosmological data. In particular, we present results of a correlation analysis between galaxy and active galactic nucleus (AGN) properties provided by the SDSS catalog with the cosmic large-scale-structure (LSS). The results indicate that the combined galaxy and LSS dataset indeed is clustered into several sub-samples of data with different average properties (for example different stellar masses or web-type classifications). The majority of data clusters appear to have a similar correlation structure between galaxy properties and the LSS. In particular we revealed a positive and linear dependency between the stellar mass, the absolute magnitude and the color of a galaxy with the corresponding cosmic density field. A remaining subset of data shows inverted correlations, which might be an artifact of non-linear redshift distortions.

Integrated survival analysis using an event-time approach in a Bayesian framework

USGS Publications Warehouse

Walsh, Daniel P.; Dreitz, VJ; Heisey, Dennis M.

2015-01-01

Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the need for having completely known fate data.

Integrated survival analysis using an event-time approach in a Bayesian framework.

PubMed

Walsh, Daniel P; Dreitz, Victoria J; Heisey, Dennis M

2015-02-01

Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the need for having completely known fate data.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Irving, J.; Koepke, C.; Elsheikh, A. H.

2017-12-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion procedure. In each case, the developed model-error approach enables to remove posterior bias and obtain a more realistic characterization of uncertainty.

Accurate age estimation in small-scale societies

PubMed Central

Smith, Daniel; Gerbault, Pascale; Dyble, Mark; Migliano, Andrea Bamberg; Thomas, Mark G.

2017-01-01

Precise estimation of age is essential in evolutionary anthropology, especially to infer population age structures and understand the evolution of human life history diversity. However, in small-scale societies, such as hunter-gatherer populations, time is often not referred to in calendar years, and accurate age estimation remains a challenge. We address this issue by proposing a Bayesian approach that accounts for age uncertainty inherent to fieldwork data. We developed a Gibbs sampling Markov chain Monte Carlo algorithm that produces posterior distributions of ages for each individual, based on a ranking order of individuals from youngest to oldest and age ranges for each individual. We first validate our method on 65 Agta foragers from the Philippines with known ages, and show that our method generates age estimations that are superior to previously published regression-based approaches. We then use data on 587 Agta collected during recent fieldwork to demonstrate how multiple partial age ranks coming from multiple camps of hunter-gatherers can be integrated. Finally, we exemplify how the distributions generated by our method can be used to estimate important demographic parameters in small-scale societies: here, age-specific fertility patterns. Our flexible Bayesian approach will be especially useful to improve cross-cultural life history datasets for small-scale societies for which reliable age records are difficult to acquire. PMID:28696282

Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 1: Method.

PubMed

Norris, Peter M; da Silva, Arlindo M

2016-07-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.

Monte Carlo Bayesian Inference on a Statistical Model of Sub-Gridcolumn Moisture Variability Using High-Resolution Cloud Observations. Part 1: Method

NASA Technical Reports Server (NTRS)

Norris, Peter M.; Da Silva, Arlindo M.

2016-01-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.

Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 1: Method

PubMed Central

Norris, Peter M.; da Silva, Arlindo M.

2018-01-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC. PMID:29618847

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

Bayesian inference for OPC modeling

NASA Astrophysics Data System (ADS)

Burbine, Andrew; Sturtevant, John; Fryer, David; Smith, Bruce W.

2016-03-01

The use of optical proximity correction (OPC) demands increasingly accurate models of the photolithographic process. Model building and inference techniques in the data science community have seen great strides in the past two decades which make better use of available information. This paper aims to demonstrate the predictive power of Bayesian inference as a method for parameter selection in lithographic models by quantifying the uncertainty associated with model inputs and wafer data. Specifically, the method combines the model builder's prior information about each modelling assumption with the maximization of each observation's likelihood as a Student's t-distributed random variable. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, a model's parameter space is explored to find the most credible parameter values. During parameter exploration, the parameters' posterior distributions are generated by applying Bayes' rule, using a likelihood function and the a priori knowledge supplied. The MCMC algorithm used, an affine invariant ensemble sampler (AIES), is implemented by initializing many walkers which semiindependently explore the space. The convergence of these walkers to global maxima of the likelihood volume determine the parameter values' highest density intervals (HDI) to reveal champion models. We show that this method of parameter selection provides insights into the data that traditional methods do not and outline continued experiments to vet the method.

Accurate age estimation in small-scale societies.

PubMed

Diekmann, Yoan; Smith, Daniel; Gerbault, Pascale; Dyble, Mark; Page, Abigail E; Chaudhary, Nikhil; Migliano, Andrea Bamberg; Thomas, Mark G

2017-08-01

Precise estimation of age is essential in evolutionary anthropology, especially to infer population age structures and understand the evolution of human life history diversity. However, in small-scale societies, such as hunter-gatherer populations, time is often not referred to in calendar years, and accurate age estimation remains a challenge. We address this issue by proposing a Bayesian approach that accounts for age uncertainty inherent to fieldwork data. We developed a Gibbs sampling Markov chain Monte Carlo algorithm that produces posterior distributions of ages for each individual, based on a ranking order of individuals from youngest to oldest and age ranges for each individual. We first validate our method on 65 Agta foragers from the Philippines with known ages, and show that our method generates age estimations that are superior to previously published regression-based approaches. We then use data on 587 Agta collected during recent fieldwork to demonstrate how multiple partial age ranks coming from multiple camps of hunter-gatherers can be integrated. Finally, we exemplify how the distributions generated by our method can be used to estimate important demographic parameters in small-scale societies: here, age-specific fertility patterns. Our flexible Bayesian approach will be especially useful to improve cross-cultural life history datasets for small-scale societies for which reliable age records are difficult to acquire.

Global Sensitivity Analysis and Parameter Calibration for an Ecosystem Carbon Model

NASA Astrophysics Data System (ADS)

Safta, C.; Ricciuto, D. M.; Sargsyan, K.; Najm, H. N.; Debusschere, B.; Thornton, P. E.

