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.

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.

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

National, regional, and global trends in systolic blood pressure since 1980: systematic analysis of health examination surveys and epidemiological studies with 786 country-years and 5·4 million participants.

PubMed

Danaei, Goodarz; Finucane, Mariel M; Lin, John K; Singh, Gitanjali M; Paciorek, Christopher J; Cowan, Melanie J; Farzadfar, Farshad; Stevens, Gretchen A; Lim, Stephen S; Riley, Leanne M; Ezzati, Majid

2011-02-12

Data for trends in blood pressure are needed to understand the effects of its dietary, lifestyle, and pharmacological determinants; set intervention priorities; and evaluate national programmes. However, few worldwide analyses of trends in blood pressure have been done. We estimated worldwide trends in population mean systolic blood pressure (SBP). We estimated trends and their uncertainties in mean SBP for adults 25 years and older in 199 countries and territories. We obtained data from published and unpublished health examination surveys and epidemiological studies (786 country-years and 5·4 million participants). For each sex, we used a Bayesian hierarchical model to estimate mean SBP by age, country, and year, accounting for whether a study was nationally representative. In 2008, age-standardised mean SBP worldwide was 128·1 mm Hg (95% uncertainty interval 126·7-129·4) in men and 124·4 mm Hg (123·0-125·9) in women. Globally, between 1980 and 2008, SBP decreased by 0·8 mm Hg per decade (-0·4 to 2·2, posterior probability of being a true decline=0·90) in men and 1·0 mm Hg per decade (-0·3 to 2·3, posterior probability=0·93) in women. Female SBP decreased by 3·5 mm Hg or more per decade in western Europe and Australasia (posterior probabilities ≥0·999). Male SBP fell most in high-income North America, by 2·8 mm Hg per decade (1·3-4·5, posterior probability >0·999), followed by Australasia and western Europe where it decreased by more than 2·0 mm Hg per decade (posterior probabilities >0·98). SBP rose in Oceania, east Africa, and south and southeast Asia for both sexes, and in west Africa for women, with the increases ranging 0·8-1·6 mm Hg per decade in men (posterior probabilities 0·72-0·91) and 1·0-2·7 mm Hg per decade for women (posterior probabilities 0·75-0·98). Female SBP was highest in some east and west African countries, with means of 135 mm Hg or greater. Male SBP was highest in Baltic and east and west African countries, where mean SBP reached 138 mm Hg or more. Men and women in western Europe had the highest SBP in high-income regions. On average, global population SBP decreased slightly since 1980, but trends varied significantly across regions and countries. SBP is currently highest in low-income and middle-income countries. Effective population-based and personal interventions should be targeted towards low-income and middle-income countries. Funding Bill & Melinda Gates Foundation and WHO. Copyright © 2011 Elsevier Ltd. All rights reserved.

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

La Russa, D

Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference. Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributionsmore » found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates. Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10{sup 7} cm−{sup 3}. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates. Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.« less

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.

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.

Generalized Wishart Mixtures for Unsupervised Classification of PolSAR Data

NASA Astrophysics Data System (ADS)

Li, Lan; Chen, Erxue; Li, Zengyuan

2013-01-01

This paper presents an unsupervised clustering algorithm based upon the expectation maximization (EM) algorithm for finite mixture modelling, using the complex wishart probability density function (PDF) for the probabilities. The mixture model enables to consider heterogeneous thematic classes which could not be better fitted by the unimodal wishart distribution. In order to make it fast and robust to calculate, we use the recently proposed generalized gamma distribution (GΓD) for the single polarization intensity data to make the initial partition. Then we use the wishart probability density function for the corresponding sample covariance matrix to calculate the posterior class probabilities for each pixel. The posterior class probabilities are used for the prior probability estimates of each class and weights for all class parameter updates. The proposed method is evaluated and compared with the wishart H-Alpha-A classification. Preliminary results show that the proposed method has better performance.

Seismic imaging of Q structures by a trans-dimensional coda-wave analysis

NASA Astrophysics Data System (ADS)

Takahashi, Tsutomu

2017-04-01

Wave scattering and intrinsic attenuation are important processes to describe incoherent and complex wave trains of high frequency seismic wave (>1Hz). The multiple lapse time window analysis (MLTWA) has been used to estimate scattering and intrinsic Q values by assuming constant Q in a study area (e.g., Hoshiba 1993). This study generalizes this MLTWA to estimate lateral variations of Q values under the Bayesian framework in dimension variable space. Study area is partitioned into small areas by means of the Voronoi tessellation. Scattering and intrinsic Q in each small area are constant. We define a misfit function for spatiotemporal variations of wave energy as with the original MLTWA, and maximize the posterior probability with changing not only Q values but the number and spatial layout of the Voronoi cells. This maximization is conducted by means of the reversible jump Markov chain Monte Carlo (rjMCMC) (Green 1995) since the number of unknown parameters (i.e., dimension of posterior probability) is variable. After a convergence to the maximum posterior, we estimate Q structures from the ensemble averages of MCMC samples around the maximum posterior probability. Synthetic tests showed stable reconstructions of input structures with reasonable error distributions. We applied this method for seismic waveform data recorded by ocean bottom seismograms at the outer-rise area off Tohoku, and estimated Q values at 4-8Hz, 8-16Hz and 16-32Hz. Intrinsic Q are nearly constant at all frequency bands, and scattering Q shows two distinct strong scattering regions at petit spot area and high seismicity area. These strong scattering are probably related to magma inclusions and fractured structure, respectively. Difference between these two areas becomes clear at high frequencies. It means that scale dependences of inhomogeneities or smaller scale inhomogeneity is important to discuss medium property and origins of structural variations. While the generalized MLTWA is based on a classical waveform modeling in constant Q medium, this method can be a fundamental basis for Q structure imaging in the crust.

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.

Data analysis in emission tomography using emission-count posteriors

NASA Astrophysics Data System (ADS)

Sitek, Arkadiusz

2012-11-01

A novel approach to the analysis of emission tomography data using the posterior probability of the number of emissions per voxel (emission count) conditioned on acquired tomographic data is explored. The posterior is derived from the prior and the Poisson likelihood of the emission-count data by marginalizing voxel activities. Based on emission-count posteriors, examples of Bayesian analysis including estimation and classification tasks in emission tomography are provided. The application of the method to computer simulations of 2D tomography is demonstrated. In particular, the minimum-mean-square-error point estimator of the emission count is demonstrated. The process of finding this estimator can be considered as a tomographic image reconstruction technique since the estimates of the number of emissions per voxel divided by voxel sensitivities and acquisition time are the estimates of the voxel activities. As an example of a classification task, a hypothesis stating that some region of interest (ROI) emitted at least or at most r-times the number of events in some other ROI is tested. The ROIs are specified by the user. The analysis described in this work provides new quantitative statistical measures that can be used in decision making in diagnostic imaging using emission tomography.

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

An Empirical Bayes Approach to Spatial Analysis

NASA Technical Reports Server (NTRS)

Morris, C. N.; Kostal, H.

1983-01-01

Multi-channel LANDSAT data are collected in several passes over agricultural areas during the growing season. How empirical Bayes modeling can be used to develop crop identification and discrimination techniques that account for spatial correlation in such data is considered. The approach models the unobservable parameters and the data separately, hoping to take advantage of the fact that the bulk of spatial correlation lies in the parameter process. The problem is then framed in terms of estimating posterior probabilities of crop types for each spatial area. Some empirical Bayes spatial estimation methods are used to estimate the logits of these probabilities.

Joint Segmentation and Deformable Registration of Brain Scans Guided by a Tumor Growth Model

PubMed Central

Gooya, Ali; Pohl, Kilian M.; Bilello, Michel; Biros, George; Davatzikos, Christos

2011-01-01

This paper presents an approach for joint segmentation and deformable registration of brain scans of glioma patients to a normal atlas. The proposed method is based on the Expectation Maximization (EM) algorithm that incorporates a glioma growth model for atlas seeding, a process which modifies the normal atlas into one with a tumor and edema. The modified atlas is registered into the patient space and utilized for the posterior probability estimation of various tissue labels. EM iteratively refines the estimates of the registration parameters, the posterior probabilities of tissue labels and the tumor growth model parameters. We have applied this approach to 10 glioma scans acquired with four Magnetic Resonance (MR) modalities (T1, T1-CE, T2 and FLAIR ) and validated the result by comparing them to manual segmentations by clinical experts. The resulting segmentations look promising and quantitatively match well with the expert provided ground truth. PMID:21995070

Joint segmentation and deformable registration of brain scans guided by a tumor growth model.

PubMed

Gooya, Ali; Pohl, Kilian M; Bilello, Michel; Biros, George; Davatzikos, Christos

2011-01-01

This paper presents an approach for joint segmentation and deformable registration of brain scans of glioma patients to a normal atlas. The proposed method is based on the Expectation Maximization (EM) algorithm that incorporates a glioma growth model for atlas seeding, a process which modifies the normal atlas into one with a tumor and edema. The modified atlas is registered into the patient space and utilized for the posterior probability estimation of various tissue labels. EM iteratively refines the estimates of the registration parameters, the posterior probabilities of tissue labels and the tumor growth model parameters. We have applied this approach to 10 glioma scans acquired with four Magnetic Resonance (MR) modalities (T1, T1-CE, T2 and FLAIR) and validated the result by comparing them to manual segmentations by clinical experts. The resulting segmentations look promising and quantitatively match well with the expert provided ground truth.

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.

Estimating population size for Capercaillie (Tetrao urogallus L.) with spatial capture-recapture models based on genotypes from one field sample

USGS Publications Warehouse

Mollet, Pierre; Kery, Marc; Gardner, Beth; Pasinelli, Gilberto; Royle, Andy

2015-01-01

We conducted a survey of an endangered and cryptic forest grouse, the capercaillie Tetrao urogallus, based on droppings collected on two sampling occasions in eight forest fragments in central Switzerland in early spring 2009. We used genetic analyses to sex and individually identify birds. We estimated sex-dependent detection probabilities and population size using a modern spatial capture-recapture (SCR) model for the data from pooled surveys. A total of 127 capercaillie genotypes were identified (77 males, 46 females, and 4 of unknown sex). The SCR model yielded atotal population size estimate (posterior mean) of 137.3 capercaillies (posterior sd 4.2, 95% CRI 130–147). The observed sex ratio was skewed towards males (0.63). The posterior mean of the sex ratio under the SCR model was 0.58 (posterior sd 0.02, 95% CRI 0.54–0.61), suggesting a male-biased sex ratio in our study area. A subsampling simulation study indicated that a reduced sampling effort representing 75% of the actual detections would still yield practically acceptable estimates of total size and sex ratio in our population. Hence, field work and financial effort could be reduced without compromising accuracy when the SCR model is used to estimate key population parameters of cryptic species.

Development of a Random Field Model for Gas Plume Detection in Multiple LWIR Images.

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

Heasler, Patrick G.

This report develops a random field model that describes gas plumes in LWIR remote sensing images. The random field model serves as a prior distribution that can be combined with LWIR data to produce a posterior that determines the probability that a gas plume exists in the scene and also maps the most probable location of any plume. The random field model is intended to work with a single pixel regression estimator--a regression model that estimates gas concentration on an individual pixel basis.

Toward accurate and precise estimates of lion density.

PubMed

Elliot, Nicholas B; Gopalaswamy, Arjun M

2017-08-01

Reliable estimates of animal density are fundamental to understanding ecological processes and population dynamics. Furthermore, their accuracy is vital to conservation because wildlife authorities rely on estimates to make decisions. However, it is notoriously difficult to accurately estimate density for wide-ranging carnivores that occur at low densities. In recent years, significant progress has been made in density estimation of Asian carnivores, but the methods have not been widely adapted to African carnivores, such as lions (Panthera leo). Although abundance indices for lions may produce poor inferences, they continue to be used to estimate density and inform management and policy. We used sighting data from a 3-month survey and adapted a Bayesian spatially explicit capture-recapture (SECR) model to estimate spatial lion density in the Maasai Mara National Reserve and surrounding conservancies in Kenya. Our unstructured spatial capture-recapture sampling design incorporated search effort to explicitly estimate detection probability and density on a fine spatial scale, making our approach robust in the context of varying detection probabilities. Overall posterior mean lion density was estimated to be 17.08 (posterior SD 1.310) lions >1 year old/100 km 2 , and the sex ratio was estimated at 2.2 females to 1 male. Our modeling framework and narrow posterior SD demonstrate that SECR methods can produce statistically rigorous and precise estimates of population parameters, and we argue that they should be favored over less reliable abundance indices. Furthermore, our approach is flexible enough to incorporate different data types, which enables robust population estimates over relatively short survey periods in a variety of systems. Trend analyses are essential to guide conservation decisions but are frequently based on surveys of differing reliability. We therefore call for a unified framework to assess lion numbers in key populations to improve management and policy decisions. © 2016 Society for Conservation Biology.

Statistics of Sxy estimates

NASA Technical Reports Server (NTRS)

Freilich, M. H.; Pawka, S. S.

1987-01-01

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.

Objective estimates based on experimental data and initial and final knowledge

NASA Technical Reports Server (NTRS)

Rosenbaum, B. M.

1972-01-01

An extension of the method of Jaynes, whereby least biased probability estimates are obtained, permits such estimates to be made which account for experimental data on hand as well as prior and posterior knowledge. These estimates can be made for both discrete and continuous sample spaces. The method allows a simple interpretation of Laplace's two rules: the principle of insufficient reason and the rule of succession. Several examples are analyzed by way of illustration.

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.

Brain tumor segmentation from multimodal magnetic resonance images via sparse representation.

PubMed

Li, Yuhong; Jia, Fucang; Qin, Jing

2016-10-01

Accurately segmenting and quantifying brain gliomas from magnetic resonance (MR) images remains a challenging task because of the large spatial and structural variability among brain tumors. To develop a fully automatic and accurate brain tumor segmentation algorithm, we present a probabilistic model of multimodal MR brain tumor segmentation. This model combines sparse representation and the Markov random field (MRF) to solve the spatial and structural variability problem. We formulate the tumor segmentation problem as a multi-classification task by labeling each voxel as the maximum posterior probability. We estimate the maximum a posteriori (MAP) probability by introducing the sparse representation into a likelihood probability and a MRF into the prior probability. Considering the MAP as an NP-hard problem, we convert the maximum posterior probability estimation into a minimum energy optimization problem and employ graph cuts to find the solution to the MAP estimation. Our method is evaluated using the Brain Tumor Segmentation Challenge 2013 database (BRATS 2013) and obtained Dice coefficient metric values of 0.85, 0.75, and 0.69 on the high-grade Challenge data set, 0.73, 0.56, and 0.54 on the high-grade Challenge LeaderBoard data set, and 0.84, 0.54, and 0.57 on the low-grade Challenge data set for the complete, core, and enhancing regions. The experimental results show that the proposed algorithm is valid and ranks 2nd compared with the state-of-the-art tumor segmentation algorithms in the MICCAI BRATS 2013 challenge. Copyright © 2016 Elsevier B.V. All rights reserved.

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

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 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

Hierarchical Bayes approach for subgroup analysis.

PubMed

Hsu, Yu-Yi; Zalkikar, Jyoti; Tiwari, Ram C

2017-01-01

In clinical data analysis, both treatment effect estimation and consistency assessment are important for a better understanding of the drug efficacy for the benefit of subjects in individual subgroups. The linear mixed-effects model has been used for subgroup analysis to describe treatment differences among subgroups with great flexibility. The hierarchical Bayes approach has been applied to linear mixed-effects model to derive the posterior distributions of overall and subgroup treatment effects. In this article, we discuss the prior selection for variance components in hierarchical Bayes, estimation and decision making of the overall treatment effect, as well as consistency assessment of the treatment effects across the subgroups based on the posterior predictive p-value. Decision procedures are suggested using either the posterior probability or the Bayes factor. These decision procedures and their properties are illustrated using a simulated example with normally distributed response and repeated measurements.

PARTS: Probabilistic Alignment for RNA joinT Secondary structure prediction

PubMed Central

Harmanci, Arif Ozgun; Sharma, Gaurav; Mathews, David H.

2008-01-01

A novel method is presented for joint prediction of alignment and common secondary structures of two RNA sequences. The joint consideration of common secondary structures and alignment is accomplished by structural alignment over a search space defined by the newly introduced motif called matched helical regions. The matched helical region formulation generalizes previously employed constraints for structural alignment and thereby better accommodates the structural variability within RNA families. A probabilistic model based on pseudo free energies obtained from precomputed base pairing and alignment probabilities is utilized for scoring structural alignments. Maximum a posteriori (MAP) common secondary structures, sequence alignment and joint posterior probabilities of base pairing are obtained from the model via a dynamic programming algorithm called PARTS. The advantage of the more general structural alignment of PARTS is seen in secondary structure predictions for the RNase P family. For this family, the PARTS MAP predictions of secondary structures and alignment perform significantly better than prior methods that utilize a more restrictive structural alignment model. For the tRNA and 5S rRNA families, the richer structural alignment model of PARTS does not offer a benefit and the method therefore performs comparably with existing alternatives. For all RNA families studied, the posterior probability estimates obtained from PARTS offer an improvement over posterior probability estimates from a single sequence prediction. When considering the base pairings predicted over a threshold value of confidence, the combination of sensitivity and positive predictive value is superior for PARTS than for the single sequence prediction. PARTS source code is available for download under the GNU public license at http://rna.urmc.rochester.edu. PMID:18304945

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

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,…

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.

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.

Structured filtering

NASA Astrophysics Data System (ADS)

Granade, Christopher; Wiebe, Nathan

2017-08-01

A major challenge facing existing sequential Monte Carlo methods for parameter estimation in physics stems from the inability of existing approaches to robustly deal with experiments that have different mechanisms that yield the results with equivalent probability. We address this problem here by proposing a form of particle filtering that clusters the particles that comprise the sequential Monte Carlo approximation to the posterior before applying a resampler. Through a new graphical approach to thinking about such models, we are able to devise an artificial-intelligence based strategy that automatically learns the shape and number of the clusters in the support of the posterior. We demonstrate the power of our approach by applying it to randomized gap estimation and a form of low circuit-depth phase estimation where existing methods from the physics literature either exhibit much worse performance or even fail completely.

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.

Assessment of accident severity in the construction industry using the Bayesian theorem.

PubMed

Alizadeh, Seyed Shamseddin; Mortazavi, Seyed Bagher; Mehdi Sepehri, Mohammad

2015-01-01

Construction is a major source of employment in many countries. In construction, workers perform a great diversity of activities, each one with a specific associated risk. The aim of this paper is to identify workers who are at risk of accidents with severe consequences and classify these workers to determine appropriate control measures. We defined 48 groups of workers and used the Bayesian theorem to estimate posterior probabilities about the severity of accidents at the level of individuals in construction sector. First, the posterior probabilities of injuries based on four variables were provided. Then the probabilities of injury for 48 groups of workers were determined. With regard to marginal frequency of injury, slight injury (0.856), fatal injury (0.086) and severe injury (0.058) had the highest probability of occurrence. It was observed that workers with <1 year's work experience (0.168) had the highest probability of injury occurrence. The first group of workers, who were extensively exposed to risk of severe and fatal accidents, involved workers ≥ 50 years old, married, with 1-5 years' work experience, who had no past accident experience. The findings provide a direction for more effective safety strategies and occupational accident prevention and emergency programmes.

Creation of the BMA ensemble for SST using a parallel processing technique

NASA Astrophysics Data System (ADS)

Kim, Kwangjin; Lee, Yang Won

2013-10-01

Despite the same purpose, each satellite product has different value because of its inescapable uncertainty. Also the satellite products have been calculated for a long time, and the kinds of the products are various and enormous. So the efforts for reducing the uncertainty and dealing with enormous data will be necessary. In this paper, we create an ensemble Sea Surface Temperature (SST) using MODIS Aqua, MODIS Terra and COMS (Communication Ocean and Meteorological Satellite). We used Bayesian Model Averaging (BMA) as ensemble method. The principle of the BMA is synthesizing the conditional probability density function (PDF) using posterior probability as weight. The posterior probability is estimated using EM algorithm. The BMA PDF is obtained by weighted average. As the result, the ensemble SST showed the lowest RMSE and MAE, which proves the applicability of BMA for satellite data ensemble. As future work, parallel processing techniques using Hadoop framework will be adopted for more efficient computation of very big satellite data.

Multinomial Logistic Regression & Bootstrapping for Bayesian Estimation of Vertical Facies Prediction in Heterogeneous Sandstone Reservoirs

NASA Astrophysics Data System (ADS)

Al-Mudhafar, W. J.

2013-12-01

Precisely prediction of rock facies leads to adequate reservoir characterization by improving the porosity-permeability relationships to estimate the properties in non-cored intervals. It also helps to accurately identify the spatial facies distribution to perform an accurate reservoir model for optimal future reservoir performance. In this paper, the facies estimation has been done through Multinomial logistic regression (MLR) with respect to the well logs and core data in a well in upper sandstone formation of South Rumaila oil field. The entire independent variables are gamma rays, formation density, water saturation, shale volume, log porosity, core porosity, and core permeability. Firstly, Robust Sequential Imputation Algorithm has been considered to impute the missing data. This algorithm starts from a complete subset of the dataset and estimates sequentially the missing values in an incomplete observation by minimizing the determinant of the covariance of the augmented data matrix. Then, the observation is added to the complete data matrix and the algorithm continues with the next observation with missing values. The MLR has been chosen to estimate the maximum likelihood and minimize the standard error for the nonlinear relationships between facies & core and log data. The MLR is used to predict the probabilities of the different possible facies given each independent variable by constructing a linear predictor function having a set of weights that are linearly combined with the independent variables by using a dot product. Beta distribution of facies has been considered as prior knowledge and the resulted predicted probability (posterior) has been estimated from MLR based on Baye's theorem that represents the relationship between predicted probability (posterior) with the conditional probability and the prior knowledge. To assess the statistical accuracy of the model, the bootstrap should be carried out to estimate extra-sample prediction error by randomly drawing datasets with replacement from the training data. Each sample has the same size of the original training set and it can be conducted N times to produce N bootstrap datasets to re-fit the model accordingly to decrease the squared difference between the estimated and observed categorical variables (facies) leading to decrease the degree of uncertainty.

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…

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.

Hidden Markov models for fault detection in dynamic systems

NASA Technical Reports Server (NTRS)

Smyth, Padhraic J. (Inventor)

1995-01-01

The invention is a system failure monitoring method and apparatus which learns the symptom-fault mapping directly from training data. The invention first estimates the state of the system at discrete intervals in time. A feature vector x of dimension k is estimated from sets of successive windows of sensor data. A pattern recognition component then models the instantaneous estimate of the posterior class probability given the features, p(w(sub i) (vertical bar)/x), 1 less than or equal to i isless than or equal to m. Finally, a hidden Markov model is used to take advantage of temporal context and estimate class probabilities conditioned on recent past history. In this hierarchical pattern of information flow, the time series data is transformed and mapped into a categorical representation (the fault classes) and integrated over time to enable robust decision-making.

Hidden Markov models for fault detection in dynamic systems

NASA Technical Reports Server (NTRS)

Smyth, Padhraic J. (Inventor)

1993-01-01

The invention is a system failure monitoring method and apparatus which learns the symptom-fault mapping directly from training data. The invention first estimates the state of the system at discrete intervals in time. A feature vector x of dimension k is estimated from sets of successive windows of sensor data. A pattern recognition component then models the instantaneous estimate of the posterior class probability given the features, p(w(sub i) perpendicular to x), 1 less than or equal to i is less than or equal to m. Finally, a hidden Markov model is used to take advantage of temporal context and estimate class probabilities conditioned on recent past history. In this hierarchical pattern of information flow, the time series data is transformed and mapped into a categorical representation (the fault classes) and integrated over time to enable robust decision-making.

Intervals for posttest probabilities: a comparison of 5 methods.

PubMed

Mossman, D; Berger, J O

2001-01-01

Several medical articles discuss methods of constructing confidence intervals for single proportions and the likelihood ratio, but scant attention has been given to the systematic study of intervals for the posterior odds, or the positive predictive value, of a test. The authors describe 5 methods of constructing confidence intervals for posttest probabilities when estimates of sensitivity, specificity, and the pretest probability of a disorder are derived from empirical data. They then evaluate each method to determine how well the intervals' coverage properties correspond to their nominal value. When the estimates of pretest probabilities, sensitivity, and specificity are derived from more than 80 subjects and are not close to 0 or 1, all methods generate intervals with appropriate coverage properties. When these conditions are not met, however, the best-performing method is an objective Bayesian approach implemented by a simple simulation using a spreadsheet. Physicians and investigators can generate accurate confidence intervals for posttest probabilities in small-sample situations using the objective Bayesian approach.

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.

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

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).

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.

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.

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

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.

Modeling Dynamic Contrast-Enhanced MRI Data with a Constrained Local AIF.

PubMed

Duan, Chong; Kallehauge, Jesper F; Pérez-Torres, Carlos J; Bretthorst, G Larry; Beeman, Scott C; Tanderup, Kari; Ackerman, Joseph J H; Garbow, Joel R

2018-02-01

This study aims to develop a constrained local arterial input function (cL-AIF) to improve quantitative analysis of dynamic contrast-enhanced (DCE)-magnetic resonance imaging (MRI) data by accounting for the contrast-agent bolus amplitude error in the voxel-specific AIF. Bayesian probability theory-based parameter estimation and model selection were used to compare tracer kinetic modeling employing either the measured remote-AIF (R-AIF, i.e., the traditional approach) or an inferred cL-AIF against both in silico DCE-MRI data and clinical, cervical cancer DCE-MRI data. When the data model included the cL-AIF, tracer kinetic parameters were correctly estimated from in silico data under contrast-to-noise conditions typical of clinical DCE-MRI experiments. Considering the clinical cervical cancer data, Bayesian model selection was performed for all tumor voxels of the 16 patients (35,602 voxels in total). Among those voxels, a tracer kinetic model that employed the voxel-specific cL-AIF was preferred (i.e., had a higher posterior probability) in 80 % of the voxels compared to the direct use of a single R-AIF. Maps of spatial variation in voxel-specific AIF bolus amplitude and arrival time for heterogeneous tissues, such as cervical cancer, are accessible with the cL-AIF approach. The cL-AIF method, which estimates unique local-AIF amplitude and arrival time for each voxel within the tissue of interest, provides better modeling of DCE-MRI data than the use of a single, measured R-AIF. The Bayesian-based data analysis described herein affords estimates of uncertainties for each model parameter, via posterior probability density functions, and voxel-wise comparison across methods/models, via model selection in data modeling.

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.

Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate From Microwave Observations

NASA Technical Reports Server (NTRS)

Chiu, J. Christine; Petty, Grant W.

2005-01-01

This paper presents a new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measurements Mission (TRMM) Microwave Imager (TMI) over the ocean, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes Theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance our understanding of theoretical benefits of the Bayesian approach, we have conducted sensitivity analyses based on two synthetic datasets for which the true conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak, due to saturation effects. It is also suggested that the choice of the estimators and the prior information are both crucial to the retrieval. In addition, the performance of our Bayesian algorithm is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

Inference with minimal Gibbs free energy in information field theory.

PubMed

Ensslin, Torsten A; Weig, Cornelius

2010-11-01

Non-linear and non-gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a gaussian signal with unknown spectrum, and (iii) inference of a poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-gaussian posterior.

Development of a score and probability estimate for detecting angle closure based on anterior segment optical coherence tomography.

PubMed

Nongpiur, Monisha E; Haaland, Benjamin A; Perera, Shamira A; Friedman, David S; He, Mingguang; Sakata, Lisandro M; Baskaran, Mani; Aung, Tin

2014-01-01

To develop a score along with an estimated probability of disease for detecting angle closure based on anterior segment optical coherence tomography (AS OCT) imaging. Cross-sectional study. A total of 2047 subjects 50 years of age and older were recruited from a community polyclinic in Singapore. All subjects underwent standardized ocular examination including gonioscopy and imaging by AS OCT (Carl Zeiss Meditec). Customized software (Zhongshan Angle Assessment Program) was used to measure AS OCT parameters. Complete data were available for 1368 subjects. Data from the right eyes were used for analysis. A stepwise logistic regression model with Akaike information criterion was used to generate a score that then was converted to an estimated probability of the presence of gonioscopic angle closure, defined as the inability to visualize the posterior trabecular meshwork for at least 180 degrees on nonindentation gonioscopy. Of the 1368 subjects, 295 (21.6%) had gonioscopic angle closure. The angle closure score was calculated from the shifted linear combination of the AS OCT parameters. The score can be converted to an estimated probability of having angle closure using the relationship: estimated probability = e(score)/(1 + e(score)), where e is the natural exponential. The score performed well in a second independent sample of 178 angle-closure subjects and 301 normal controls, with an area under the receiver operating characteristic curve of 0.94. A score derived from a single AS OCT image, coupled with an estimated probability, provides an objective platform for detection of angle closure. Copyright © 2014 Elsevier Inc. All rights reserved.

Sequential bearings-only-tracking initiation with particle filtering method.

PubMed

Liu, Bin; Hao, Chengpeng

2013-01-01

The tracking initiation problem is examined in the context of autonomous bearings-only-tracking (BOT) of a single appearing/disappearing target in the presence of clutter measurements. In general, this problem suffers from a combinatorial explosion in the number of potential tracks resulted from the uncertainty in the linkage between the target and the measurement (a.k.a the data association problem). In addition, the nonlinear measurements lead to a non-Gaussian posterior probability density function (pdf) in the optimal Bayesian sequential estimation framework. The consequence of this nonlinear/non-Gaussian context is the absence of a closed-form solution. This paper models the linkage uncertainty and the nonlinear/non-Gaussian estimation problem jointly with solid Bayesian formalism. A particle filtering (PF) algorithm is derived for estimating the model's parameters in a sequential manner. Numerical results show that the proposed solution provides a significant benefit over the most commonly used methods, IPDA and IMMPDA. The posterior Cramér-Rao bounds are also involved for performance evaluation.

A Bayesian approach to the modelling of α Cen A

NASA Astrophysics Data System (ADS)

Bazot, M.; Bourguignon, S.; Christensen-Dalsgaard, J.

2012-12-01

Determining the physical characteristics of a star is an inverse problem consisting of estimating the parameters of models for the stellar structure and evolution, and knowing certain observable quantities. We use a Bayesian approach to solve this problem for α Cen A, which allows us to incorporate prior information on the parameters to be estimated, in order to better constrain the problem. Our strategy is based on the use of a Markov chain Monte Carlo (MCMC) algorithm to estimate the posterior probability densities of the stellar parameters: mass, age, initial chemical composition, etc. We use the stellar evolutionary code ASTEC to model the star. To constrain this model both seismic and non-seismic observations were considered. Several different strategies were tested to fit these values, using either two free parameters or five free parameters in ASTEC. We are thus able to show evidence that MCMC methods become efficient with respect to more classical grid-based strategies when the number of parameters increases. The results of our MCMC algorithm allow us to derive estimates for the stellar parameters and robust uncertainties thanks to the statistical analysis of the posterior probability densities. We are also able to compute odds for the presence of a convective core in α Cen A. When using core-sensitive seismic observational constraints, these can rise above ˜40 per cent. The comparison of results to previous studies also indicates that these seismic constraints are of critical importance for our knowledge of the structure of this star.

Sex estimation of the tibia in modern Turkish: A computed tomography study.

PubMed

Ekizoglu, Oguzhan; Er, Ali; Bozdag, Mustafa; Akcaoglu, Mustafa; Can, Ismail Ozgur; García-Donas, Julieta G; Kranioti, Elena F

2016-11-01

The utilization of computed tomography is beneficial for the analysis of skeletal remains and it has important advantages for anthropometric studies. The present study investigated morphometry of left tibia using CT images of a contemporary Turkish population. Seven parameters were measured on 203 individuals (124 males and 79 females) within the 19-92-years age group. The first objective of this study was to provide population-specific sex estimation equations for the contemporary Turkish population based on CT images. A second objective was to test the sex estimation formulae on Southern Europeans by Kranioti and Apostol (2015). Univariate discriminant functions resulted in classification accuracy that ranged from 66 to 86%. The best single variable was found to be upper epiphyseal breadth (86%) followed by lower epiphyseal breadth (85%). Multivariate discriminant functions resulted in classification accuracy for cross-validated data ranged from 79 to 86%. Applying the multivariate sex estimation formulae on Southern Europeans (SE) by Kranioti and Apostol in our sample resulted in very high classification accuracy ranging from 81 to 88%. In addition, 35.5-47% of the total Turkish sample is correctly classified with over 95% posterior probability, which is actually higher than the one reported for the original sample (25-43%). We conclude that the tibia is a very useful bone for sex estimation in the contemporary Turkish population. Moreover, our test results support the hypothesis that the SE formulae are sufficient for the contemporary Turkish population and they can be used safely for criminal investigations when posterior probabilities are over 95%. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

GLISTR: Glioma Image Segmentation and Registration

PubMed Central

Pohl, Kilian M.; Bilello, Michel; Cirillo, Luigi; Biros, George; Melhem, Elias R.; Davatzikos, Christos

2015-01-01

We present a generative approach for simultaneously registering a probabilistic atlas of a healthy population to brain magnetic resonance (MR) scans showing glioma and segmenting the scans into tumor as well as healthy tissue labels. The proposed method is based on the expectation maximization (EM) algorithm that incorporates a glioma growth model for atlas seeding, a process which modifies the original atlas into one with tumor and edema adapted to best match a given set of patient’s images. The modified atlas is registered into the patient space and utilized for estimating the posterior probabilities of various tissue labels. EM iteratively refines the estimates of the posterior probabilities of tissue labels, the deformation field and the tumor growth model parameters. Hence, in addition to segmentation, the proposed method results in atlas registration and a low-dimensional description of the patient scans through estimation of tumor model parameters. We validate the method by automatically segmenting 10 MR scans and comparing the results to those produced by clinical experts and two state-of-the-art methods. The resulting segmentations of tumor and edema outperform the results of the reference methods, and achieve a similar accuracy from a second human rater. We additionally apply the method to 122 patients scans and report the estimated tumor model parameters and their relations with segmentation and registration results. Based on the results from this patient population, we construct a statistical atlas of the glioma by inverting the estimated deformation fields to warp the tumor segmentations of patients scans into a common space. PMID:22907965

Estimation of Posterior Probabilities Using Multivariate Smoothing Splines and Generalized Cross-Validation.