2013-12-01

We present uncertainty quantification results for a process-based ecosystem carbon model. The model employs 18 parameters and is driven by meteorological data corresponding to years 1992-2006 at the Harvard Forest site. Daily Net Ecosystem Exchange (NEE) observations were available to calibrate the model parameters and test the performance of the model. Posterior distributions show good predictive capabilities for the calibrated model. A global sensitivity analysis was first performed to determine the important model parameters based on their contribution to the variance of NEE. We then proceed to calibrate the model parameters in a Bayesian framework. The daily discrepancies between measured and predicted NEE values were modeled as independent and identically distributed Gaussians with prescribed daily variance according to the recorded instrument error. All model parameters were assumed to have uninformative priors with bounds set according to expert opinion. The global sensitivity results show that the rate of leaf fall (LEAFALL) is responsible for approximately 25% of the total variance in the average NEE for 1992-2005. A set of 4 other parameters, Nitrogen use efficiency (NUE), base rate for maintenance respiration (BR_MR), growth respiration fraction (RG_FRAC), and allocation to plant stem pool (ASTEM) contribute between 5% and 12% to the variance in average NEE, while the rest of the parameters have smaller contributions. The posterior distributions, sampled with a Markov Chain Monte Carlo algorithm, exhibit significant correlations between model parameters. However LEAFALL, the most important parameter for the average NEE, is not informed by the observational data, while less important parameters show significant updates between their prior and posterior densities. The Fisher information matrix values, indicating which parameters are most informed by the experimental observations, are examined to augment the comparison between the calibration and global sensitivity analysis results.

Variational learning and bits-back coding: an information-theoretic view to Bayesian learning.

PubMed

Honkela, Antti; Valpola, Harri

2004-07-01

The bits-back coding first introduced by Wallace in 1990 and later by Hinton and van Camp in 1993 provides an interesting link between Bayesian learning and information-theoretic minimum-description-length (MDL) learning approaches. The bits-back coding allows interpreting the cost function used in the variational Bayesian method called ensemble learning as a code length in addition to the Bayesian view of misfit of the posterior approximation and a lower bound of model evidence. Combining these two viewpoints provides interesting insights to the learning process and the functions of different parts of the model. In this paper, the problem of variational Bayesian learning of hierarchical latent variable models is used to demonstrate the benefits of the two views. The code-length interpretation provides new views to many parts of the problem such as model comparison and pruning and helps explain many phenomena occurring in learning.

Bayesian enhancement two-stage design for single-arm phase II clinical trials with binary and time-to-event endpoints.

PubMed

Shi, Haolun; Yin, Guosheng

2018-02-21

Simon's two-stage design is one of the most commonly used methods in phase II clinical trials with binary endpoints. The design tests the null hypothesis that the response rate is less than an uninteresting level, versus the alternative hypothesis that the response rate is greater than a desirable target level. From a Bayesian perspective, we compute the posterior probabilities of the null and alternative hypotheses given that a promising result is declared in Simon's design. Our study reveals that because the frequentist hypothesis testing framework places its focus on the null hypothesis, a potentially efficacious treatment identified by rejecting the null under Simon's design could have only less than 10% posterior probability of attaining the desirable target level. Due to the indifference region between the null and alternative, rejecting the null does not necessarily mean that the drug achieves the desirable response level. To clarify such ambiguity, we propose a Bayesian enhancement two-stage (BET) design, which guarantees a high posterior probability of the response rate reaching the target level, while allowing for early termination and sample size saving in case that the drug's response rate is smaller than the clinically uninteresting level. Moreover, the BET design can be naturally adapted to accommodate survival endpoints. We conduct extensive simulation studies to examine the empirical performance of our design and present two trial examples as applications. © 2018, The International Biometric Society.

Coincident Detection Significance in Multimessenger Astronomy

NASA Astrophysics Data System (ADS)

Ashton, G.; Burns, E.; Dal Canton, T.; Dent, T.; Eggenstein, H.-B.; Nielsen, A. B.; Prix, R.; Was, M.; Zhu, S. J.

2018-06-01

We derive a Bayesian criterion for assessing whether signals observed in two separate data sets originate from a common source. The Bayes factor for a common versus unrelated origin of signals includes an overlap integral of the posterior distributions over the common-source parameters. Focusing on multimessenger gravitational-wave astronomy, we apply the method to the spatial and temporal association of independent gravitational-wave and electromagnetic (or neutrino) observations. As an example, we consider the coincidence between the recently discovered gravitational-wave signal GW170817 from a binary neutron star merger and the gamma-ray burst GRB 170817A: we find that the common-source model is enormously favored over a model describing them as unrelated signals.

Strong consistency of nonparametric Bayes density estimation on compact metric spaces with applications to specific manifolds

PubMed Central

Bhattacharya, Abhishek; Dunson, David B.

2012-01-01

This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any continuous density. The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. These conditions are verified on compact Euclidean spaces using multivariate Gaussian kernels, on the hypersphere using a von Mises-Fisher kernel and on the planar shape space using complex Watson kernels. PMID:22984295

Feasibility study of direct spectra measurements for Thomson scattered signals for KSTAR fusion-grade plasmas

NASA Astrophysics Data System (ADS)

Park, K.-R.; Kim, K.-h.; Kwak, S.; Svensson, J.; Lee, J.; Ghim, Y.-c.

2017-11-01

Feasibility study of direct spectra measurements of Thomson scattered photons for fusion-grade plasmas is performed based on a forward model of the KSTAR Thomson scattering system. Expected spectra in the forward model are calculated based on Selden function including the relativistic polarization correction. Noise in the signal is modeled with photon noise and Gaussian electrical noise. Electron temperature and density are inferred using Bayesian probability theory. Based on bias error, full width at half maximum and entropy of posterior distributions, spectral measurements are found to be feasible. Comparisons between spectrometer-based and polychromator-based Thomson scattering systems are performed with varying quantum efficiency and electrical noise levels.

Modeling stream fish distributions using interval-censored detection times.

PubMed

Ferreira, Mário; Filipe, Ana Filipa; Bardos, David C; Magalhães, Maria Filomena; Beja, Pedro

2016-08-01

Controlling for imperfect detection is important for developing species distribution models (SDMs). Occupancy-detection models based on the time needed to detect a species can be used to address this problem, but this is hindered when times to detection are not known precisely. Here, we extend the time-to-detection model to deal with detections recorded in time intervals and illustrate the method using a case study on stream fish distribution modeling. We collected electrofishing samples of six fish species across a Mediterranean watershed in Northeast Portugal. Based on a Bayesian hierarchical framework, we modeled the probability of water presence in stream channels, and the probability of species occupancy conditional on water presence, in relation to environmental and spatial variables. We also modeled time-to-first detection conditional on occupancy in relation to local factors, using modified interval-censored exponential survival models. Posterior distributions of occupancy probabilities derived from the models were used to produce species distribution maps. Simulations indicated that the modified time-to-detection model provided unbiased parameter estimates despite interval-censoring. There was a tendency for spatial variation in detection rates to be primarily influenced by depth and, to a lesser extent, stream width. Species occupancies were consistently affected by stream order, elevation, and annual precipitation. Bayesian P-values and AUCs indicated that all models had adequate fit and high discrimination ability, respectively. Mapping of predicted occupancy probabilities showed widespread distribution by most species, but uncertainty was generally higher in tributaries and upper reaches. The interval-censored time-to-detection model provides a practical solution to model occupancy-detection when detections are recorded in time intervals. This modeling framework is useful for developing SDMs while controlling for variation in detection rates, as it uses simple data that can be readily collected by field ecologists.