DTIC Science & Technology

1983-09-01

Ciencia y Tecnologia -Mexico, by ONR under Contract No. N00014-77-C-0675, and by ARO under Contract No. DAAG29-80-K-0042. LUJ THE VIE~W, rTIJ. ’~v ’’~c...Department of Statis- tics. For financial support I thank the Consejo Nacional de Ciencia y Tecnologia - Mexico, and the Department of Statistics of the

Using Latent Class Analysis to Model Temperament Types.

PubMed

Loken, Eric

2004-10-01

Mixture models are appropriate for data that arise from a set of qualitatively different subpopulations. In this study, latent class analysis was applied to observational data from a laboratory assessment of infant temperament at four months of age. The EM algorithm was used to fit the models, and the Bayesian method of posterior predictive checks was used for model selection. Results show at least three types of infant temperament, with patterns consistent with those identified by previous researchers who classified the infants using a theoretically based system. Multiple imputation of group memberships is proposed as an alternative to assigning subjects to the latent class with maximum posterior probability in order to reflect variance due to uncertainty in the parameter estimation. Latent class membership at four months of age predicted longitudinal outcomes at four years of age. The example illustrates issues relevant to all mixture models, including estimation, multi-modality, model selection, and comparisons based on the latent group indicators.

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 computer program for estimation from incomplete multinomial data

NASA Technical Reports Server (NTRS)

Credeur, K. R.

1978-01-01

Coding is given for maximum likelihood and Bayesian estimation of the vector p of multinomial cell probabilities from incomplete data. Also included is coding to calculate and approximate elements of the posterior mean and covariance matrices. The program is written in FORTRAN 4 language for the Control Data CYBER 170 series digital computer system with network operating system (NOS) 1.1. The program requires approximately 44000 octal locations of core storage. A typical case requires from 72 seconds to 92 seconds on CYBER 175 depending on the value of the prior parameter.

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

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.

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.

Bayes factor and posterior probability: Complementary statistical evidence to p-value.

PubMed

Lin, Ruitao; Yin, Guosheng

2015-09-01

As a convention, a p-value is often computed in hypothesis testing and compared with the nominal level of 0.05 to determine whether to reject the null hypothesis. Although the smaller the p-value, the more significant the statistical test, it is difficult to perceive the p-value in a probability scale and quantify it as the strength of the data against the null hypothesis. In contrast, the Bayesian posterior probability of the null hypothesis has an explicit interpretation of how strong the data support the null. We make a comparison of the p-value and the posterior probability by considering a recent clinical trial. The results show that even when we reject the null hypothesis, there is still a substantial probability (around 20%) that the null is true. Not only should we examine whether the data would have rarely occurred under the null hypothesis, but we also need to know whether the data would be rare under the alternative. As a result, the p-value only provides one side of the information, for which the Bayes factor and posterior probability may offer complementary evidence. Copyright © 2015 Elsevier Inc. All rights reserved.

A novel Bayesian framework for discriminative feature extraction in Brain-Computer Interfaces.

PubMed

Suk, Heung-Il; Lee, Seong-Whan

2013-02-01

As there has been a paradigm shift in the learning load from a human subject to a computer, machine learning has been considered as a useful tool for Brain-Computer Interfaces (BCIs). In this paper, we propose a novel Bayesian framework for discriminative feature extraction for motor imagery classification in an EEG-based BCI in which the class-discriminative frequency bands and the corresponding spatial filters are optimized by means of the probabilistic and information-theoretic approaches. In our framework, the problem of simultaneous spatiospectral filter optimization is formulated as the estimation of an unknown posterior probability density function (pdf) that represents the probability that a single-trial EEG of predefined mental tasks can be discriminated in a state. In order to estimate the posterior pdf, we propose a particle-based approximation method by extending a factored-sampling technique with a diffusion process. An information-theoretic observation model is also devised to measure discriminative power of features between classes. From the viewpoint of classifier design, the proposed method naturally allows us to construct a spectrally weighted label decision rule by linearly combining the outputs from multiple classifiers. We demonstrate the feasibility and effectiveness of the proposed method by analyzing the results and its success on three public databases.

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.

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.

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.

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1972-01-01

The error variance of the process prior multivariate normal distributions of the parameters of the models are assumed to be specified, prior probabilities of the models being correct. A rule for termination of sampling is proposed. Upon termination, the model with the largest posterior probability is chosen as correct. If sampling is not terminated, posterior probabilities of the models and posterior distributions of the parameters are computed. An experiment was chosen to maximize the expected Kullback-Leibler information function. Monte Carlo simulation experiments were performed to investigate large and small sample behavior of the sequential adaptive procedure.

Learning about Posterior Probability: Do Diagrams and Elaborative Interrogation Help?

ERIC Educational Resources Information Center

Clinton, Virginia; Alibali, Martha Wagner; Nathan, Mitchel J.

2016-01-01

To learn from a text, students must make meaningful connections among related ideas in that text. This study examined the effectiveness of two methods of improving connections--elaborative interrogation and diagrams--in written lessons about posterior probability. Undergraduate students (N = 198) read a lesson in one of three questioning…

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.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

A Meta-Analysis and Multisite Time-Series Analysis of the Differential Toxicity of Major Fine Particulate Matter Constituents

PubMed Central

Levy, Jonathan I.; Diez, David; Dou, Yiping; Barr, Christopher D.; Dominici, Francesca

2012-01-01

Health risk assessments of particulate matter less than 2.5 μm in diameter (PM2.5) often assume that all constituents of PM2.5 are equally toxic. While investigators in previous epidemiologic studies have evaluated health risks from various PM2.5 constituents, few have conducted the analyses needed to directly inform risk assessments. In this study, the authors performed a literature review and conducted a multisite time-series analysis of hospital admissions and exposure to PM2.5 constituents (elemental carbon, organic carbon matter, sulfate, and nitrate) in a population of 12 million US Medicare enrollees for the period 2000–2008. The literature review illustrated a general lack of multiconstituent models or insight about probabilities of differential impacts per unit of concentration change. Consistent with previous results, the multisite time-series analysis found statistically significant associations between short-term changes in elemental carbon and cardiovascular hospital admissions. Posterior probabilities from multiconstituent models provided evidence that some individual constituents were more toxic than others, and posterior parameter estimates coupled with correlations among these estimates provided necessary information for risk assessment. Ratios of constituent toxicities, commonly used in risk assessment to describe differential toxicity, were extremely uncertain for all comparisons. These analyses emphasize the subtlety of the statistical techniques and epidemiologic studies necessary to inform risk assessments of particle constituents. PMID:22510275

A Unified Approach to Genotype Imputation and Haplotype-Phase Inference for Large Data Sets of Trios and Unrelated Individuals

PubMed Central

Browning, Brian L.; Browning, Sharon R.

2009-01-01

We present methods for imputing data for ungenotyped markers and for inferring haplotype phase in large data sets of unrelated individuals and parent-offspring trios. Our methods make use of known haplotype phase when it is available, and our methods are computationally efficient so that the full information in large reference panels with thousands of individuals is utilized. We demonstrate that substantial gains in imputation accuracy accrue with increasingly large reference panel sizes, particularly when imputing low-frequency variants, and that unphased reference panels can provide highly accurate genotype imputation. We place our methodology in a unified framework that enables the simultaneous use of unphased and phased data from trios and unrelated individuals in a single analysis. For unrelated individuals, our imputation methods produce well-calibrated posterior genotype probabilities and highly accurate allele-frequency estimates. For trios, our haplotype-inference method is four orders of magnitude faster than the gold-standard PHASE program and has excellent accuracy. Our methods enable genotype imputation to be performed with unphased trio or unrelated reference panels, thus accounting for haplotype-phase uncertainty in the reference panel. We present a useful measure of imputation accuracy, allelic R2, and show that this measure can be estimated accurately from posterior genotype probabilities. Our methods are implemented in version 3.0 of the BEAGLE software package. PMID:19200528

Leveraging Genomic Annotations and Pleiotropic Enrichment for Improved Replication Rates in Schizophrenia GWAS

PubMed Central

Wang, Yunpeng; Thompson, Wesley K.; Schork, Andrew J.; Holland, Dominic; Chen, Chi-Hua; Bettella, Francesco; Desikan, Rahul S.; Li, Wen; Witoelar, Aree; Zuber, Verena; Devor, Anna; Nöthen, Markus M.; Rietschel, Marcella; Chen, Qiang; Werge, Thomas; Cichon, Sven; Weinberger, Daniel R.; Djurovic, Srdjan; O’Donovan, Michael; Visscher, Peter M.; Andreassen, Ole A.; Dale, Anders M.

2016-01-01

Most of the genetic architecture of schizophrenia (SCZ) has not yet been identified. Here, we apply a novel statistical algorithm called Covariate-Modulated Mixture Modeling (CM3), which incorporates auxiliary information (heterozygosity, total linkage disequilibrium, genomic annotations, pleiotropy) for each single nucleotide polymorphism (SNP) to enable more accurate estimation of replication probabilities, conditional on the observed test statistic (“z-score”) of the SNP. We use a multiple logistic regression on z-scores to combine information from auxiliary information to derive a “relative enrichment score” for each SNP. For each stratum of these relative enrichment scores, we obtain nonparametric estimates of posterior expected test statistics and replication probabilities as a function of discovery z-scores, using a resampling-based approach that repeatedly and randomly partitions meta-analysis sub-studies into training and replication samples. We fit a scale mixture of two Gaussians model to each stratum, obtaining parameter estimates that minimize the sum of squared differences of the scale-mixture model with the stratified nonparametric estimates. We apply this approach to the recent genome-wide association study (GWAS) of SCZ (n = 82,315), obtaining a good fit between the model-based and observed effect sizes and replication probabilities. We observed that SNPs with low enrichment scores replicate with a lower probability than SNPs with high enrichment scores even when both they are genome-wide significant (p < 5x10-8). There were 693 and 219 independent loci with model-based replication rates ≥80% and ≥90%, respectively. Compared to analyses not incorporating relative enrichment scores, CM3 increased out-of-sample yield for SNPs that replicate at a given rate. This demonstrates that replication probabilities can be more accurately estimated using prior enrichment information with CM3. PMID:26808560

Development of a program for toric intraocular lens calculation considering posterior corneal astigmatism, incision-induced posterior corneal astigmatism, and effective lens position.

PubMed

Eom, Youngsub; Ryu, Dongok; Kim, Dae Wook; Yang, Seul Ki; Song, Jong Suk; Kim, Sug-Whan; Kim, Hyo Myung

2016-10-01

To evaluate the toric intraocular lens (IOL) calculation considering posterior corneal astigmatism, incision-induced posterior corneal astigmatism, and effective lens position (ELP). Two thousand samples of corneal parameters with keratometric astigmatism ≥ 1.0 D were obtained using bootstrap methods. The probability distributions for incision-induced keratometric and posterior corneal astigmatisms, as well as ELP were estimated from the literature review. The predicted residual astigmatism error using method D with an IOL add power calculator (IAPC) was compared with those derived using methods A, B, and C through Monte-Carlo simulation. Method A considered the keratometric astigmatism and incision-induced keratometric astigmatism, method B considered posterior corneal astigmatism in addition to the A method, method C considered incision-induced posterior corneal astigmatism in addition to the B method, and method D considered ELP in addition to the C method. To verify the IAPC used in this study, the predicted toric IOL cylinder power and its axis using the IAPC were compared with ray-tracing simulation results. The median magnitude of the predicted residual astigmatism error using method D (0.25 diopters [D]) was smaller than that derived using methods A (0.42 D), B (0.38 D), and C (0.28 D) respectively. Linear regression analysis indicated that the predicted toric IOL cylinder power and its axis had excellent goodness-of-fit between the IAPC and ray-tracing simulation. The IAPC is a simple but accurate method for predicting the toric IOL cylinder power and its axis considering posterior corneal astigmatism, incision-induced posterior corneal astigmatism, and ELP.

An efficient algorithm to compute marginal posterior genotype probabilities for every member of a pedigree with loops

PubMed Central

2009-01-01

Background Marginal posterior genotype probabilities need to be computed for genetic analyses such as geneticcounseling in humans and selective breeding in animal and plant species. Methods In this paper, we describe a peeling based, deterministic, exact algorithm to compute efficiently genotype probabilities for every member of a pedigree with loops without recourse to junction-tree methods from graph theory. The efficiency in computing the likelihood by peeling comes from storing intermediate results in multidimensional tables called cutsets. Computing marginal genotype probabilities for individual i requires recomputing the likelihood for each of the possible genotypes of individual i. This can be done efficiently by storing intermediate results in two types of cutsets called anterior and posterior cutsets and reusing these intermediate results to compute the likelihood. Examples A small example is used to illustrate the theoretical concepts discussed in this paper, and marginal genotype probabilities are computed at a monogenic disease locus for every member in a real cattle pedigree. PMID:19958551

Assessing an ensemble Kalman filter inference of Manning's n coefficient of an idealized tidal inlet against a polynomial chaos-based MCMC

NASA Astrophysics Data System (ADS)

Siripatana, Adil; Mayo, Talea; Sraj, Ihab; Knio, Omar; Dawson, Clint; Le Maitre, Olivier; Hoteit, Ibrahim

2017-08-01

Bayesian estimation/inversion is commonly used to quantify and reduce modeling uncertainties in coastal ocean model, especially in the framework of parameter estimation. Based on Bayes rule, the posterior probability distribution function (pdf) of the estimated quantities is obtained conditioned on available data. It can be computed either directly, using a Markov chain Monte Carlo (MCMC) approach, or by sequentially processing the data following a data assimilation approach, which is heavily exploited in large dimensional state estimation problems. The advantage of data assimilation schemes over MCMC-type methods arises from the ability to algorithmically accommodate a large number of uncertain quantities without significant increase in the computational requirements. However, only approximate estimates are generally obtained by this approach due to the restricted Gaussian prior and noise assumptions that are generally imposed in these methods. This contribution aims at evaluating the effectiveness of utilizing an ensemble Kalman-based data assimilation method for parameter estimation of a coastal ocean model against an MCMC polynomial chaos (PC)-based scheme. We focus on quantifying the uncertainties of a coastal ocean ADvanced CIRCulation (ADCIRC) model with respect to the Manning's n coefficients. Based on a realistic framework of observation system simulation experiments (OSSEs), we apply an ensemble Kalman filter and the MCMC method employing a surrogate of ADCIRC constructed by a non-intrusive PC expansion for evaluating the likelihood, and test both approaches under identical scenarios. We study the sensitivity of the estimated posteriors with respect to the parameters of the inference methods, including ensemble size, inflation factor, and PC order. A full analysis of both methods, in the context of coastal ocean model, suggests that an ensemble Kalman filter with appropriate ensemble size and well-tuned inflation provides reliable mean estimates and uncertainties of Manning's n coefficients compared to the full posterior distributions inferred by MCMC.

Cumulative probability of neodymium: YAG laser posterior capsulotomy after phacoemulsification.

PubMed

Ando, Hiroshi; Ando, Nobuyo; Oshika, Tetsuro

2003-11-01

To retrospectively analyze the cumulative probability of neodymium:YAG (Nd:YAG) laser posterior capsulotomy after phacoemulsification and to evaluate the risk factors. Ando Eye Clinic, Kanagawa, Japan. In 3997 eyes that had phacoemulsification with an intact continuous curvilinear capsulorhexis, the cumulative probability of posterior capsulotomy was computed by Kaplan-Meier survival analysis and risk factors were analyzed using the Cox proportional hazards regression model. The variables tested were sex; age; type of cataract; preoperative best corrected visual acuity (BCVA); presence of diabetes mellitus, diabetic retinopathy, or retinitis pigmentosa; type of intraocular lens (IOL); and the year the operation was performed. The IOLs were categorized as 3-piece poly(methyl methacrylate) (PMMA), 1-piece PMMA, 3-piece silicone, and acrylic foldable. The cumulative probability of capsulotomy after cataract surgery was 1.95%, 18.50%, and 32.70% at 1, 3, and 5 years, respectively. Positive risk factors included a better preoperative BCVA (P =.0005; risk ratio [RR], 1.7; 95% confidence interval [CI], 1.3-2.5) and the presence of retinitis pigmentosa (P<.0001; RR, 6.6; 95% CI, 3.7-11.6). Women had a significantly greater probability of Nd:YAG laser posterior capsulotomy (P =.016; RR, 1.4; 95% CI, 1.1-1.8). The type of IOL was significantly related to the probability of Nd:YAG laser capsulotomy, with the foldable acrylic IOL having a significantly lower probability of capsulotomy. The 1-piece PMMA IOL had a significantly higher risk than 3-piece PMMA and 3-piece silicone IOLs. The probability of Nd:YAG laser capsulotomy was higher in women, in eyes with a better preoperative BCVA, and in patients with retinitis pigmentosa. The foldable acrylic IOL had a significantly lower probability of capsulotomy.

Spatially explicit models for inference about density in unmarked or partially marked populations

USGS Publications Warehouse

Chandler, Richard B.; Royle, J. Andrew

2013-01-01

Recently developed spatial capture–recapture (SCR) models represent a major advance over traditional capture–recapture (CR) models because they yield explicit estimates of animal density instead of population size within an unknown area. Furthermore, unlike nonspatial CR methods, SCR models account for heterogeneity in capture probability arising from the juxtaposition of animal activity centers and sample locations. Although the utility of SCR methods is gaining recognition, the requirement that all individuals can be uniquely identified excludes their use in many contexts. In this paper, we develop models for situations in which individual recognition is not possible, thereby allowing SCR concepts to be applied in studies of unmarked or partially marked populations. The data required for our model are spatially referenced counts made on one or more sample occasions at a collection of closely spaced sample units such that individuals can be encountered at multiple locations. Our approach includes a spatial point process for the animal activity centers and uses the spatial correlation in counts as information about the number and location of the activity centers. Camera-traps, hair snares, track plates, sound recordings, and even point counts can yield spatially correlated count data, and thus our model is widely applicable. A simulation study demonstrated that while the posterior mean exhibits frequentist bias on the order of 5–10% in small samples, the posterior mode is an accurate point estimator as long as adequate spatial correlation is present. Marking a subset of the population substantially increases posterior precision and is recommended whenever possible. We applied our model to avian point count data collected on an unmarked population of the northern parula (Parula americana) and obtained a density estimate (posterior mode) of 0.38 (95% CI: 0.19–1.64) birds/ha. Our paper challenges sampling and analytical conventions in ecology by demonstrating that neither spatial independence nor individual recognition is needed to estimate population density—rather, spatial dependence can be informative about individual distribution and density.

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.

optBINS: Optimal Binning for histograms

NASA Astrophysics Data System (ADS)

Knuth, Kevin H.

2018-03-01

optBINS (optimal binning) determines the optimal number of bins in a uniform bin-width histogram by deriving the posterior probability for the number of bins in a piecewise-constant density model after assigning a multinomial likelihood and a non-informative prior. The maximum of the posterior probability occurs at a point where the prior probability and the the joint likelihood are balanced. The interplay between these opposing factors effectively implements Occam's razor by selecting the most simple model that best describes the data.

SU-G-JeP2-02: A Unifying Multi-Atlas Approach to Electron Density Mapping Using Multi-Parametric MRI for Radiation Treatment Planning

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

Ren, S; Tianjin University, Tianjin; Hara, W

Purpose: MRI has a number of advantages over CT as a primary modality for radiation treatment planning (RTP). However, one key bottleneck problem still remains, which is the lack of electron density information in MRI. In the work, a reliable method to map electron density is developed by leveraging the differential contrast of multi-parametric MRI. Methods: We propose a probabilistic Bayesian approach for electron density mapping based on T1 and T2-weighted MRI, using multiple patients as atlases. For each voxel, we compute two conditional probabilities: (1) electron density given its image intensity on T1 and T2-weighted MR images, and (2)more » electron density given its geometric location in a reference anatomy. The two sources of information (image intensity and spatial location) are combined into a unifying posterior probability density function using the Bayesian formalism. The mean value of the posterior probability density function provides the estimated electron density. Results: We evaluated the method on 10 head and neck patients and performed leave-one-out cross validation (9 patients as atlases and remaining 1 as test). The proposed method significantly reduced the errors in electron density estimation, with a mean absolute HU error of 138, compared with 193 for the T1-weighted intensity approach and 261 without density correction. For bone detection (HU>200), the proposed method had an accuracy of 84% and a sensitivity of 73% at specificity of 90% (AUC = 87%). In comparison, the AUC for bone detection is 73% and 50% using the intensity approach and without density correction, respectively. Conclusion: The proposed unifying method provides accurate electron density estimation and bone detection based on multi-parametric MRI of the head with highly heterogeneous anatomy. This could allow for accurate dose calculation and reference image generation for patient setup in MRI-based radiation treatment planning.« less

Estimated Probability of a Cervical Spine Injury During an ISS Mission

NASA Technical Reports Server (NTRS)

Brooker, John E.; Weaver, Aaron S.; Myers, Jerry G.

2013-01-01

Introduction: The Integrated Medical Model (IMM) utilizes historical data, cohort data, and external simulations as input factors to provide estimates of crew health, resource utilization and mission outcomes. The Cervical Spine Injury Module (CSIM) is an external simulation designed to provide the IMM with parameter estimates for 1) a probability distribution function (PDF) of the incidence rate, 2) the mean incidence rate, and 3) the standard deviation associated with the mean resulting from injury/trauma of the neck. Methods: An injury mechanism based on an idealized low-velocity blunt impact to the superior posterior thorax of an ISS crewmember was used as the simulated mission environment. As a result of this impact, the cervical spine is inertially loaded from the mass of the head producing an extension-flexion motion deforming the soft tissues of the neck. A multibody biomechanical model was developed to estimate the kinematic and dynamic response of the head-neck system from a prescribed acceleration profile. Logistic regression was performed on a dataset containing AIS1 soft tissue neck injuries from rear-end automobile collisions with published Neck Injury Criterion values producing an injury transfer function (ITF). An injury event scenario (IES) was constructed such that crew 1 is moving through a primary or standard translation path transferring large volume equipment impacting stationary crew 2. The incidence rate for this IES was estimated from in-flight data and used to calculate the probability of occurrence. The uncertainty in the model input factors were estimated from representative datasets and expressed in terms of probability distributions. A Monte Carlo Method utilizing simple random sampling was employed to propagate both aleatory and epistemic uncertain factors. Scatterplots and partial correlation coefficients (PCC) were generated to determine input factor sensitivity. CSIM was developed in the SimMechanics/Simulink environment with a Monte Carlo wrapper (MATLAB) used to integrate the components of the module. Results: The probability of generating an AIS1 soft tissue neck injury from the extension/flexion motion induced by a low-velocity blunt impact to the superior posterior thorax was fitted with a lognormal PDF with mean 0.26409, standard deviation 0.11353, standard error of mean 0.00114, and 95% confidence interval [0.26186, 0.26631]. Combining the probability of an AIS1 injury with the probability of IES occurrence was fitted with a Johnson SI PDF with mean 0.02772, standard deviation 0.02012, standard error of mean 0.00020, and 95% confidence interval [0.02733, 0.02812]. The input factor sensitivity analysis in descending order was IES incidence rate, ITF regression coefficient 1, impactor initial velocity, ITF regression coefficient 2, and all others (equipment mass, crew 1 body mass, crew 2 body mass) insignificant. Verification and Validation (V&V): The IMM V&V, based upon NASA STD 7009, was implemented which included an assessment of the data sets used to build CSIM. The documentation maintained includes source code comments and a technical report. The software code and documentation is under Subversion configuration management. Kinematic validation was performed by comparing the biomechanical model output to established corridors.

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

DOE PAGES

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

2017-11-15

In Hezaveh et al. (2017) we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data,more » as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single hyperparameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that neural networks can be a fast alternative to Monte Carlo Markov Chains for parameter uncertainty estimation in many practical applications, allowing more than seven orders of magnitude improvement in speed.« less

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

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

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

In Hezaveh et al. (2017) we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data,more » as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single hyperparameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that neural networks can be a fast alternative to Monte Carlo Markov Chains for parameter uncertainty estimation in many practical applications, allowing more than seven orders of magnitude improvement in speed.« less

Testing the molecular clock using mechanistic models of fossil preservation and molecular evolution

PubMed Central

2017-01-01

Molecular sequence data provide information about relative times only, and fossil-based age constraints are the ultimate source of information about absolute times in molecular clock dating analyses. Thus, fossil calibrations are critical to molecular clock dating, but competing methods are difficult to evaluate empirically because the true evolutionary time scale is never known. Here, we combine mechanistic models of fossil preservation and sequence evolution in simulations to evaluate different approaches to constructing fossil calibrations and their impact on Bayesian molecular clock dating, and the relative impact of fossil versus molecular sampling. We show that divergence time estimation is impacted by the model of fossil preservation, sampling intensity and tree shape. The addition of sequence data may improve molecular clock estimates, but accuracy and precision is dominated by the quality of the fossil calibrations. Posterior means and medians are poor representatives of true divergence times; posterior intervals provide a much more accurate estimate of divergence times, though they may be wide and often do not have high coverage probability. Our results highlight the importance of increased fossil sampling and improved statistical approaches to generating calibrations, which should incorporate the non-uniform nature of ecological and temporal fossil species distributions. PMID:28637852

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…

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.

Gaussianization for fast and accurate inference from cosmological data

NASA Astrophysics Data System (ADS)

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

2016-06-01

We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box-Cox transformations and generalizations thereof. This permits an analytical reconstruction of the posterior from a point sample, like a Markov chain, and simplifies the subsequent joint analysis with other experiments. This way, a multivariate posterior density can be reported efficiently, by compressing the information contained in Markov Chain Monte Carlo samples. Further, the model evidence integral (I.e. the marginal likelihood) can be computed analytically. This method is analogous to the search for normal parameters in the cosmic microwave background, but is more general. The search for the optimally Gaussianizing transformation is performed computationally through a maximum-likelihood formalism; its quality can be judged by how well the credible regions of the posterior are reproduced. We demonstrate that our method outperforms kernel density estimates in this objective. Further, we select marginal posterior samples from Planck data with several distinct strongly non-Gaussian features, and verify the reproduction of the marginal contours. To demonstrate evidence computation, we Gaussianize the joint distribution of data from weak lensing and baryon acoustic oscillations, for different cosmological models, and find a preference for flat Λcold dark matter. Comparing to values computed with the Savage-Dickey density ratio, and Population Monte Carlo, we find good agreement of our method within the spread of the other two.

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.

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).

Declining Abundance of Beaked Whales (Family Ziphiidae) in the California Current Large Marine Ecosystem

PubMed Central

Moore, Jeffrey E.; Barlow, Jay P.

2013-01-01

Beaked whales are among the most diverse yet least understood groups of marine mammals. A diverse set of mostly anthropogenic threats necessitates improvement in our ability to assess population status for this cryptic group. The Southwest Fisheries Science Center (NOAA) conducted six ship line-transect cetacean abundance surveys in the California Current off the contiguous western United States between 1991 and 2008. We used a Bayesian hidden-process modeling approach to estimate abundance and population trends of beaked whales using sightings data from these surveys. We also compiled records of beaked whale stranding events (3 genera, at least 8 species) on adjacent beaches from 1900 to 2012, to help assess population status of beaked whales in the northern part of the California Current. Bayesian posterior summaries for trend parameters provide strong evidence of declining beaked whale abundance in the study area. The probability of negative trend for Cuvier's beaked whale (Ziphius cavirostris) during 1991–2008 was 0.84, with 1991 and 2008 estimates of 10771 (CV = 0.51) and ≈7550 (CV = 0.55), respectively. The probability of decline for Mesoplodon spp. (pooled across species) was 0.96, with 1991 and 2008 estimates of 2206 (CV = 0.46) and 811 (CV = 0.65). The mean posterior estimates for average rate of decline were 2.9% and 7.0% per year. There was no evidence of abundance trend for Baird's beaked whale (Berardius bairdii), for which annual abundance estimates in the survey area ranged from ≈900 to 1300 (CV≈1.3). Stranding data were consistent with the survey results. Causes of apparent declines are unknown. Direct impacts of fisheries (bycatch) can be ruled out, but impacts of anthropogenic sound (e.g., naval active sonar) and ecosystem change are plausible hypotheses that merit investigation. PMID:23341907

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 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

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.

Phylogenomics of a rapid radiation: is chromosomal evolution linked to increased diversification in north american spiny lizards (Genus Sceloporus)?

PubMed

Leaché, Adam D; Banbury, Barbara L; Linkem, Charles W; de Oca, Adrián Nieto-Montes

2016-03-22

Resolving the short phylogenetic branches that result from rapid evolutionary diversification often requires large numbers of loci. We collected targeted sequence capture data from 585 nuclear loci (541 ultraconserved elements and 44 protein-coding genes) to estimate the phylogenetic relationships among iguanian lizards in the North American genus Sceloporus. We tested for diversification rate shifts to determine if rapid radiation in the genus is correlated with chromosomal evolution. The phylogenomic trees that we obtained for Sceloporus using concatenation and coalescent-based species tree inference provide strong support for the monophyly and interrelationships among nearly all major groups. The diversification analysis supported one rate shift on the Sceloporus phylogeny approximately 20-25 million years ago that is associated with the doubling of the speciation rate from 0.06 species/million years (Ma) to 0.15 species/Ma. The posterior probability for this rate shift occurring on the branch leading to the Sceloporus species groups exhibiting increased chromosomal diversity is high (posterior probability = 0.997). Despite high levels of gene tree discordance, we were able to estimate a phylogenomic tree for Sceloporus that solves some of the taxonomic problems caused by previous analyses of fewer loci. The taxonomic changes that we propose using this new phylogenomic tree help clarify the number and composition of the major species groups in the genus. Our study provides new evidence for a putative link between chromosomal evolution and the rapid divergence and radiation of Sceloporus across North America.

Nonlinear detection for a high rate extended binary phase shift keying system.

PubMed

Chen, Xian-Qing; Wu, Le-Nan

2013-03-28

The algorithm and the results of a nonlinear detector using a machine learning technique called support vector machine (SVM) on an efficient modulation system with high data rate and low energy consumption is presented in this paper. Simulation results showed that the performance achieved by the SVM detector is comparable to that of a conventional threshold decision (TD) detector. The two detectors detect the received signals together with the special impacting filter (SIF) that can improve the energy utilization efficiency. However, unlike the TD detector, the SVM detector concentrates not only on reducing the BER of the detector, but also on providing accurate posterior probability estimates (PPEs), which can be used as soft-inputs of the LDPC decoder. The complexity of this detector is considered in this paper by using four features and simplifying the decision function. In addition, a bandwidth efficient transmission is analyzed with both SVM and TD detector. The SVM detector is more robust to sampling rate than TD detector. We find that the SVM is suitable for extended binary phase shift keying (EBPSK) signal detection and can provide accurate posterior probability for LDPC decoding.

Nonlinear Detection for a High Rate Extended Binary Phase Shift Keying System

PubMed Central

Chen, Xian-Qing; Wu, Le-Nan

2013-01-01

The algorithm and the results of a nonlinear detector using a machine learning technique called support vector machine (SVM) on an efficient modulation system with high data rate and low energy consumption is presented in this paper. Simulation results showed that the performance achieved by the SVM detector is comparable to that of a conventional threshold decision (TD) detector. The two detectors detect the received signals together with the special impacting filter (SIF) that can improve the energy utilization efficiency. However, unlike the TD detector, the SVM detector concentrates not only on reducing the BER of the detector, but also on providing accurate posterior probability estimates (PPEs), which can be used as soft-inputs of the LDPC decoder. The complexity of this detector is considered in this paper by using four features and simplifying the decision function. In addition, a bandwidth efficient transmission is analyzed with both SVM and TD detector. The SVM detector is more robust to sampling rate than TD detector. We find that the SVM is suitable for extended binary phase shift keying (EBPSK) signal detection and can provide accurate posterior probability for LDPC decoding. PMID:23539034

Relevance Vector Machine Learning for Neonate Pain Intensity Assessment Using Digital Imaging

PubMed Central

Gholami, Behnood; Tannenbaum, Allen R.

2011-01-01

Pain assessment in patients who are unable to verbally communicate is a challenging problem. The fundamental limitations in pain assessment in neonates stem from subjective assessment criteria, rather than quantifiable and measurable data. This often results in poor quality and inconsistent treatment of patient pain management. Recent advancements in pattern recognition techniques using relevance vector machine (RVM) learning techniques can assist medical staff in assessing pain by constantly monitoring the patient and providing the clinician with quantifiable data for pain management. The RVM classification technique is a Bayesian extension of the support vector machine (SVM) algorithm, which achieves comparable performance to SVM while providing posterior probabilities for class memberships and a sparser model. If classes represent “pure” facial expressions (i.e., extreme expressions that an observer can identify with a high degree of confidence), then the posterior probability of the membership of some intermediate facial expression to a class can provide an estimate of the intensity of such an expression. In this paper, we use the RVM classification technique to distinguish pain from nonpain in neonates as well as assess their pain intensity levels. We also correlate our results with the pain intensity assessed by expert and nonexpert human examiners. PMID:20172803

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.

Sea Ice Concentration Estimation Using Active and Passive Remote Sensing Data Fusion

NASA Astrophysics Data System (ADS)

Zhang, Y.; Li, F.; Zhang, S.; Zhu, T.