THE POSTERIOR DISTRIBUTION OF sin(i) VALUES FOR EXOPLANETS WITH M{sub T} sin(i) DETERMINED FROM RADIAL VELOCITY DATA

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

Ho, Shirley; Turner, Edwin L., E-mail: cwho@lbl.gov

2011-09-20

Radial velocity (RV) observations of an exoplanet system giving a value of M{sub T} sin(i) condition (i.e., give information about) not only the planet's true mass M{sub T} but also the value of sin(i) for that system (where i is the orbital inclination angle). Thus, the value of sin(i) for a system with any particular observed value of M{sub T} sin(i) cannot be assumed to be drawn randomly from a distribution corresponding to an isotropic i distribution, i.e., the presumptive prior distribution. Rather, the posterior distribution from which it is drawn depends on the intrinsic distribution of M{sub T} formore » the exoplanet population being studied. We give a simple Bayesian derivation of this relationship and apply it to several 'toy models' for the intrinsic distribution of M{sub T} , on which we have significant information from available RV data in some mass ranges but little or none in others. The results show that the effect can be an important one. For example, even for simple power-law distributions of M{sub T} , the median value of sin(i) in an observed RV sample can vary between 0.860 and 0.023 (as compared to the 0.866 value for an isotropic i distribution) for indices of the power law in the range between -2 and +1, respectively. Over the same range of indices, the 95% confidence interval on M{sub T} varies from 1.0001-2.405 ({alpha} = -2) to 1.13-94.34 ({alpha} = +2) times larger than M{sub T} sin(i) due to sin(i) uncertainty alone. More complex, but still simple and plausible, distributions of M{sub T} yield more complicated and somewhat unintuitive posterior sin(i) distributions. In particular, if the M{sub T} distribution contains any characteristic mass scale M{sub c} , the posterior sin(i) distribution will depend on the ratio of M{sub T} sin(i) to M{sub c} , often in a non-trivial way. Our qualitative conclusion is that RV studies of exoplanets, both individual objects and statistical samples, should regard the sin(i) factor as more than a 'numerical constant of order unity' with simple and well-understood statistical properties. We argue that reports of M{sub T} sin(i) determinations should be accompanied by a statement of the corresponding confidence bounds on M{sub T} at, say, the 95% level based on an explicitly stated assumed form of the true M{sub T} distribution in order to reflect more accurately the mass uncertainties associated with RV studies.« less

Bayesian analysis of the astrobiological implications of life’s early emergence on Earth

PubMed Central

Spiegel, David S.; Turner, Edwin L.

2012-01-01

Life arose on Earth sometime in the first few hundred million years after the young planet had cooled to the point that it could support water-based organisms on its surface. The early emergence of life on Earth has been taken as evidence that the probability of abiogenesis is high, if starting from young Earth-like conditions. We revisit this argument quantitatively in a Bayesian statistical framework. By constructing a simple model of the probability of abiogenesis, we calculate a Bayesian estimate of its posterior probability, given the data that life emerged fairly early in Earth’s history and that, billions of years later, curious creatures noted this fact and considered its implications. We find that, given only this very limited empirical information, the choice of Bayesian prior for the abiogenesis probability parameter has a dominant influence on the computed posterior probability. Although terrestrial life's early emergence provides evidence that life might be abundant in the universe if early-Earth-like conditions are common, the evidence is inconclusive and indeed is consistent with an arbitrarily low intrinsic probability of abiogenesis for plausible uninformative priors. Finding a single case of life arising independently of our lineage (on Earth, elsewhere in the solar system, or on an extrasolar planet) would provide much stronger evidence that abiogenesis is not extremely rare in the universe. PMID:22198766

Bayesian analysis of the astrobiological implications of life's early emergence on Earth.

PubMed

Spiegel, David S; Turner, Edwin L

2012-01-10

Life arose on Earth sometime in the first few hundred million years after the young planet had cooled to the point that it could support water-based organisms on its surface. The early emergence of life on Earth has been taken as evidence that the probability of abiogenesis is high, if starting from young Earth-like conditions. We revisit this argument quantitatively in a bayesian statistical framework. By constructing a simple model of the probability of abiogenesis, we calculate a bayesian estimate of its posterior probability, given the data that life emerged fairly early in Earth's history and that, billions of years later, curious creatures noted this fact and considered its implications. We find that, given only this very limited empirical information, the choice of bayesian prior for the abiogenesis probability parameter has a dominant influence on the computed posterior probability. Although terrestrial life's early emergence provides evidence that life might be abundant in the universe if early-Earth-like conditions are common, the evidence is inconclusive and indeed is consistent with an arbitrarily low intrinsic probability of abiogenesis for plausible uninformative priors. Finding a single case of life arising independently of our lineage (on Earth, elsewhere in the solar system, or on an extrasolar planet) would provide much stronger evidence that abiogenesis is not extremely rare in the universe.

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.

Unsupervised Bayesian linear unmixing of gene expression microarrays.

PubMed

Bazot, Cécile; Dobigeon, Nicolas; Tourneret, Jean-Yves; Zaas, Aimee K; Ginsburg, Geoffrey S; Hero, Alfred O

2013-03-19

This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters. Firstly, the proposed uBLU method is applied to several simulated datasets with known ground truth and compared with previous factor decomposition methods, such as principal component analysis (PCA), non negative matrix factorization (NMF), Bayesian factor regression modeling (BFRM), and the gradient-based algorithm for general matrix factorization (GB-GMF). Secondly, we illustrate the application of uBLU on a real time-evolving gene expression dataset from a recent viral challenge study in which individuals have been inoculated with influenza A/H3N2/Wisconsin. We show that the uBLU method significantly outperforms the other methods on the simulated and real data sets considered here. The results obtained on synthetic and real data illustrate the accuracy of the proposed uBLU method when compared to other factor decomposition methods from the literature (PCA, NMF, BFRM, and GB-GMF). The uBLU method identifies an inflammatory component closely associated with clinical symptom scores collected during the study. Using a constrained model allows recovery of all the inflammatory genes in a single factor.