2017-12-01

In this abstract, a decision-level fusion method by utilizing SAR and passive microwave remote sensing data for sea ice concentration estimation is investigated. Sea ice concentration product from passive microwave concentration retrieval methods has large uncertainty within thin ice zone. Passive microwave data including SSM/I, AMSR-E, and AMSR-2 provide daily and long time series observations covering whole polar sea ice scene, and SAR images provide rich sea ice details with high spatial resolution including deformation and polarimetric features. In the proposed method, the merits from passive microwave data and SAR data are considered. Sea ice concentration products from ASI and sea ice category label derived from CRF framework in SAR imagery are calibrated under least distance protocol. For SAR imagery, incident angle and azimuth angle were used to correct backscattering values from slant range to ground range in order to improve geocoding accuracy. The posterior probability distribution between category label from SAR imagery and passive microwave sea ice concentration product is modeled and integrated under Bayesian network, where Gaussian statistical distribution from ASI sea ice concentration products serves as the prior term, which represented as an uncertainty of sea ice concentration. Empirical model based likelihood term is constructed under Bernoulli theory, which meets the non-negative and monotonically increasing conditions. In the posterior probability estimation procedure, final sea ice concentration is obtained using MAP criterion, which equals to minimize the cost function and it can be calculated with nonlinear iteration method. The proposed algorithm is tested on multiple satellite SAR data sets including GF-3, Sentinel-1A, RADARSAT-2 and Envisat ASAR. Results show that the proposed algorithm can improve the accuracy of ASI sea ice concentration products and reduce the uncertainty along the ice edge.

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

NASA Astrophysics Data System (ADS)

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

2017-11-01

In Hezaveh et al. we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational-lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data, as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single variational parameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that the application of approximate Bayesian neural networks to astrophysical modeling problems can be a fast alternative to Monte Carlo Markov Chains, allowing orders of magnitude improvement in speed.

Confidence level estimation in multi-target classification problems

NASA Astrophysics Data System (ADS)

Chang, Shi; Isaacs, Jason; Fu, Bo; Shin, Jaejeong; Zhu, Pingping; Ferrari, Silvia

2018-04-01

This paper presents an approach for estimating the confidence level in automatic multi-target classification performed by an imaging sensor on an unmanned vehicle. An automatic target recognition algorithm comprised of a deep convolutional neural network in series with a support vector machine classifier detects and classifies targets based on the image matrix. The joint posterior probability mass function of target class, features, and classification estimates is learned from labeled data, and recursively updated as additional images become available. Based on the learned joint probability mass function, the approach presented in this paper predicts the expected confidence level of future target classifications, prior to obtaining new images. The proposed approach is tested with a set of simulated sonar image data. The numerical results show that the estimated confidence level provides a close approximation to the actual confidence level value determined a posteriori, i.e. after the new image is obtained by the on-board sensor. Therefore, the expected confidence level function presented in this paper can be used to adaptively plan the path of the unmanned vehicle so as to optimize the expected confidence levels and ensure that all targets are classified with satisfactory confidence after the path is executed.

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.

Maximum entropy approach to statistical inference for an ocean acoustic waveguide.

PubMed

Knobles, D P; Sagers, J D; Koch, R A

2012-02-01

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations. © 2012 Acoustical Society of America

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 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.

Accommodating Chromosome Inversions in Linkage Analysis

PubMed Central

Chen, Gary K.; Slaten, Erin; Ophoff, Roel A.; Lange, Kenneth

2006-01-01

This work develops a population-genetics model for polymorphic chromosome inversions. The model precisely describes how an inversion changes the nature of and approach to linkage equilibrium. The work also describes algorithms and software for allele-frequency estimation and linkage analysis in the presence of an inversion. The linkage algorithms implemented in the software package Mendel estimate recombination parameters and calculate the posterior probability that each pedigree member carries the inversion. Application of Mendel to eight Centre d'Étude du Polymorphisme Humain pedigrees in a region containing a common inversion on 8p23 illustrates its potential for providing more-precise estimates of the location of an unmapped marker or trait gene. Our expanded cytogenetic analysis of these families further identifies inversion carriers and increases the evidence of linkage. PMID:16826515

Evaluation of sampling, cookery, and shear force protocols for objective evaluation of lamb longissimus tenderness.

PubMed

Shackelford, S D; Wheeler, T L; Koohmaraie, M

2004-03-01

Experiments were conducted to compare the effects of two cookery methods, two shear force procedures, and sampling location within non-callipyge and callipyge lamb LM on the magnitude, variance, and repeatability of LM shear force data. In Exp. 1, 15 non-callipyge and 15 callipyge carcasses were sampled, and Warner-Bratzler shear force (WBSF) was determined for both sides of each carcass at three locations along the length (anterior to posterior) of the LM, whereas slice shear force (SSF) was determined for both sides of each carcass at only one location. For approximately half the carcasses within each genotype, LM chops were cooked for a constant amount of time using a belt grill, and chops of the remaining carcasses were cooked to a constant endpoint temperature using open-hearth electric broilers. Regardless of cooking method and sampling location, repeatability estimates were at least 0.8 for LM WBSF and SSF. For WBSF, repeatability estimates were slightly higher at the anterior location (0.93 to 0.98) than the posterior location (0.88 to 0.90). The difference in repeatability between locations was probably a function of a greater level of variation in shear force at the anterior location. For callipyge LM, WBSF was higher (P < 0.001) at the anterior location than at the middle or posterior locations. For non-callipyge LM, WBSF was lower (P < 0.001) at the anterior location than at the middle or posterior locations. Consequently, the difference in WBSF between callipyge and non-callipyge LM was largest at the anterior location. Experiment 2 was conducted to obtain an estimate of the repeatability of SSF for lamb LM chops cooked with the belt grill using a larger number of animals (n = 87). In Exp. 2, LM chops were obtained from matching locations of both sides of 44 non-callipyge and 43 callipyge carcasses. Chops were cooked with a belt grill and SSF was measured, and repeatability was estimated to be 0.95. Repeatable estimates of lamb LM tenderness can be achieved either by cooking to a constant endpoint temperature with electric broilers or cooking for a constant amount of time with a belt grill. Likewise, repeatable estimates of lamb LM tenderness can be achieved with WBSF or SSF. However, use of belt grill cookery and the SSF technique could decrease time requirements which would decrease research costs.

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.

Naive Probability: A Mental Model Theory of Extensional Reasoning.

ERIC Educational Resources Information Center

Johnson-Laird, P. N.; Legrenzi, Paolo; Girotto, Vittorio; Legrenzi, Maria Sonino; Caverni, Jean-Paul

1999-01-01

Outlines a theory of naive probability in which individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an "extensional" way. The theory accommodates reasoning based on numerical premises, and explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem.…

Estimation of sensitivity and specificity of pregnancy diagnosis using transrectal ultrasonography and ELISA for pregnancy-associated glycoprotein in dairy cows using a Bayesian latent class model.

PubMed

Shephard, R W; Morton, J M

2018-01-01

To determine the sensitivity (Se) and specificity (Sp) of pregnancy diagnosis using transrectal ultrasonography and an ELISA for pregnancy-associated glycoprotein (PAG) in milk, in lactating dairy cows in seasonally calving herds approximately 85-100 days after the start of the herd's breeding period. Paired results were used from pregnancy diagnosis using transrectal ultrasonography and ELISA for PAG in milk carried out approximately 85 and 100 days after the start of the breeding period, respectively, from 879 cows from four herds in Victoria, Australia. A Bayesian latent class model was used to estimate the proportion of cows pregnant, the Se and Sp of each test, and covariances between test results in pregnant and non-pregnant cows. Prior probability estimates were defined using beta distributions for the expected proportion of cows pregnant, Se and Sp for each test, and covariances between tests. Markov Chain Monte Carlo iterations identified posterior distributions for each of the unknown variables. Posterior distributions for each parameter were described using medians and 95% probability (i.e. credible) intervals (PrI). The posterior median estimates for Se and Sp for each test were used to estimate positive predictive and negative predictive values across a range of pregnancy proportions. The estimate for proportion pregnant was 0.524 (95% PrI = 0.485-0.562). For pregnancy diagnosis using transrectal ultrasonography, Se and Sp were 0.939 (95% PrI = 0.890-0.974) and 0.943 (95% PrI = 0.885-0.984), respectively; for ELISA, Se and Sp were 0.963 (95% PrI = 0.919-0.990) and 0.870 (95% PrI = 0.806-0.931), respectively. The estimated covariance between test results was 0.033 (95% PrI = 0.008-0.046) and 0.035 (95% PrI = 0.018-0.078) for pregnant and non-pregnant cows, respectively. Pregnancy diagnosis results using transrectal ultrasonography had a higher positive predictive value but lower negative predictive value than results from the ELISA across the range of pregnancy proportions assessed. Pregnancy diagnosis using transrectal ultrasonography and ELISA for PAG in milk had similar Se but differed in predictive values. Pregnancy diagnosis in seasonally calving herds around 85-100 days after the start of the breeding period using the ELISA is expected to result in a higher negative predictive value but lower positive predictive value than pregnancy diagnosis using transrectal ultrasonography. Thus, with the ELISA, a higher proportion of the cows with negative results will be non-pregnant, relative to results from transrectal ultrasonography, but a lower proportion of cows with positive results will be pregnant.

Testing the molecular clock using mechanistic models of fossil preservation and molecular evolution.

PubMed

Warnock, Rachel C M; Yang, Ziheng; Donoghue, Philip C J

2017-06-28

Molecular sequence data provide information about relative times only, and fossil-based age constraints are the ultimate source of information about absolute times in molecular clock dating analyses. Thus, fossil calibrations are critical to molecular clock dating, but competing methods are difficult to evaluate empirically because the true evolutionary time scale is never known. Here, we combine mechanistic models of fossil preservation and sequence evolution in simulations to evaluate different approaches to constructing fossil calibrations and their impact on Bayesian molecular clock dating, and the relative impact of fossil versus molecular sampling. We show that divergence time estimation is impacted by the model of fossil preservation, sampling intensity and tree shape. The addition of sequence data may improve molecular clock estimates, but accuracy and precision is dominated by the quality of the fossil calibrations. Posterior means and medians are poor representatives of true divergence times; posterior intervals provide a much more accurate estimate of divergence times, though they may be wide and often do not have high coverage probability. Our results highlight the importance of increased fossil sampling and improved statistical approaches to generating calibrations, which should incorporate the non-uniform nature of ecological and temporal fossil species distributions. © 2017 The Authors.

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.

Generalized Maximum Entropy

NASA Technical Reports Server (NTRS)

Cheeseman, Peter; Stutz, John

2005-01-01

A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].

Calibration of micromechanical parameters for DEM simulations by using the particle filter

NASA Astrophysics Data System (ADS)

Cheng, Hongyang; Shuku, Takayuki; Thoeni, Klaus; Yamamoto, Haruyuki

2017-06-01

The calibration of DEM models is typically accomplished by trail and error. However, the procedure lacks of objectivity and has several uncertainties. To deal with these issues, the particle filter is employed as a novel approach to calibrate DEM models of granular soils. The posterior probability distribution of the microparameters that give numerical results in good agreement with the experimental response of a Toyoura sand specimen is approximated by independent model trajectories, referred as `particles', based on Monte Carlo sampling. The soil specimen is modeled by polydisperse packings with different numbers of spherical grains. Prepared in `stress-free' states, the packings are subjected to triaxial quasistatic loading. Given the experimental data, the posterior probability distribution is incrementally updated, until convergence is reached. The resulting `particles' with higher weights are identified as the calibration results. The evolutions of the weighted averages and posterior probability distribution of the micro-parameters are plotted to show the advantage of using a particle filter, i.e., multiple solutions are identified for each parameter with known probabilities of reproducing the experimental response.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

Maximum Entropy Approach in Dynamic Contrast-Enhanced Magnetic Resonance Imaging.

PubMed

Farsani, Zahra Amini; Schmid, Volker J

2017-01-01

In the estimation of physiological kinetic parameters from Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) data, the determination of the arterial input function (AIF) plays a key role. This paper proposes a Bayesian method to estimate the physiological parameters of DCE-MRI along with the AIF in situations, where no measurement of the AIF is available. In the proposed algorithm, the maximum entropy method (MEM) is combined with the maximum a posterior approach (MAP). To this end, MEM is used to specify a prior probability distribution of the unknown AIF. The ability of this method to estimate the AIF is validated using the Kullback-Leibler divergence. Subsequently, the kinetic parameters can be estimated with MAP. The proposed algorithm is evaluated with a data set from a breast cancer MRI study. The application shows that the AIF can reliably be determined from the DCE-MRI data using MEM. Kinetic parameters can be estimated subsequently. The maximum entropy method is a powerful tool to reconstructing images from many types of data. This method is useful for generating the probability distribution based on given information. The proposed method gives an alternative way to assess the input function from the existing data. The proposed method allows a good fit of the data and therefore a better estimation of the kinetic parameters. In the end, this allows for a more reliable use of DCE-MRI. Schattauer GmbH.

Improved Analysis of GW150914 Using a Fully Spin-Precessing Waveform Model

NASA Astrophysics Data System (ADS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Bacon, P.; Bader, M. K. M.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Bejger, M.; Bell, A. S.; Berger, B. K.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Birnholtz, O.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Boer, M.; Bogaert, G.; Bogan, C.; Bohe, A.; Bond, C.; Bondu, F.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Broida, J. E.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Brunett, S.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cabero, M.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, C.; Casentini, J.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Cheeseboro, B. D.; Chen, H. Y.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Cominsky, L.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Cowan, E. E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dal Canton, T.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dasgupta, A.; Da Silva Costa, C. F.; Dattilo, V.; Dave, I.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; De, S.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Devine, R. C.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Girolamo, T.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Virgilio, A.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Engels, W.; Essick, R. C.; Etienne, Z.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Fauchon-Jones, E.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Fenyvesi, E.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fiorucci, D.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fournier, J.-D.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gaebel, S.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gaur, G.; Gehrels, N.; Gemme, G.; Geng, P.; Genin, E.; Gennai, A.; George, J.; Gergely, L.; Germain, V.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glaefke, A.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Grado, A.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Healy, J.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Henry, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hofman, D.; Holt, K.; Holz, D. E.; Hopkins, P.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Indik, N.; Ingram, D. R.; Inta, R.; Isa, H. N.; Isac, J.-M.; Isi, M.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jang, H.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jian, L.; Jiménez-Forteza, F.; Johnson, W. W.; Johnson-McDaniel, N. K.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; K, Haris; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Kapadia, S. J.; Karki, S.; Karvinen, K. S.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kennedy, R.; Key, J. S.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, Chi-Woong; Kim, Chunglee; Kim, J.; Kim, K.; Kim, N.; Kim, W.; Kim, Y.-M.; Kimbrell, S. J.; King, E. J.; King, P. J.; Kissel, J. S.; Klein, B.; Kleybolte, L.; Klimenko, S.; Koehlenbeck, S. M.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, P.; Kumar, R.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lange, J.; Lantz, B.; Lasky, P. D.; Laxen, M.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E. O.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, K.; Lenon, A.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Lewis, J. B.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Lockerbie, N. A.; Lombardi, A. L.; London, L. T.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lousto, C. O.; Lovelace, G.; Lück, H.; Lundgren, A. P.; Lynch, R.; Ma, Y.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña-Sandoval, F.; Magaña Zertuche, L.; Magee, R. M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Mastrogiovanni, S.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McRae, T.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Melatos, A.; Mendell, G.; Mercer, R. A.; Merilh, E. L.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Metzdorff, R.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, A. L.; Miller, A.; Miller, B. B.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Nedkova, K.; Nelemans, G.; Nelson, T. J. N.; Neri, M.; Neunzert, A.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; O'Shaughnessy, R.; Ottaway, D. J.; Overmier, H.; Owen, B. J.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patricelli, B.; Patrick, Z.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perreca, A.; Perri, L. M.; Pfeiffer, H. P.; Phelps, M.; Piccinni, O. J.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poe, M.; Poggiani, R.; Popolizio, P.; Post, A.; Powell, J.; Prasad, J.; Predoi, V.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prix, R.; Prodi, G. A.; Prokhorov, L.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Qiu, S.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rajan, C.; Rakhmanov, M.; Rapagnani, P.; Raymond, V.; Razzano, M.; Re, V.; Read, J.; Reed, C. M.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Rew, H.; Reyes, S. D.; Ricci, F.; Riles, K.; Rizzo, M.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Sakellariadou, M.; Salconi, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sanchez, E. J.; Sandberg, V.; Sandeen, B.; Sanders, J. R.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Sauter, O. E. S.; Savage, R. L.; Sawadsky, A.; Schale, P.; Schilling, R.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Scott, J.; Scott, S. M.; Sellers, D.; Sengupta, A. S.; Sentenac, D.; Sequino, V.; Sergeev, A.; Setyawati, Y.; Shaddock, D. A.; Shaffer, T.; Shahriar, M. S.; Shaltev, M.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sieniawska, M.; Sigg, D.; Silva, A. D.; Singer, A.; Singer, L. P.; Singh, A.; Singh, R.; Singhal, A.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, J. R.; Smith, N. D.; Smith, R. J. E.; Son, E. J.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Stevenson, S. P.; Stone, R.; Strain, K. A.; Straniero, N.; Stratta, G.; Strauss, N. A.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sunil, S.; Sutton, P. J.; Swinkels, B. L.; Szczepańczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Tarabrin, S. P.; Taracchini, A.; Taylor, R.; Theeg, T.; Thirugnanasambandam, M. P.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Toland, K.; Tomlinson, C.; Tonelli, M.; Tornasi, Z.; Torres, C. V.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trifirò, D.; Tringali, M. C.; Trozzo, L.; Tse, M.; Turconi, M.; Tuyenbayev, D.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; Vallisneri, M.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; Van Den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van der Sluys, M. V.; van Heijningen, J. V.; Vano-Vinuales, A.; van Veggel, A. A.; Vardaro, M.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Vetrano, F.; Viceré, A.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Voss, D. V.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, X.; Wang, Y.; Ward, R. L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; Whiting, B. F.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Woehler, J.; Worden, J.; Wright, J. L.; Wu, D. S.; Wu, G.; Yablon, J.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yu, H.; Yvert, M.; ZadroŻny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zevin, M.; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; Boyle, M.; Brügmann, B.; Campanelli, M.; Chu, T.; Clark, M.; Haas, R.; Hemberger, D.; Hinder, I.; Kidder, L. E.; Kinsey, M.; Laguna, P.; Ossokine, S.; Pan, Y.; Röver, C.; Scheel, M.; Szilagyi, B.; Teukolsky, S.; Zlochower, Y.; LIGO Scientific Collaboration; Virgo Collaboration

2016-10-01

This paper presents updated estimates of source parameters for GW150914, a binary black-hole coalescence event detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) in 2015 [Abbott et al. Phys. Rev. Lett. 116, 061102 (2016).]. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] presented parameter estimation of the source using a 13-dimensional, phenomenological precessing-spin model (precessing IMRPhenom) and an 11-dimensional nonprecessing effective-one-body (EOB) model calibrated to numerical-relativity simulations, which forces spin alignment (nonprecessing EOBNR). Here, we present new results that include a 15-dimensional precessing-spin waveform model (precessing EOBNR) developed within the EOB formalism. We find good agreement with the parameters estimated previously [Abbott et al. Phys. Rev. Lett. 116, 241102 (2016).], and we quote updated component masses of 35-3+5 M⊙ and 3 0-4+3 M⊙ (where errors correspond to 90% symmetric credible intervals). We also present slightly tighter constraints on the dimensionless spin magnitudes of the two black holes, with a primary spin estimate <0.65 and a secondary spin estimate <0.75 at 90% probability. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] estimated the systematic parameter-extraction errors due to waveform-model uncertainty by combining the posterior probability densities of precessing IMRPhenom and nonprecessing EOBNR. Here, we find that the two precessing-spin models are in closer agreement, suggesting that these systematic errors are smaller than previously quoted.

Effect of posterior crown margin placement on gingival health.

PubMed

Reitemeier, Bernd; Hänsel, Kristina; Walter, Michael H; Kastner, Christian; Toutenburg, Helge

2002-02-01

The clinical impact of posterior crown margin placement on gingival health has not been thoroughly quantified. This study evaluated the effect of posterior crown margin placement with multivariate analysis. Ten general dentists reviewed 240 patients with 480 metal-ceramic crowns in a prospective clinical trial. The alloy was randomly selected from 2 high gold, 1 low gold, and 1 palladium alloy. Variables were the alloy used, oral hygiene index score before treatment, location of crown margins at baseline, and plaque index and sulcus bleeding index scores recorded for restored and control teeth after 1 year. The effect of crown margin placement on sulcular bleeding and plaque accumulation was analyzed with regression models (P<.05). The probability of plaque at 1 year increased with increasing oral hygiene index score before treatment. The lingual surfaces demonstrated the highest probability of plaque. The risk of bleeding at intrasulcular posterior crown margins was approximately twice that at supragingival margins. Poor oral hygiene before treatment and plaque also were associated with sulcular bleeding. Facial sites exhibited a lower probability of sulcular bleeding than lingual surfaces. Type of alloy did not influence sulcular bleeding. In this study, placement of crown margins was one of several parameters that affected gingival health.

Particle Filter with State Permutations for Solving Image Jigsaw Puzzles

PubMed Central

Yang, Xingwei; Adluru, Nagesh; Latecki, Longin Jan

2016-01-01

We deal with an image jigsaw puzzle problem, which is defined as reconstructing an image from a set of square and non-overlapping image patches. It is known that a general instance of this problem is NP-complete, and it is also challenging for humans, since in the considered setting the original image is not given. Recently a graphical model has been proposed to solve this and related problems. The target label probability function is then maximized using loopy belief propagation. We also formulate the problem as maximizing a label probability function and use exactly the same pairwise potentials. Our main contribution is a novel inference approach in the sampling framework of Particle Filter (PF). Usually in the PF framework it is assumed that the observations arrive sequentially, e.g., the observations are naturally ordered by their time stamps in the tracking scenario. Based on this assumption, the posterior density over the corresponding hidden states is estimated. In the jigsaw puzzle problem all observations (puzzle pieces) are given at once without any particular order. Therefore, we relax the assumption of having ordered observations and extend the PF framework to estimate the posterior density by exploring different orders of observations and selecting the most informative permutations of observations. This significantly broadens the scope of applications of the PF inference. Our experimental results demonstrate that the proposed inference framework significantly outperforms the loopy belief propagation in solving the image jigsaw puzzle problem. In particular, the extended PF inference triples the accuracy of the label assignment compared to that using loopy belief propagation. PMID:27795660

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…

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

Adjusting for founder relatedness in a linkage analysis using prior information.

PubMed

Sheehan, N A; Egeland, T

2008-01-01

In genetic linkage studies, while the pedigrees are generally known, background relatedness between the founding individuals, assumed by definition to be unrelated, can seriously affect the results of the analysis. Likelihood approaches to relationship estimation from genetic marker data can all be expressed in terms of finding the most likely pedigree connecting the individuals of interest. When the true relationship is the main focus, the set of all possible alternative pedigrees can be too large to consider. However, prior information is often available which, when incorporated in a formal and structured way, can restrict this set to a manageable size thus enabling the calculation of a posterior distribution from which inferences can be drawn. Here, the unknown relationships are more of a nuisance factor than of interest in their own right, so the focus is on adjusting the results of the analysis rather than on direct estimation. In this paper, we show how prior information on founder relationships can be exploited in some applications to generate a set of candidate extended pedigrees. We then weight the relevant pedigree-specific likelihoods by their posterior probabilities to adjust the lod score statistics. (c) 2007 S. Karger AG, Basel

Enhancing Data Assimilation by Evolutionary Particle Filter and Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Moradkhani, H.; Abbaszadeh, P.; Yan, H.

2016-12-01

Particle Filters (PFs) have received increasing attention by the researchers from different disciplines in hydro-geosciences as an effective method to improve model predictions in nonlinear and non-Gaussian dynamical systems. The implication of dual state and parameter estimation by means of data assimilation in hydrology and geoscience has evolved since 2005 from SIR-PF to PF-MCMC and now to the most effective and robust framework through evolutionary PF approach based on Genetic Algorithm (GA) and Markov Chain Monte Carlo (MCMC), the so-called EPF-MCMC. In this framework, the posterior distribution undergoes an evolutionary process to update an ensemble of prior states that more closely resemble realistic posterior probability distribution. The premise of this approach is that the particles move to optimal position using the GA optimization coupled with MCMC increasing the number of effective particles, hence the particle degeneracy is avoided while the particle diversity is improved. The proposed algorithm is applied on a conceptual and highly nonlinear hydrologic model and the effectiveness, robustness and reliability of the method in jointly estimating the states and parameters and also reducing the uncertainty is demonstrated for few river basins across the United States.

Rapid assessment of avoidable blindness in Bhutan.

PubMed

Lepcha, Nor Tshering; Chettri, Chandra Kumar; Getshen, Kunzang; Rai, Bhim Bahadur; Ramaswamy, Shamanna Bindiganavale; Saibaba, Saravanan; Nirmalan, Praveen Kumar; Demarchis, Emilia Hansson; Tabin, Geoffrey; Morley, Michael; Morley, Katharine

2013-08-01

To conduct a rapid assessment of avoidable blindness survey in Bhutan to obtain estimates of blindness, visual impairment, and cataract surgical coverage, outcomes and barriers among persons ≥50 years old. A total of 82 clusters of 50 people ≥50 years were selected using probability proportionate to size sampling. Eligible participants were selected from households using compact segment sampling, and underwent ophthalmic examination for visual acuity, followed by penlight and direct ophthalmoscopy. Participants with cataract were interviewed regarding surgical outcomes and barriers to surgery. Overall, 4046 of 4100 persons enumerated (98.7%) underwent ophthalmic examination. Adjusting for age and sex, the prevalence of bilaterally blind persons with available correction was 1.5% (95% confidence interval 1.09-1.89). Most blindness (67.1%) and severe visual impairment (74.1%) resulted from cataract, but 22.1% resulted from posterior segment pathology. Cataract surgical coverage for bilaterally blind persons was 72.7%. Almost 90% of patients reported moderate or good satisfaction, despite poor surgical outcomes in 23.6%. The prevalence of blindness in people aged ≥50 years in Bhutan was relatively low when compared with neighboring countries and World Health Organization sub-region estimates. Areas for improvement include community outreach, surgical outcomes, and posterior segment diseases.

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.

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.

Stereotactic probability and variability of speech arrest and anomia sites during stimulation mapping of the language dominant hemisphere.

PubMed

Chang, Edward F; Breshears, Jonathan D; Raygor, Kunal P; Lau, Darryl; Molinaro, Annette M; Berger, Mitchel S

2017-01-01

OBJECTIVE Functional mapping using direct cortical stimulation is the gold standard for the prevention of postoperative morbidity during resective surgery in dominant-hemisphere perisylvian regions. Its role is necessitated by the significant interindividual variability that has been observed for essential language sites. The aim in this study was to determine the statistical probability distribution of eliciting aphasic errors for any given stereotactically based cortical position in a patient cohort and to quantify the variability at each cortical site. METHODS Patients undergoing awake craniotomy for dominant-hemisphere primary brain tumor resection between 1999 and 2014 at the authors' institution were included in this study, which included counting and picture-naming tasks during dense speech mapping via cortical stimulation. Positive and negative stimulation sites were collected using an intraoperative frameless stereotactic neuronavigation system and were converted to Montreal Neurological Institute coordinates. Data were iteratively resampled to create mean and standard deviation probability maps for speech arrest and anomia. Patients were divided into groups with a "classic" or an "atypical" location of speech function, based on the resultant probability maps. Patient and clinical factors were then assessed for their association with an atypical location of speech sites by univariate and multivariate analysis. RESULTS Across 102 patients undergoing speech mapping, the overall probabilities of speech arrest and anomia were 0.51 and 0.33, respectively. Speech arrest was most likely to occur with stimulation of the posterior inferior frontal gyrus (maximum probability from individual bin = 0.025), and variance was highest in the dorsal premotor cortex and the posterior superior temporal gyrus. In contrast, stimulation within the posterior perisylvian cortex resulted in the maximum mean probability of anomia (maximum probability = 0.012), with large variance in the regions surrounding the posterior superior temporal gyrus, including the posterior middle temporal, angular, and supramarginal gyri. Patients with atypical speech localization were far more likely to have tumors in canonical Broca's or Wernicke's areas (OR 7.21, 95% CI 1.67-31.09, p < 0.01) or to have multilobar tumors (OR 12.58, 95% CI 2.22-71.42, p < 0.01), than were patients with classic speech localization. CONCLUSIONS This study provides statistical probability distribution maps for aphasic errors during cortical stimulation mapping in a patient cohort. Thus, the authors provide an expected probability of inducing speech arrest and anomia from specific 10-mm 2 cortical bins in an individual patient. In addition, they highlight key regions of interindividual mapping variability that should be considered preoperatively. They believe these results will aid surgeons in their preoperative planning of eloquent cortex resection.

An Alternative Version of Conditional Probabilities and Bayes' Rule: An Application of Probability Logic

ERIC Educational Resources Information Center

Satake, Eiki; Amato, Philip P.

2008-01-01

This paper presents an alternative version of formulas of conditional probabilities and Bayes' rule that demonstrate how the truth table of elementary mathematical logic applies to the derivations of the conditional probabilities of various complex, compound statements. This new approach is used to calculate the prior and posterior probabilities…

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.

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.

A flexible Bayesian hierarchical model of preterm birth risk among US Hispanic subgroups in relation to maternal nativity and education

PubMed Central

2011-01-01

Background Previous research has documented heterogeneity in the effects of maternal education on adverse birth outcomes by nativity and Hispanic subgroup in the United States. In this article, we considered the risk of preterm birth (PTB) using 9 years of vital statistics birth data from New York City. We employed finer categorizations of exposure than used previously and estimated the risk dose-response across the range of education by nativity and ethnicity. Methods Using Bayesian random effects logistic regression models with restricted quadratic spline terms for years of completed maternal education, we calculated and plotted the estimated posterior probabilities of PTB (gestational age < 37 weeks) for each year of education by ethnic and nativity subgroups adjusted for only maternal age, as well as with more extensive covariate adjustments. We then estimated the posterior risk difference between native and foreign born mothers by ethnicity over the continuous range of education exposures. Results The risk of PTB varied substantially by education, nativity and ethnicity. Native born groups showed higher absolute risk of PTB and declining risk associated with higher levels of education beyond about 10 years, as did foreign-born Puerto Ricans. For most other foreign born groups, however, risk of PTB was flatter across the education range. For Mexicans, Central Americans, Dominicans, South Americans and "Others", the protective effect of foreign birth diminished progressively across the educational range. Only for Puerto Ricans was there no nativity advantage for the foreign born, although small numbers of foreign born Cubans limited precision of estimates for that group. Conclusions Using flexible Bayesian regression models with random effects allowed us to estimate absolute risks without strong modeling assumptions. Risk comparisons for any sub-groups at any exposure level were simple to calculate. Shrinkage of posterior estimates through the use of random effects allowed for finer categorization of exposures without restricting joint effects to follow a fixed parametric scale. Although foreign born Hispanic women with the least education appeared to generally have low risk, this seems likely to be a marker for unmeasured environmental and behavioral factors, rather than a causally protective effect of low education itself. PMID:21504612

A flexible Bayesian hierarchical model of preterm birth risk among US Hispanic subgroups in relation to maternal nativity and education.

PubMed

Kaufman, Jay S; MacLehose, Richard F; Torrone, Elizabeth A; Savitz, David A

2011-04-19

Previous research has documented heterogeneity in the effects of maternal education on adverse birth outcomes by nativity and Hispanic subgroup in the United States. In this article, we considered the risk of preterm birth (PTB) using 9 years of vital statistics birth data from New York City. We employed finer categorizations of exposure than used previously and estimated the risk dose-response across the range of education by nativity and ethnicity. Using Bayesian random effects logistic regression models with restricted quadratic spline terms for years of completed maternal education, we calculated and plotted the estimated posterior probabilities of PTB (gestational age < 37 weeks) for each year of education by ethnic and nativity subgroups adjusted for only maternal age, as well as with more extensive covariate adjustments. We then estimated the posterior risk difference between native and foreign born mothers by ethnicity over the continuous range of education exposures. The risk of PTB varied substantially by education, nativity and ethnicity. Native born groups showed higher absolute risk of PTB and declining risk associated with higher levels of education beyond about 10 years, as did foreign-born Puerto Ricans. For most other foreign born groups, however, risk of PTB was flatter across the education range. For Mexicans, Central Americans, Dominicans, South Americans and "Others", the protective effect of foreign birth diminished progressively across the educational range. Only for Puerto Ricans was there no nativity advantage for the foreign born, although small numbers of foreign born Cubans limited precision of estimates for that group. Using flexible Bayesian regression models with random effects allowed us to estimate absolute risks without strong modeling assumptions. Risk comparisons for any sub-groups at any exposure level were simple to calculate. Shrinkage of posterior estimates through the use of random effects allowed for finer categorization of exposures without restricting joint effects to follow a fixed parametric scale. Although foreign born Hispanic women with the least education appeared to generally have low risk, this seems likely to be a marker for unmeasured environmental and behavioral factors, rather than a causally protective effect of low education itself.

A new LDPC decoding scheme for PDM-8QAM BICM coherent optical communication system

NASA Astrophysics Data System (ADS)

Liu, Yi; Zhang, Wen-bo; Xi, Li-xia; Tang, Xian-feng; Zhang, Xiao-guang

2015-11-01

A new log-likelihood ratio (LLR) message estimation method is proposed for polarization-division multiplexing eight quadrature amplitude modulation (PDM-8QAM) bit-interleaved coded modulation (BICM) optical communication system. The formulation of the posterior probability is theoretically analyzed, and the way to reduce the pre-decoding bit error rate ( BER) of the low density parity check (LDPC) decoder for PDM-8QAM constellations is presented. Simulation results show that it outperforms the traditional scheme, i.e., the new post-decoding BER is decreased down to 50% of that of the traditional post-decoding algorithm.