Random Partition Distribution Indexed by Pairwise Information

PubMed Central

Dahl, David B.; Day, Ryan; Tsai, Jerry W.

2017-01-01

We propose a random partition distribution indexed by pairwise similarity information such that partitions compatible with the similarities are given more probability. The use of pairwise similarities, in the form of distances, is common in some clustering algorithms (e.g., hierarchical clustering), but we show how to use this type of information to define a prior partition distribution for flexible Bayesian modeling. A defining feature of the distribution is that it allocates probability among partitions within a given number of subsets, but it does not shift probability among sets of partitions with different numbers of subsets. Our distribution places more probability on partitions that group similar items yet keeps the total probability of partitions with a given number of subsets constant. The distribution of the number of subsets (and its moments) is available in closed-form and is not a function of the similarities. Our formulation has an explicit probability mass function (with a tractable normalizing constant) so the full suite of MCMC methods may be used for posterior inference. We compare our distribution with several existing partition distributions, showing that our formulation has attractive properties. We provide three demonstrations to highlight the features and relative performance of our distribution. PMID:29276318

Evolution of the human immunodeficiency virus envelope gene is dominated by purifying selection.

PubMed

Edwards, C T T; Holmes, E C; Pybus, O G; Wilson, D J; Viscidi, R P; Abrams, E J; Phillips, R E; Drummond, A J

2006-11-01

The evolution of the human immunodeficiency virus (HIV-1) during chronic infection involves the rapid, continuous turnover of genetic diversity. However, the role of natural selection, relative to random genetic drift, in governing this process is unclear. We tested a stochastic model of genetic drift using partial envelope sequences sampled longitudinally in 28 infected children. In each case the Bayesian posterior (empirical) distribution of coalescent genealogies was estimated using Markov chain Monte Carlo methods. Posterior predictive simulation was then used to generate a null distribution of genealogies assuming neutrality, with the null and empirical distributions compared using four genealogy-based summary statistics sensitive to nonneutral evolution. Because both null and empirical distributions were generated within a coalescent framework, we were able to explicitly account for the confounding influence of demography. From the distribution of corrected P-values across patients, we conclude that empirical genealogies are more asymmetric than expected if evolution is driven by mutation and genetic drift only, with an excess of low-frequency polymorphisms in the population. This indicates that although drift may still play an important role, natural selection has a strong influence on the evolution of HIV-1 envelope. A negative relationship between effective population size and substitution rate indicates that as the efficacy of selection increases, a smaller proportion of mutations approach fixation in the population. This suggests the presence of deleterious mutations. We therefore conclude that intrahost HIV-1 evolution in envelope is dominated by purifying selection against low-frequency deleterious mutations that do not reach fixation.

Bayesian additive decision trees of biomarker by treatment interactions for predictive biomarker detection and subgroup identification.

PubMed

Zhao, Yang; Zheng, Wei; Zhuo, Daisy Y; Lu, Yuefeng; Ma, Xiwen; Liu, Hengchang; Zeng, Zhen; Laird, Glen

2017-10-11

Personalized medicine, or tailored therapy, has been an active and important topic in recent medical research. Many methods have been proposed in the literature for predictive biomarker detection and subgroup identification. In this article, we propose a novel decision tree-based approach applicable in randomized clinical trials. We model the prognostic effects of the biomarkers using additive regression trees and the biomarker-by-treatment effect using a single regression tree. Bayesian approach is utilized to periodically revise the split variables and the split rules of the decision trees, which provides a better overall fitting. Gibbs sampler is implemented in the MCMC procedure, which updates the prognostic trees and the interaction tree separately. We use the posterior distribution of the interaction tree to construct the predictive scores of the biomarkers and to identify the subgroup where the treatment is superior to the control. Numerical simulations show that our proposed method performs well under various settings comparing to existing methods. We also demonstrate an application of our method in a real clinical trial.

Explicitly integrating parameter, input, and structure uncertainties into Bayesian Neural Networks for probabilistic hydrologic forecasting

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

Zhang, Xuesong; Liang, Faming; Yu, Beibei

2011-11-09

Estimating uncertainty of hydrologic forecasting is valuable to water resources and other relevant decision making processes. Recently, Bayesian Neural Networks (BNNs) have been proved powerful tools for quantifying uncertainty of streamflow forecasting. In this study, we propose a Markov Chain Monte Carlo (MCMC) framework to incorporate the uncertainties associated with input, model structure, and parameter into BNNs. This framework allows the structure of the neural networks to change by removing or adding connections between neurons and enables scaling of input data by using rainfall multipliers. The results show that the new BNNs outperform the BNNs that only consider uncertainties associatedmore » with parameter and model structure. Critical evaluation of posterior distribution of neural network weights, number of effective connections, rainfall multipliers, and hyper-parameters show that the assumptions held in our BNNs are not well supported. Further understanding of characteristics of different uncertainty sources and including output error into the MCMC framework are expected to enhance the application of neural networks for uncertainty analysis of hydrologic forecasting.« less

Bayesian Analysis of the Glacial-Interglacial Methane Increase Constrained by Stable Isotopes and Earth System Modeling

NASA Astrophysics Data System (ADS)

Hopcroft, Peter O.; Valdes, Paul J.; Kaplan, Jed O.

2018-04-01

The observed rise in atmospheric methane (CH4) from 375 ppbv during the Last Glacial Maximum (LGM: 21,000 years ago) to 680 ppbv during the late preindustrial era is not well understood. Atmospheric chemistry considerations implicate an increase in CH4 sources, but process-based estimates fail to reproduce the required amplitude. CH4 stable isotopes provide complementary information that can help constrain the underlying causes of the increase. We combine Earth System model simulations of the late preindustrial and LGM CH4 cycles, including process-based estimates of the isotopic discrimination of vegetation, in a box model of atmospheric CH4 and its isotopes. Using a Bayesian approach, we show how model-based constraints and ice core observations may be combined in a consistent probabilistic framework. The resultant posterior distributions point to a strong reduction in wetland and other biogenic CH4 emissions during the LGM, with a modest increase in the geological source, or potentially natural or anthropogenic fires, accounting for the observed enrichment of δ13CH4.

A Bayesian Network Meta-Analysis to Synthesize the Influence of Contexts of Scaffolding Use on Cognitive Outcomes in STEM Education.

PubMed

Belland, Brian R; Walker, Andrew E; Kim, Nam Ju

2017-12-01

Computer-based scaffolding provides temporary support that enables students to participate in and become more proficient at complex skills like problem solving, argumentation, and evaluation. While meta-analyses have addressed between-subject differences on cognitive outcomes resulting from scaffolding, none has addressed within-subject gains. This leaves much quantitative scaffolding literature not covered by existing meta-analyses. To address this gap, this study used Bayesian network meta-analysis to synthesize within-subjects (pre-post) differences resulting from scaffolding in 56 studies. We generated the posterior distribution using 20,000 Markov Chain Monte Carlo samples. Scaffolding has a consistently strong effect across student populations, STEM (science, technology, engineering, and mathematics) disciplines, and assessment levels, and a strong effect when used with most problem-centered instructional models (exception: inquiry-based learning and modeling visualization) and educational levels (exception: secondary education). Results also indicate some promising areas for future scaffolding research, including scaffolding among students with learning disabilities, for whom the effect size was particularly large (ḡ = 3.13).

Impact of Bayesian Priors on the Characterization of Binary Black Hole Coalescences

NASA Astrophysics Data System (ADS)

Vitale, Salvatore; Gerosa, Davide; Haster, Carl-Johan; Chatziioannou, Katerina; Zimmerman, Aaron

2017-12-01

In a regime where data are only mildly informative, prior choices can play a significant role in Bayesian statistical inference, potentially affecting the inferred physics. We show this is indeed the case for some of the parameters inferred from current gravitational-wave measurements of binary black hole coalescences. We reanalyze the first detections performed by the twin LIGO interferometers using alternative (and astrophysically motivated) prior assumptions. We find different prior distributions can introduce deviations in the resulting posteriors that impact the physical interpretation of these systems. For instance, (i) limits on the 90% credible interval on the effective black hole spin χeff are subject to variations of ˜10 % if a prior with black hole spins mostly aligned to the binary's angular momentum is considered instead of the standard choice of isotropic spin directions, and (ii) under priors motivated by the initial stellar mass function, we infer tighter constraints on the black hole masses, and in particular, we find no support for any of the inferred masses within the putative mass gap M ≲5 M⊙.

A taxonomic monograph of Nearctic Scolytus Geoffroy (Coleoptera, Curculionidae, Scolytinae)

PubMed Central

Smith, Sarah M.; Cognato, Anthony I.

2014-01-01

Abstract The Nearctic bark beetle genus Scolytus Geoffroy was revised based in part on a molecular and morphological phylogeny. Monophyly of the native species was tested using mitochondrial (COI) and nuclear (28S, CAD, ArgK) genes and 43 morphological characters in parsimony and Bayesian phylogenetic analyses. Parsimony analyses of molecular and combined datasets provided mixed results while Bayesian analysis recovered most nodes with posterior probabilities >90%. Native hardwood- and conifer-feeding Scolytus species were recovered as paraphyletic. Native Nearctic species were recovered as paraphyletic with hardwood-feeding species sister to Palearctic hardwood-feeding species rather than to native conifer-feeding species. The Nearctic conifer-feeding species were monophyletic. Twenty-five species were recognized. Four new synonyms were discovered: Scolytus praeceps LeConte, 1868 (= Scolytus abietis Blackman, 1934; = Scolytus opacus Blackman, 1934), Scolytus reflexus Blackman, 1934 (= Scolytus virgatus Bright, 1972; = Scolytus wickhami Blackman, 1934). Two species were reinstated: Scolytus fiskei Blackman, 1934 and Scolytus silvaticus Bright, 1972. A diagnosis, description, distribution, host records and images were provided for each species and a key is presented to all species. PMID:25408617

Impact of Bayesian Priors on the Characterization of Binary Black Hole Coalescences.

PubMed

Vitale, Salvatore; Gerosa, Davide; Haster, Carl-Johan; Chatziioannou, Katerina; Zimmerman, Aaron

2017-12-22

In a regime where data are only mildly informative, prior choices can play a significant role in Bayesian statistical inference, potentially affecting the inferred physics. We show this is indeed the case for some of the parameters inferred from current gravitational-wave measurements of binary black hole coalescences. We reanalyze the first detections performed by the twin LIGO interferometers using alternative (and astrophysically motivated) prior assumptions. We find different prior distributions can introduce deviations in the resulting posteriors that impact the physical interpretation of these systems. For instance, (i) limits on the 90% credible interval on the effective black hole spin χ_{eff} are subject to variations of ∼10% if a prior with black hole spins mostly aligned to the binary's angular momentum is considered instead of the standard choice of isotropic spin directions, and (ii) under priors motivated by the initial stellar mass function, we infer tighter constraints on the black hole masses, and in particular, we find no support for any of the inferred masses within the putative mass gap M≲5  M_{⊙}.

A Bayesian Network Meta-Analysis to Synthesize the Influence of Contexts of Scaffolding Use on Cognitive Outcomes in STEM Education

PubMed Central

Belland, Brian R.; Walker, Andrew E.; Kim, Nam Ju

2017-01-01

Computer-based scaffolding provides temporary support that enables students to participate in and become more proficient at complex skills like problem solving, argumentation, and evaluation. While meta-analyses have addressed between-subject differences on cognitive outcomes resulting from scaffolding, none has addressed within-subject gains. This leaves much quantitative scaffolding literature not covered by existing meta-analyses. To address this gap, this study used Bayesian network meta-analysis to synthesize within-subjects (pre–post) differences resulting from scaffolding in 56 studies. We generated the posterior distribution using 20,000 Markov Chain Monte Carlo samples. Scaffolding has a consistently strong effect across student populations, STEM (science, technology, engineering, and mathematics) disciplines, and assessment levels, and a strong effect when used with most problem-centered instructional models (exception: inquiry-based learning and modeling visualization) and educational levels (exception: secondary education). Results also indicate some promising areas for future scaffolding research, including scaffolding among students with learning disabilities, for whom the effect size was particularly large (ḡ = 3.13). PMID:29200508

A pitfall of piecewise-polytropic equation of state inference

NASA Astrophysics Data System (ADS)

Raaijmakers, Geert; Riley, Thomas E.; Watts, Anna L.