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.

Model-based decoding, information estimation, and change-point detection techniques for multineuron spike trains.

PubMed

Pillow, Jonathan W; Ahmadian, Yashar; Paninski, Liam

2011-01-01

One of the central problems in systems neuroscience is to understand how neural spike trains convey sensory information. Decoding methods, which provide an explicit means for reading out the information contained in neural spike responses, offer a powerful set of tools for studying the neural coding problem. Here we develop several decoding methods based on point-process neural encoding models, or forward models that predict spike responses to stimuli. These models have concave log-likelihood functions, which allow efficient maximum-likelihood model fitting and stimulus decoding. We present several applications of the encoding model framework to the problem of decoding stimulus information from population spike responses: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus, the most probable stimulus to have generated an observed single- or multiple-neuron spike train response, given some prior distribution over the stimulus; (2) a gaussian approximation to the posterior stimulus distribution that can be used to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the spike trains emitted by a neural population; and (4) a framework for the detection of change-point times (the time at which the stimulus undergoes a change in mean or variance) by marginalizing over the posterior stimulus distribution. We provide several examples illustrating the performance of these estimators with simulated and real neural data.

Planning spatial sampling of the soil from an uncertain reconnaissance variogram

NASA Astrophysics Data System (ADS)

Lark, R. Murray; Hamilton, Elliott M.; Kaninga, Belinda; Maseka, Kakoma K.; Mutondo, Moola; Sakala, Godfrey M.; Watts, Michael J.

2017-12-01

An estimated variogram of a soil property can be used to support a rational choice of sampling intensity for geostatistical mapping. However, it is known that estimated variograms are subject to uncertainty. In this paper we address two practical questions. First, how can we make a robust decision on sampling intensity, given the uncertainty in the variogram? Second, what are the costs incurred in terms of oversampling because of uncertainty in the variogram model used to plan sampling? To achieve this we show how samples of the posterior distribution of variogram parameters, from a computational Bayesian analysis, can be used to characterize the effects of variogram parameter uncertainty on sampling decisions. We show how one can select a sample intensity so that a target value of the kriging variance is not exceeded with some specified probability. This will lead to oversampling, relative to the sampling intensity that would be specified if there were no uncertainty in the variogram parameters. One can estimate the magnitude of this oversampling by treating the tolerable grid spacing for the final sample as a random variable, given the target kriging variance and the posterior sample values. We illustrate these concepts with some data on total uranium content in a relatively sparse sample of soil from agricultural land near mine tailings in the Copperbelt Province of Zambia.

Reduction of Poisson noise in measured time-resolved data for time-domain diffuse optical tomography.

PubMed

Okawa, S; Endo, Y; Hoshi, Y; Yamada, Y

2012-01-01

A method to reduce noise for time-domain diffuse optical tomography (DOT) is proposed. Poisson noise which contaminates time-resolved photon counting data is reduced by use of maximum a posteriori estimation. The noise-free data are modeled as a Markov random process, and the measured time-resolved data are assumed as Poisson distributed random variables. The posterior probability of the occurrence of the noise-free data is formulated. By maximizing the probability, the noise-free data are estimated, and the Poisson noise is reduced as a result. The performances of the Poisson noise reduction are demonstrated in some experiments of the image reconstruction of time-domain DOT. In simulations, the proposed method reduces the relative error between the noise-free and noisy data to about one thirtieth, and the reconstructed DOT image was smoothed by the proposed noise reduction. The variance of the reconstructed absorption coefficients decreased by 22% in a phantom experiment. The quality of DOT, which can be applied to breast cancer screening etc., is improved by the proposed noise reduction.

Per-field crop classification in irrigated agricultural regions in middle Asia using random forest and support vector machine ensemble

NASA Astrophysics Data System (ADS)

Löw, Fabian; Schorcht, Gunther; Michel, Ulrich; Dech, Stefan; Conrad, Christopher

2012-10-01

Accurate crop identification and crop area estimation are important for studies on irrigated agricultural systems, yield and water demand modeling, and agrarian policy development. In this study a novel combination of Random Forest (RF) and Support Vector Machine (SVM) classifiers is presented that (i) enhances crop classification accuracy and (ii) provides spatial information on map uncertainty. The methodology was implemented over four distinct irrigated sites in Middle Asia using RapidEye time series data. The RF feature importance statistics was used as feature-selection strategy for the SVM to assess possible negative effects on classification accuracy caused by an oversized feature space. The results of the individual RF and SVM classifications were combined with rules based on posterior classification probability and estimates of classification probability entropy. SVM classification performance was increased by feature selection through RF. Further experimental results indicate that the hybrid classifier improves overall classification accuracy in comparison to the single classifiers as well as useŕs and produceŕs accuracy.

Structural Information from Single-molecule FRET Experiments Using the Fast Nano-positioning System

PubMed Central

Röcker, Carlheinz; Nagy, Julia; Michaelis, Jens

2017-01-01

Single-molecule Förster Resonance Energy Transfer (smFRET) can be used to obtain structural information on biomolecular complexes in real-time. Thereby, multiple smFRET measurements are used to localize an unknown dye position inside a protein complex by means of trilateration. In order to obtain quantitative information, the Nano-Positioning System (NPS) uses probabilistic data analysis to combine structural information from X-ray crystallography with single-molecule fluorescence data to calculate not only the most probable position but the complete three-dimensional probability distribution, termed posterior, which indicates the experimental uncertainty. The concept was generalized for the analysis of smFRET networks containing numerous dye molecules. The latest version of NPS, Fast-NPS, features a new algorithm using Bayesian parameter estimation based on Markov Chain Monte Carlo sampling and parallel tempering that allows for the analysis of large smFRET networks in a comparably short time. Moreover, Fast-NPS allows the calculation of the posterior by choosing one of five different models for each dye, that account for the different spatial and orientational behavior exhibited by the dye molecules due to their local environment. Here we present a detailed protocol for obtaining smFRET data and applying the Fast-NPS. We provide detailed instructions for the acquisition of the three input parameters of Fast-NPS: the smFRET values, as well as the quantum yield and anisotropy of the dye molecules. Recently, the NPS has been used to elucidate the architecture of an archaeal open promotor complex. This data is used to demonstrate the influence of the five different dye models on the posterior distribution. PMID:28287526

Structural Information from Single-molecule FRET Experiments Using the Fast Nano-positioning System.

PubMed

Dörfler, Thilo; Eilert, Tobias; Röcker, Carlheinz; Nagy, Julia; Michaelis, Jens

2017-02-09

Single-molecule Förster Resonance Energy Transfer (smFRET) can be used to obtain structural information on biomolecular complexes in real-time. Thereby, multiple smFRET measurements are used to localize an unknown dye position inside a protein complex by means of trilateration. In order to obtain quantitative information, the Nano-Positioning System (NPS) uses probabilistic data analysis to combine structural information from X-ray crystallography with single-molecule fluorescence data to calculate not only the most probable position but the complete three-dimensional probability distribution, termed posterior, which indicates the experimental uncertainty. The concept was generalized for the analysis of smFRET networks containing numerous dye molecules. The latest version of NPS, Fast-NPS, features a new algorithm using Bayesian parameter estimation based on Markov Chain Monte Carlo sampling and parallel tempering that allows for the analysis of large smFRET networks in a comparably short time. Moreover, Fast-NPS allows the calculation of the posterior by choosing one of five different models for each dye, that account for the different spatial and orientational behavior exhibited by the dye molecules due to their local environment. Here we present a detailed protocol for obtaining smFRET data and applying the Fast-NPS. We provide detailed instructions for the acquisition of the three input parameters of Fast-NPS: the smFRET values, as well as the quantum yield and anisotropy of the dye molecules. Recently, the NPS has been used to elucidate the architecture of an archaeal open promotor complex. This data is used to demonstrate the influence of the five different dye models on the posterior distribution.

A Comparison of Grizzly Bear Demographic Parameters Estimated from Non-Spatial and Spatial Open Population Capture-Recapture Models.

PubMed

Whittington, Jesse; Sawaya, Michael A

2015-01-01

Capture-recapture studies are frequently used to monitor the status and trends of wildlife populations. Detection histories from individual animals are used to estimate probability of detection and abundance or density. The accuracy of abundance and density estimates depends on the ability to model factors affecting detection probability. Non-spatial capture-recapture models have recently evolved into spatial capture-recapture models that directly include the effect of distances between an animal's home range centre and trap locations on detection probability. Most studies comparing non-spatial and spatial capture-recapture biases focussed on single year models and no studies have compared the accuracy of demographic parameter estimates from open population models. We applied open population non-spatial and spatial capture-recapture models to three years of grizzly bear DNA-based data from Banff National Park and simulated data sets. The two models produced similar estimates of grizzly bear apparent survival, per capita recruitment, and population growth rates but the spatial capture-recapture models had better fit. Simulations showed that spatial capture-recapture models produced more accurate parameter estimates with better credible interval coverage than non-spatial capture-recapture models. Non-spatial capture-recapture models produced negatively biased estimates of apparent survival and positively biased estimates of per capita recruitment. The spatial capture-recapture grizzly bear population growth rates and 95% highest posterior density averaged across the three years were 0.925 (0.786-1.071) for females, 0.844 (0.703-0.975) for males, and 0.882 (0.779-0.981) for females and males combined. The non-spatial capture-recapture population growth rates were 0.894 (0.758-1.024) for females, 0.825 (0.700-0.948) for males, and 0.863 (0.771-0.957) for both sexes. The combination of low densities, low reproductive rates, and predominantly negative population growth rates suggest that Banff National Park's population of grizzly bears requires continued conservation-oriented management actions.

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

PubMed

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

2010-12-01

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

Quantifying uncertainty in geoacoustic inversion. II. Application to broadband, shallow-water data.

PubMed

Dosso, Stan E; Nielsen, Peter L

2002-01-01

This paper applies the new method of fast Gibbs sampling (FGS) to estimate the uncertainties of seabed geoacoustic parameters in a broadband, shallow-water acoustic survey, with the goal of interpreting the survey results and validating the method for experimental data. FGS applies a Bayesian approach to geoacoustic inversion based on sampling the posterior probability density to estimate marginal probability distributions and parameter covariances. This requires knowledge of the statistical distribution of the data errors, including both measurement and theory errors, which is generally not available. Invoking the simplifying assumption of independent, identically distributed Gaussian errors allows a maximum-likelihood estimate of the data variance and leads to a practical inversion algorithm. However, it is necessary to validate these assumptions, i.e., to verify that the parameter uncertainties obtained represent meaningful estimates. To this end, FGS is applied to a geoacoustic experiment carried out at a site off the west coast of Italy where previous acoustic and geophysical studies have been performed. The parameter uncertainties estimated via FGS are validated by comparison with: (i) the variability in the results of inverting multiple independent data sets collected during the experiment; (ii) the results of FGS inversion of synthetic test cases designed to simulate the experiment and data errors; and (iii) the available geophysical ground truth. Comparisons are carried out for a number of different source bandwidths, ranges, and levels of prior information, and indicate that FGS provides reliable and stable uncertainty estimates for the geoacoustic inverse problem.

Improved Analysis of GW150914 Using a Fully Spin-Precessing Waveform Model

NASA Technical Reports Server (NTRS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Camp, J. B.;

On the applicability of surrogate-based Markov chain Monte Carlo-Bayesian inversion to the Community Land Model: Case studies at flux tower sites: SURROGATE-BASED MCMC FOR CLM

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

Huang, Maoyi; Ray, Jaideep; Hou, Zhangshuan

2016-07-04

The Community Land Model (CLM) has been widely used in climate and Earth system modeling. Accurate estimation of model parameters is needed for reliable model simulations and predictions under current and future conditions, respectively. In our previous work, a subset of hydrological parameters has been identified to have significant impact on surface energy fluxes at selected flux tower sites based on parameter screening and sensitivity analysis, which indicate that the parameters could potentially be estimated from surface flux observations at the towers. To date, such estimates do not exist. In this paper, we assess the feasibility of applying a Bayesianmore » model calibration technique to estimate CLM parameters at selected flux tower sites under various site conditions. The parameters are estimated as a joint probability density function (PDF) that provides estimates of uncertainty of the parameters being inverted, conditional on climatologically-average latent heat fluxes derived from observations. We find that the simulated mean latent heat fluxes from CLM using the calibrated parameters are generally improved at all sites when compared to those obtained with CLM simulations using default parameter sets. Further, our calibration method also results in credibility bounds around the simulated mean fluxes which bracket the measured data. The modes (or maximum a posteriori values) and 95% credibility intervals of the site-specific posterior PDFs are tabulated as suggested parameter values for each site. Analysis of relationships between the posterior PDFs and site conditions suggests that the parameter values are likely correlated with the plant functional type, which needs to be confirmed in future studies by extending the approach to more sites.« less

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.

On the applicability of surrogate-based MCMC-Bayesian inversion to the Community Land Model: Case studies at Flux tower sites

DOE PAGES

Huang, Maoyi; Ray, Jaideep; Hou, Zhangshuan; ...

2016-06-01

The Community Land Model (CLM) has been widely used in climate and Earth system modeling. Accurate estimation of model parameters is needed for reliable model simulations and predictions under current and future conditions, respectively. In our previous work, a subset of hydrological parameters has been identified to have significant impact on surface energy fluxes at selected flux tower sites based on parameter screening and sensitivity analysis, which indicate that the parameters could potentially be estimated from surface flux observations at the towers. To date, such estimates do not exist. In this paper, we assess the feasibility of applying a Bayesianmore » model calibration technique to estimate CLM parameters at selected flux tower sites under various site conditions. The parameters are estimated as a joint probability density function (PDF) that provides estimates of uncertainty of the parameters being inverted, conditional on climatologically average latent heat fluxes derived from observations. We find that the simulated mean latent heat fluxes from CLM using the calibrated parameters are generally improved at all sites when compared to those obtained with CLM simulations using default parameter sets. Further, our calibration method also results in credibility bounds around the simulated mean fluxes which bracket the measured data. The modes (or maximum a posteriori values) and 95% credibility intervals of the site-specific posterior PDFs are tabulated as suggested parameter values for each site. As a result, analysis of relationships between the posterior PDFs and site conditions suggests that the parameter values are likely correlated with the plant functional type, which needs to be confirmed in future studies by extending the approach to more sites.« less

On the applicability of surrogate-based MCMC-Bayesian inversion to the Community Land Model: Case studies at Flux tower sites

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

Huang, Maoyi; Ray, Jaideep; Hou, Zhangshuan

The Community Land Model (CLM) has been widely used in climate and Earth system modeling. Accurate estimation of model parameters is needed for reliable model simulations and predictions under current and future conditions, respectively. In our previous work, a subset of hydrological parameters has been identified to have significant impact on surface energy fluxes at selected flux tower sites based on parameter screening and sensitivity analysis, which indicate that the parameters could potentially be estimated from surface flux observations at the towers. To date, such estimates do not exist. In this paper, we assess the feasibility of applying a Bayesianmore » model calibration technique to estimate CLM parameters at selected flux tower sites under various site conditions. The parameters are estimated as a joint probability density function (PDF) that provides estimates of uncertainty of the parameters being inverted, conditional on climatologically average latent heat fluxes derived from observations. We find that the simulated mean latent heat fluxes from CLM using the calibrated parameters are generally improved at all sites when compared to those obtained with CLM simulations using default parameter sets. Further, our calibration method also results in credibility bounds around the simulated mean fluxes which bracket the measured data. The modes (or maximum a posteriori values) and 95% credibility intervals of the site-specific posterior PDFs are tabulated as suggested parameter values for each site. As a result, analysis of relationships between the posterior PDFs and site conditions suggests that the parameter values are likely correlated with the plant functional type, which needs to be confirmed in future studies by extending the approach to more sites.« less

On the applicability of surrogate-based Markov chain Monte Carlo-Bayesian inversion to the Community Land Model: Case studies at flux tower sites

NASA Astrophysics Data System (ADS)

Huang, Maoyi; Ray, Jaideep; Hou, Zhangshuan; Ren, Huiying; Liu, Ying; Swiler, Laura

2016-07-01

The Community Land Model (CLM) has been widely used in climate and Earth system modeling. Accurate estimation of model parameters is needed for reliable model simulations and predictions under current and future conditions, respectively. In our previous work, a subset of hydrological parameters has been identified to have significant impact on surface energy fluxes at selected flux tower sites based on parameter screening and sensitivity analysis, which indicate that the parameters could potentially be estimated from surface flux observations at the towers. To date, such estimates do not exist. In this paper, we assess the feasibility of applying a Bayesian model calibration technique to estimate CLM parameters at selected flux tower sites under various site conditions. The parameters are estimated as a joint probability density function (PDF) that provides estimates of uncertainty of the parameters being inverted, conditional on climatologically average latent heat fluxes derived from observations. We find that the simulated mean latent heat fluxes from CLM using the calibrated parameters are generally improved at all sites when compared to those obtained with CLM simulations using default parameter sets. Further, our calibration method also results in credibility bounds around the simulated mean fluxes which bracket the measured data. The modes (or maximum a posteriori values) and 95% credibility intervals of the site-specific posterior PDFs are tabulated as suggested parameter values for each site. Analysis of relationships between the posterior PDFs and site conditions suggests that the parameter values are likely correlated with the plant functional type, which needs to be confirmed in future studies by extending the approach to more sites.