2018-05-01

The only messenger radiation in the Universe which one can use to statistically probe the Equation of State (EOS) of cold dense matter is that originating from the near-field vicinities of compact stars. Constraining gravitational masses and equatorial radii of rotating compact stars is a major goal for current and future telescope missions, with a primary purpose of constraining the EOS. From a Bayesian perspective it is necessary to carefully discuss prior definition; in this context a complicating issue is that in practice there exist pathologies in the general relativistic mapping between spaces of local (interior source matter) and global (exterior spacetime) parameters. In a companion paper, these issues were raised on a theoretical basis. In this study we reproduce a probability transformation procedure from the literature in order to map a joint posterior distribution of Schwarzschild gravitational masses and radii into a joint posterior distribution of EOS parameters. We demonstrate computationally that EOS parameter inferences are sensitive to the choice to define a prior on a joint space of these masses and radii, instead of on a joint space interior source matter parameters. We focus on the piecewise-polytropic EOS model, which is currently standard in the field of astrophysical dense matter study. We discuss the implications of this issue for the field.

An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations

PubMed Central

Farr, W. M.; Mandel, I.; Stevens, D.

2015-01-01

Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient ‘global’ proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580

Know the Planet, Know the Star: Precise Stellar Densities from Kepler Transit Light Curves

NASA Astrophysics Data System (ADS)

Sandford, Emily; Kipping, David

2017-12-01

The properties of a transiting planet’s host star are written in its transit light curve. The light curve can reveal the stellar density ({ρ }* ) and the limb-darkening profile in addition to the characteristics of the planet and its orbit. For planets with strong prior constraints on orbital eccentricity, we may measure these stellar properties directly from the light curve; this method promises to aid greatly in the characterization of transiting planet host stars targeted by the upcoming NASA Transiting Exoplanet Survey Satellite mission and any long-period, singly transiting planets discovered in the same systems. Using Bayesian inference, we fit a transit model, including a nonlinear limb-darkening law, to 66 Kepler transiting planet hosts to measure their stellar properties. We present posterior distributions of ρ *, limb-darkening coefficients, and other system parameters for these stars. We measure densities to within 5% for the majority of our target stars, with the dominant precision-limiting factor being the signal-to-noise ratio of the transits. Of our measured stellar densities, 95% are in 3σ or better agreement with previously published literature values. We make posterior distributions for all of our target Kepler objects of interest available online at 10.5281/zenodo.1028515.

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.

Testing comparative phylogeographic models of marine vicariance and dispersal using a hierarchical Bayesian approach

PubMed Central

2008-01-01

Background Marine allopatric speciation is an enigma because pelagic larval dispersal can potentially connect disjunct populations thereby preventing reproductive and morphological divergence. Here we present a new hierarchical approximate Bayesian computation model (HABC) that tests two hypotheses of marine allopatric speciation: 1.) "soft vicariance", where a speciation involves fragmentation of a large widespread ancestral species range that was previously connected by long distance gene flow; and 2.) peripatric colonization, where speciations in peripheral archipelagos emerge from sweepstakes colonizations from central source regions. The HABC approach analyzes all the phylogeographic datasets at once in order to make across taxon-pair inferences about biogeographic processes while explicitly allowing for uncertainty in the demographic differences within each taxon-pair. Our method uses comparative phylogeographic data that consists of single locus mtDNA sequences from multiple co-distributed taxa containing pairs of central and peripheral populations. We use the method on two comparative phylogeographic data sets consisting of cowrie gastropod endemics co-distributed in the Hawaiian (11 taxon-pairs) and Marquesan archipelagos (7 taxon-pairs). Results Given the Marquesan data, we find strong evidence of simultaneous colonization across all seven cowrie gastropod endemics co-distributed in the Marquesas. In contrast, the lower sample sizes in the Hawaiian data lead to greater uncertainty associated with the Hawaiian estimates. Although, the hyper-parameter estimates point to soft vicariance in a subset of the 11 Hawaiian taxon-pairs, the hyper-prior and hyper-posterior are too similar to make a definitive conclusion. Both results are not inconsistent with what is known about the geologic history of the archipelagos. Simulations verify that our method can successfully distinguish these two histories across a wide range of conditions given sufficient sampling. Conclusion Although soft vicariance and colonization are likely to produce similar genetic patterns when a single taxon-pair is used, our hierarchical Bayesian model can potentially detect if either history is a dominant process across co-distributed taxon-pairs. As comparative phylogeographic datasets grow to include > 100 co-distributed taxon-pairs, the HABC approach will be well suited to dissect temporal patterns in community assembly and evolution, thereby providing a bridge linking comparative phylogeography with community ecology. PMID:19038027

Estimating safety effects of pavement management factors utilizing Bayesian random effect models.

PubMed

Jiang, Ximiao; Huang, Baoshan; Zaretzki, Russell L; Richards, Stephen; Yan, Xuedong

2013-01-01

Previous studies of pavement management factors that relate to the occurrence of traffic-related crashes are rare. Traditional research has mostly employed summary statistics of bidirectional pavement quality measurements in extended longitudinal road segments over a long time period, which may cause a loss of important information and result in biased parameter estimates. The research presented in this article focuses on crash risk of roadways with overall fair to good pavement quality. Real-time and location-specific data were employed to estimate the effects of pavement management factors on the occurrence of crashes. This research is based on the crash data and corresponding pavement quality data for the Tennessee state route highways from 2004 to 2009. The potential temporal and spatial correlations among observations caused by unobserved factors were considered. Overall 6 models were built accounting for no correlation, temporal correlation only, and both the temporal and spatial correlations. These models included Poisson, negative binomial (NB), one random effect Poisson and negative binomial (OREP, ORENB), and two random effect Poisson and negative binomial (TREP, TRENB) models. The Bayesian method was employed to construct these models. The inference is based on the posterior distribution from the Markov chain Monte Carlo (MCMC) simulation. These models were compared using the deviance information criterion. Analysis of the posterior distribution of parameter coefficients indicates that the pavement management factors indexed by Present Serviceability Index (PSI) and Pavement Distress Index (PDI) had significant impacts on the occurrence of crashes, whereas the variable rutting depth was not significant. Among other factors, lane width, median width, type of terrain, and posted speed limit were significant in affecting crash frequency. The findings of this study indicate that a reduction in pavement roughness would reduce the likelihood of traffic-related crashes. Hence, maintaining a low level of pavement roughness is strongly suggested. In addition, the results suggested that the temporal correlation among observations was significant and that the ORENB model outperformed all other models.

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.

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times.

PubMed

dos Reis, Mario; Yang, Ziheng

2011-07-01

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.

A bayesian analysis for identifying DNA copy number variations using a compound poisson process.

PubMed

Chen, Jie; Yiğiter, Ayten; Wang, Yu-Ping; Deng, Hong-Wen

2010-01-01

To study chromosomal aberrations that may lead to cancer formation or genetic diseases, the array-based Comparative Genomic Hybridization (aCGH) technique is often used for detecting DNA copy number variants (CNVs). Various methods have been developed for gaining CNVs information based on aCGH data. However, most of these methods make use of the log-intensity ratios in aCGH data without taking advantage of other information such as the DNA probe (e.g., biomarker) positions/distances contained in the data. Motivated by the specific features of aCGH data, we developed a novel method that takes into account the estimation of a change point or locus of the CNV in aCGH data with its associated biomarker position on the chromosome using a compound Poisson process. We used a Bayesian approach to derive the posterior probability for the estimation of the CNV locus. To detect loci of multiple CNVs in the data, a sliding window process combined with our derived Bayesian posterior probability was proposed. To evaluate the performance of the method in the estimation of the CNV locus, we first performed simulation studies. Finally, we applied our approach to real data from aCGH experiments, demonstrating its applicability.

Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference

NASA Astrophysics Data System (ADS)

Alsing, Justin; Heavens, Alan; Jaffe, Andrew H.

2017-04-01

We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the Canada-France-Hawaii Telescope (CFHTLenS) weak lensing survey - the first application of this method to data. In the first approach, we sample the joint posterior distribution of the shear maps and power spectra by Gibbs sampling, with minimal model assumptions. In the second approach, we sample the joint posterior of the shear maps and cosmological parameters, providing a new, accurate and principled approach to cosmological parameter inference from cosmic shear data. As a first demonstration on data, we perform a two-bin tomographic analysis to constrain cosmological parameters and investigate the possibility of photometric redshift bias in the CFHTLenS data. Under the baseline ΛCDM (Λ cold dark matter) model, we constrain S_8 = σ _8(Ω _m/0.3)^{0.5} = 0.67+0.03-0.03 (68 per cent), consistent with previous CFHTLenS analyses but in tension with Planck. Adding neutrino mass as a free parameter, we are able to constrain ∑mν < 4.6 eV (95 per cent) using CFHTLenS data alone. Including a linear redshift-dependent photo-z bias Δz = p2(z - p1), we find p_1=-0.25+0.53-0.60 and p_2 = -0.15+0.17-0.15, and tension with Planck is only alleviated under very conservative prior assumptions. Neither the non-minimal neutrino mass nor photo-z bias models are significantly preferred by the CFHTLenS (two-bin tomography) data.

Reaction time in ankle movements: a diffusion model analysis

PubMed Central

Michmizos, Konstantinos P.; Krebs, Hermano Igo

2015-01-01

Reaction time (RT) is one of the most commonly used measures of neurological function and dysfunction. Despite the extensive studies on it, no study has ever examined the RT in the ankle. Twenty-two subjects were recruited to perform simple, 2- and 4-choice RT tasks by visually guiding a cursor inside a rectangular target with their ankle. RT did not change with spatial accuracy constraints imposed by different target widths in the direction of the movement. RT increased as a linear function of potential target stimuli, as would be predicted by Hick–Hyman law. Although the slopes of the regressions were similar, the intercept in dorsal–plantar (DP) direction was significantly smaller than the intercept in inversion–eversion (IE) direction. To explain this difference, we used a hierarchical Bayesian estimation of the Ratcliff's (Psychol Rev 85:59, 1978) diffusion model parameters and divided processing time into cognitive components. The model gave a good account of RTs, their distribution and accuracy values, and hence provided a testimony that the non-decision processing time (overlap of posterior distributions between DP and IE < 0.045), the boundary separation (overlap of the posterior distributions < 0.1) and the evidence accumulation rate (overlap of the posterior distributions < 0.01) components of the RT accounted for the intercept difference between DP and IE. The model also proposed that there was no systematic change in non-decision processing time or drift rate when spatial accuracy constraints were altered. The results were in agreement with the memory drum hypothesis and could be further justified neurophysiologically by the larger innervation of the muscles controlling DP movements. This study might contribute to assessing deficits in sensorimotor control of the ankle and enlighten a possible target for correction in the framework of our on-going effort to develop robotic therapeutic interventions to the ankle of children with cerebral palsy. PMID:25030966

Estimating a Markovian Epidemic Model Using Household Serial Interval Data from the Early Phase of an Epidemic

PubMed Central

Black, Andrew J.; Ross, Joshua V.

2013-01-01

The clinical serial interval of an infectious disease is the time between date of symptom onset in an index case and the date of symptom onset in one of its secondary cases. It is a quantity which is commonly collected during a pandemic and is of fundamental importance to public health policy and mathematical modelling. In this paper we present a novel method for calculating the serial interval distribution for a Markovian model of household transmission dynamics. This allows the use of Bayesian MCMC methods, with explicit evaluation of the likelihood, to fit to serial interval data and infer parameters of the underlying model. We use simulated and real data to verify the accuracy of our methodology and illustrate the importance of accounting for household size. The output of our approach can be used to produce posterior distributions of population level epidemic characteristics. PMID:24023679

bayesPop: Probabilistic Population Projections

PubMed Central

Ševčíková, Hana; Raftery, Adrian E.

2016-01-01

We describe bayesPop, an R package for producing probabilistic population projections for all countries. This uses probabilistic projections of total fertility and life expectancy generated by Bayesian hierarchical models. It produces a sample from the joint posterior predictive distribution of future age- and sex-specific population counts, fertility rates and mortality rates, as well as future numbers of births and deaths. It provides graphical ways of summarizing this information, including trajectory plots and various kinds of probabilistic population pyramids. An expression language is introduced which allows the user to produce the predictive distribution of a wide variety of derived population quantities, such as the median age or the old age dependency ratio. The package produces aggregated projections for sets of countries, such as UN regions or trading blocs. The methodology has been used by the United Nations to produce their most recent official population projections for all countries, published in the World Population Prospects. PMID:28077933

Bayesian analysis of Jolly-Seber type models

USGS Publications Warehouse

Matechou, Eleni; Nicholls, Geoff K.; Morgan, Byron J. T.; Collazo, Jaime A.; Lyons, James E.

2016-01-01

We propose the use of finite mixtures of continuous distributions in modelling the process by which new individuals, that arrive in groups, become part of a wildlife population. We demonstrate this approach using a data set of migrating semipalmated sandpipers (Calidris pussila) for which we extend existing stopover models to allow for individuals to have different behaviour in terms of their stopover duration at the site. We demonstrate the use of reversible jump MCMC methods to derive posterior distributions for the model parameters and the models, simultaneously. The algorithm moves between models with different numbers of arrival groups as well as between models with different numbers of behavioural groups. The approach is shown to provide new ecological insights about the stopover behaviour of semipalmated sandpipers but is generally applicable to any population in which animals arrive in groups and potentially exhibit heterogeneity in terms of one or more other processes.

Network inference using informative priors

PubMed Central

Mukherjee, Sach; Speed, Terence P.

2008-01-01

Recent years have seen much interest in the study of systems characterized by multiple interacting components. A class of statistical models called graphical models, in which graphs are used to represent probabilistic relationships between variables, provides a framework for formal inference regarding such systems. In many settings, the object of inference is the network structure itself. This problem of “network inference” is well known to be a challenging one. However, in scientific settings there is very often existing information regarding network connectivity. A natural idea then is to take account of such information during inference. This article addresses the question of incorporating prior information into network inference. We focus on directed models called Bayesian networks, and use Markov chain Monte Carlo to draw samples from posterior distributions over network structures. We introduce prior distributions on graphs capable of capturing information regarding network features including edges, classes of edges, degree distributions, and sparsity. We illustrate our approach in the context of systems biology, applying our methods to network inference in cancer signaling. PMID:18799736

Network inference using informative priors.

PubMed

Mukherjee, Sach; Speed, Terence P

2008-09-23

Recent years have seen much interest in the study of systems characterized by multiple interacting components. A class of statistical models called graphical models, in which graphs are used to represent probabilistic relationships between variables, provides a framework for formal inference regarding such systems. In many settings, the object of inference is the network structure itself. This problem of "network inference" is well known to be a challenging one. However, in scientific settings there is very often existing information regarding network connectivity. A natural idea then is to take account of such information during inference. This article addresses the question of incorporating prior information into network inference. We focus on directed models called Bayesian networks, and use Markov chain Monte Carlo to draw samples from posterior distributions over network structures. We introduce prior distributions on graphs capable of capturing information regarding network features including edges, classes of edges, degree distributions, and sparsity. We illustrate our approach in the context of systems biology, applying our methods to network inference in cancer signaling.

Bayesian assessment of overtriage and undertriage at a level I trauma centre.

PubMed

DiDomenico, Paul B; Pietzsch, Jan B; Paté-Cornell, M Elisabeth

2008-07-13

We analysed the trauma triage system at a specific level I trauma centre to assess rates of over- and undertriage and to support recommendations for system improvements. The triage process is designed to estimate the severity of patient injury and allocate resources accordingly, with potential errors of overestimation (overtriage) consuming excess resources and underestimation (undertriage) potentially leading to medical errors.We first modelled the overall trauma system using risk analysis methods to understand interdependencies among the actions of the participants. We interviewed six experienced trauma surgeons to obtain their expert opinion of the over- and undertriage rates occurring in the trauma centre. We then assessed actual over- and undertriage rates in a random sample of 86 trauma cases collected over a six-week period at the same centre. We employed Bayesian analysis to quantitatively combine the data with the prior probabilities derived from expert opinion in order to obtain posterior distributions. The results were estimates of overtriage and undertriage in 16.1 and 4.9% of patients, respectively. This Bayesian approach, which provides a quantitative assessment of the error rates using both case data and expert opinion, provides a rational means of obtaining a best estimate of the system's performance. The overall approach that we describe in this paper can be employed more widely to analyse complex health care delivery systems, with the objective of reduced errors, patient risk and excess costs.

A Poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Ma, Jun; Yang, Gang; Du, Bo; Zhang, Liangpei

2017-06-01

A new Bayesian method named Poisson Nonnegative Matrix Factorization with Parameter Subspace Clustering Constraint (PNMF-PSCC) has been presented to extract endmembers from Hyperspectral Imagery (HSI). First, the method integrates the liner spectral mixture model with the Bayesian framework and it formulates endmember extraction into a Bayesian inference problem. Second, the Parameter Subspace Clustering Constraint (PSCC) is incorporated into the statistical program to consider the clustering of all pixels in the parameter subspace. The PSCC could enlarge differences among ground objects and helps finding endmembers with smaller spectrum divergences. Meanwhile, the PNMF-PSCC method utilizes the Poisson distribution as the prior knowledge of spectral signals to better explain the quantum nature of light in imaging spectrometer. Third, the optimization problem of PNMF-PSCC is formulated into maximizing the joint density via the Maximum A Posterior (MAP) estimator. The program is finally solved by iteratively optimizing two sub-problems via the Alternating Direction Method of Multipliers (ADMM) framework and the FURTHESTSUM initialization scheme. Five state-of-the art methods are implemented to make comparisons with the performance of PNMF-PSCC on both the synthetic and real HSI datasets. Experimental results show that the PNMF-PSCC outperforms all the five methods in Spectral Angle Distance (SAD) and Root-Mean-Square-Error (RMSE), and especially it could identify good endmembers for ground objects with smaller spectrum divergences.

Uncertainty quantification for nuclear density functional theory and information content of new measurements.

PubMed

McDonnell, J D; Schunck, N; Higdon, D; Sarich, J; Wild, S M; Nazarewicz, W

2015-03-27

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. The example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood.

PubMed

Karabatsos, George

2018-06-01

This article introduces a Bayesian method for testing the axioms of additive conjoint measurement. The method is based on an importance sampling algorithm that performs likelihood-free, approximate Bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem. This new method improves upon previous methods because it provides an omnibus test of the entire hierarchy of cancellation axioms, beyond double cancellation. It does so while accounting for the posterior uncertainty that is inherent in the empirical orderings that are implied by these axioms, together. The new method is illustrated through a test of the cancellation axioms on a classic survey data set, and through the analysis of simulated data.