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.

Random forest learning of ultrasonic statistical physics and object spaces for lesion detection in 2D sonomammography

NASA Astrophysics Data System (ADS)

Sheet, Debdoot; Karamalis, Athanasios; Kraft, Silvan; Noël, Peter B.; Vag, Tibor; Sadhu, Anup; Katouzian, Amin; Navab, Nassir; Chatterjee, Jyotirmoy; Ray, Ajoy K.

2013-03-01

Breast cancer is the most common form of cancer in women. Early diagnosis can significantly improve lifeexpectancy and allow different treatment options. Clinicians favor 2D ultrasonography for breast tissue abnormality screening due to high sensitivity and specificity compared to competing technologies. However, inter- and intra-observer variability in visual assessment and reporting of lesions often handicaps its performance. Existing Computer Assisted Diagnosis (CAD) systems though being able to detect solid lesions are often restricted in performance. These restrictions are inability to (1) detect lesion of multiple sizes and shapes, and (2) differentiate between hypo-echoic lesions from their posterior acoustic shadowing. In this work we present a completely automatic system for detection and segmentation of breast lesions in 2D ultrasound images. We employ random forests for learning of tissue specific primal to discriminate breast lesions from surrounding normal tissues. This enables it to detect lesions of multiple shapes and sizes, as well as discriminate between hypo-echoic lesion from associated posterior acoustic shadowing. The primal comprises of (i) multiscale estimated ultrasonic statistical physics and (ii) scale-space characteristics. The random forest learns lesion vs. background primal from a database of 2D ultrasound images with labeled lesions. For segmentation, the posterior probabilities of lesion pixels estimated by the learnt random forest are hard thresholded to provide a random walks segmentation stage with starting seeds. Our method achieves detection with 99.19% accuracy and segmentation with mean contour-to-contour error < 3 pixels on a set of 40 images with 49 lesions.

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.

Part 2. Development of Enhanced Statistical Methods for Assessing Health Effects Associated with an Unknown Number of Major Sources of Multiple Air Pollutants.

PubMed

Park, Eun Sug; Symanski, Elaine; Han, Daikwon; Spiegelman, Clifford

2015-06-01

A major difficulty with assessing source-specific health effects is that source-specific exposures cannot be measured directly; rather, they need to be estimated by a source-apportionment method such as multivariate receptor modeling. The uncertainty in source apportionment (uncertainty in source-specific exposure estimates and model uncertainty due to the unknown number of sources and identifiability conditions) has been largely ignored in previous studies. Also, spatial dependence of multipollutant data collected from multiple monitoring sites has not yet been incorporated into multivariate receptor modeling. The objectives of this project are (1) to develop a multipollutant approach that incorporates both sources of uncertainty in source-apportionment into the assessment of source-specific health effects and (2) to develop enhanced multivariate receptor models that can account for spatial correlations in the multipollutant data collected from multiple sites. We employed a Bayesian hierarchical modeling framework consisting of multivariate receptor models, health-effects models, and a hierarchical model on latent source contributions. For the health model, we focused on the time-series design in this project. Each combination of number of sources and identifiability conditions (additional constraints on model parameters) defines a different model. We built a set of plausible models with extensive exploratory data analyses and with information from previous studies, and then computed posterior model probability to estimate model uncertainty. Parameter estimation and model uncertainty estimation were implemented simultaneously by Markov chain Monte Carlo (MCMC*) methods. We validated the methods using simulated data. We illustrated the methods using PM2.5 (particulate matter ≤ 2.5 μm in aerodynamic diameter) speciation data and mortality data from Phoenix, Arizona, and Houston, Texas. The Phoenix data included counts of cardiovascular deaths and daily PM2.5 speciation data from 1995-1997. The Houston data included respiratory mortality data and 24-hour PM2.5 speciation data sampled every six days from a region near the Houston Ship Channel in years 2002-2005. We also developed a Bayesian spatial multivariate receptor modeling approach that, while simultaneously dealing with the unknown number of sources and identifiability conditions, incorporated spatial correlations in the multipollutant data collected from multiple sites into the estimation of source profiles and contributions based on the discrete process convolution model for multivariate spatial processes. This new modeling approach was applied to 24-hour ambient air concentrations of 17 volatile organic compounds (VOCs) measured at nine monitoring sites in Harris County, Texas, during years 2000 to 2005. Simulation results indicated that our methods were accurate in identifying the true model and estimated parameters were close to the true values. The results from our methods agreed in general with previous studies on the source apportionment of the Phoenix data in terms of estimated source profiles and contributions. However, we had a greater number of statistically insignificant findings, which was likely a natural consequence of incorporating uncertainty in the estimated source contributions into the health-effects parameter estimation. For the Houston data, a model with five sources (that seemed to be Sulfate-Rich Secondary Aerosol, Motor Vehicles, Industrial Combustion, Soil/Crustal Matter, and Sea Salt) showed the highest posterior model probability among the candidate models considered when fitted simultaneously to the PM2.5 and mortality data. There was a statistically significant positive association between respiratory mortality and same-day PM2.5 concentrations attributed to one of the sources (probably industrial combustion). The Bayesian spatial multivariate receptor modeling approach applied to the VOC data led to a highest posterior model probability for a model with five sources (that seemed to be refinery, petrochemical production, gasoline evaporation, natural gas, and vehicular exhaust) among several candidate models, with the number of sources varying between three and seven and with different identifiability conditions. Our multipollutant approach assessing source-specific health effects is more advantageous than a single-pollutant approach in that it can estimate total health effects from multiple pollutants and can also identify emission sources that are responsible for adverse health effects. Our Bayesian approach can incorporate not only uncertainty in the estimated source contributions, but also model uncertainty that has not been addressed in previous studies on assessing source-specific health effects. The new Bayesian spatial multivariate receptor modeling approach enables predictions of source contributions at unmonitored sites, minimizing exposure misclassification and providing improved exposure estimates along with their uncertainty estimates, as well as accounting for uncertainty in the number of sources and identifiability conditions.

State-space modeling to support management of brucellosis in the Yellowstone bison population

USGS Publications Warehouse

Hobbs, N. Thompson; Geremia, Chris; Treanor, John; Wallen, Rick; White, P.J.; Hooten, Mevin B.; Rhyan, Jack C.

2015-01-01

The bison (Bison bison) of the Yellowstone ecosystem, USA, exemplify the difficulty of conserving large mammals that migrate across the boundaries of conservation areas. Bison are infected with brucellosis (Brucella abortus) and their seasonal movements can expose livestock to infection. Yellowstone National Park has embarked on a program of adaptive management of bison, which requires a model that assimilates data to support management decisions. We constructed a Bayesian state-space model to reveal the influence of brucellosis on the Yellowstone bison population. A frequency-dependent model of brucellosis transmission was superior to a density-dependent model in predicting out-of-sample observations of horizontal transmission probability. A mixture model including both transmission mechanisms converged on frequency dependence. Conditional on the frequency-dependent model, brucellosis median transmission rate was 1.87 yr−1. The median of the posterior distribution of the basic reproductive ratio (R0) was 1.75. Seroprevalence of adult females varied around 60% over two decades, but only 9.6 of 100 adult females were infectious. Brucellosis depressed recruitment; estimated population growth rate λ averaged 1.07 for an infected population and 1.11 for a healthy population. We used five-year forecasting to evaluate the ability of different actions to meet management goals relative to no action. Annually removing 200 seropositive female bison increased by 30-fold the probability of reducing seroprevalence below 40% and increased by a factor of 120 the probability of achieving a 50% reduction in transmission probability relative to no action. Annually vaccinating 200 seronegative animals increased the likelihood of a 50% reduction in transmission probability by fivefold over no action. However, including uncertainty in the ability to implement management by representing stochastic variation in the number of accessible bison dramatically reduced the probability of achieving goals using interventions relative to no action. Because the width of the posterior predictive distributions of future population states expands rapidly with increases in the forecast horizon, managers must accept high levels of uncertainty. These findings emphasize the necessity of iterative, adaptive management with relatively short-term commitment to action and frequent reevaluation in response to new data and model forecasts. We believe our approach has broad applications.

Posterior probability of linkage and maximal lod score.

PubMed

Génin, E; Martinez, M; Clerget-Darpoux, F

1995-01-01

To detect linkage between a trait and a marker, Morton (1955) proposed to calculate the lod score z(theta 1) at a given value theta 1 of the recombination fraction. If z(theta 1) reaches +3 then linkage is concluded. However, in practice, lod scores are calculated for different values of the recombination fraction between 0 and 0.5 and the test is based on the maximum value of the lod score Zmax. The impact of this deviation of the test on the probability that in fact linkage does not exist, when linkage was concluded, is documented here. This posterior probability of no linkage can be derived by using Bayes' theorem. It is less than 5% when the lod score at a predetermined theta 1 is used for the test. But, for a Zmax of +3, we showed that it can reach 16.4%. Thus, considering a composite alternative hypothesis instead of a single one decreases the reliability of the test. The reliability decreases rapidly when Zmax is less than +3. Given a Zmax of +2.5, there is a 33% chance that linkage does not exist. Moreover, the posterior probability depends not only on the value of Zmax but also jointly on the family structures and on the genetic model. For a given Zmax, the chance that linkage exists may then vary.

Estimation of flock/herd-level true Mycobacterium avium subspecies paratuberculosis prevalence on sheep, beef cattle and deer farms in New Zealand using a novel Bayesian model.

PubMed

Verdugo, Cristobal; Jones, Geoff; Johnson, Wes; Wilson, Peter; Stringer, Lesley; Heuer, Cord

2014-12-01

The study aimed to estimate the national- and island-level flock/herd true prevalence (HTP) of Mycobacterium avium subsp. paratuberculosis (MAP) infection in pastoral farmed sheep, beef cattle and deer in New Zealand. A random sample of 238 single- or multi-species farms was selected from a postal surveyed population of 1940 farms. The sample included 162 sheep flocks, 116 beef cattle and 99 deer herds from seven of 16 geographical regions. Twenty animals from each species present on farm were randomly selected for blood and faecal sampling. Pooled faecal culture testing was conducted using a single pool (sheep flocks) or two pools (beef cattle/deer herds) of 20 and 10 samples per pool, respectively. To increase flock/herd-level sensitivity, sera from all 20 animals from culture negative flocks/herds were individually tested by Pourquier(®) ELISA (sheep and cattle) or Paralisa™ (deer). Results were adjusted for sensitivity and specificity of diagnostic tests using a novel Bayesian latent class model. Outcomes were adjusted by their sampling fractions to obtain HTP estimates at national level. For each species, the posterior probability (POPR) of HTP differences between New Zealand North (NI) and South (SI) Islands was obtained. Across all species, 69% of farms had at least one species test positive. Sheep flocks had the highest HTP estimate (76%, posterior probability interval (PPI) 70-81%), followed by deer (46%, PPI 38-55%) and beef herds (42%, PPI 35-50%). Differences were observed between the two main islands of New Zealand, with higher HTP in sheep and beef cattle flocks/herds in the NI. Sheep flock HTP was 80% in the NI compared with 70% (POPR=0.96) in the SI, while the HTP for beef cattle was 44% in the NI and 38% in the SI (POPR=0.80). Conversely, deer HTP was higher in the SI (54%) than the NI (33%, POPR=0.99). Infection with MAP is endemic at high prevalence in sheep, beef cattle and deer flocks/herds across New Zealand. Copyright © 2014 Elsevier B.V. All rights reserved.

A Probabilistic Strategy for Understanding Action Selection

PubMed Central

Kim, Byounghoon; Basso, Michele A.

2010-01-01

Brain regions involved in transforming sensory signals into movement commands are the likely sites where decisions are formed. Once formed, a decision must be read-out from the activity of populations of neurons to produce a choice of action. How this occurs remains unresolved. We recorded from four superior colliculus (SC) neurons simultaneously while monkeys performed a target selection task. We implemented three models to gain insight into the computational principles underlying population coding of action selection. We compared the population vector average (PVA), winner-takes-all (WTA) and a Bayesian model, maximum a posteriori estimate (MAP) to determine which predicted choices most often. The probabilistic model predicted more trials correctly than both the WTA and the PVA. The MAP model predicted 81.88% whereas WTA predicted 71.11% and PVA/OLE predicted the least number of trials at 55.71 and 69.47%. Recovering MAP estimates using simulated, non-uniform priors that correlated with monkeys’ choice performance, improved the accuracy of the model by 2.88%. A dynamic analysis revealed that the MAP estimate evolved over time and the posterior probability of the saccade choice reached a maximum at the time of the saccade. MAP estimates also scaled with choice performance accuracy. Although there was overlap in the prediction abilities of all the models, we conclude that movement choice from populations of neurons may be best understood by considering frameworks based on probability. PMID:20147560

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 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 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.

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

Central posterior capsule pigmentation in a patient with pigment dispersion and previous ocular trauma: a case report.

PubMed

Al-Mezaine, Hani S

2010-01-01

We report a 55-year-old man with unusually dense, unilateral central posterior capsule pigmentation associated with the characteristic clinical features of pigment dispersion syndrome, including a Krukenberg's spindle and dense trabecular pigmentation in both eyes. A history of an old blunt ocular trauma probably caused separation of the anterior hyaloid from the back of the lens, thereby creating an avenue by which pigment could reach the potential space of Berger's from the posterior chamber.

Central posterior capsule pigmentation in a patient with pigment dispersion and previous ocular trauma: A case report

PubMed Central

Al-Mezaine, Hani S

2010-01-01

We report a 55-year-old man with unusually dense, unilateral central posterior capsule pigmentation associated with the characteristic clinical features of pigment dispersion syndrome, including a Krukenberg's spindle and dense trabecular pigmentation in both eyes. A history of an old blunt ocular trauma probably caused separation of the anterior hyaloid from the back of the lens, thereby creating an avenue by which pigment could reach the potential space of Berger's from the posterior chamber. PMID:20534930

The natural history of hepatitis C infection acquired through injection drug use: meta-analysis and meta-regression.

PubMed

John-Baptiste, Ava; Krahn, Murray; Heathcote, Jenny; Laporte, Audery; Tomlinson, George

2010-08-01

Our aim was to estimate the rate of progression to cirrhosis for those infected with hepatitis C virus (HCV) through injection drug use. We searched the published literature for articles assessing cirrhosis in this population and abstracted data on cirrhosis prevalence, mean duration of infection, mean age, mean alanine aminotransferase (ALT) enzyme levels, proportion of males, proportion HIV co-infected, proportion consuming excessive alcohol, and study setting. Summary progression rates were estimated using weighted averages and random effects Poisson meta-regression. The impact of co-variates was assessed by estimating the posterior probability that the relative risk (RR) of progression exceeded 1.0. A total of 47 published articles were identified. After adjusting for covariates in 44 studies representing 6457 patients, the estimated rate of progression to cirrhosis, was 8.1 per 1000 person-years (95% credible region (CR), 3.9-14.7). This corresponds to a 20-year cirrhosis prevalence of 14.8% (95% CR, 7.5-25.5). A 5% increase in the proportion of male participants and a 5% increase in the proportion consuming excessive alcohol were associated with faster progression (probability RR>1=0.97 and 0.92, respectively). A 5% increase in the proportion of HIV co-infected, an increase in ALT of 5 IU/L and studies in settings with a high risk of referral bias were not associated with faster progression (probability RR>1=0.42, 0.65, and 0.43, respectively). Analysis of aggregate level data suggests that for patients who contracted HCV through injection drug use prognosis is poor in populations with many male patients and high levels of alcohol consumption. Copyright 2010 European Association for the Study of the Liver. Published by Elsevier B.V. All rights reserved.

A Dirichlet-Multinomial Bayes Classifier for Disease Diagnosis with Microbial Compositions.

PubMed

Gao, Xiang; Lin, Huaiying; Dong, Qunfeng

2017-01-01

Dysbiosis of microbial communities is associated with various human diseases, raising the possibility of using microbial compositions as biomarkers for disease diagnosis. We have developed a Bayes classifier by modeling microbial compositions with Dirichlet-multinomial distributions, which are widely used to model multicategorical count data with extra variation. The parameters of the Dirichlet-multinomial distributions are estimated from training microbiome data sets based on maximum likelihood. The posterior probability of a microbiome sample belonging to a disease or healthy category is calculated based on Bayes' theorem, using the likelihood values computed from the estimated Dirichlet-multinomial distribution, as well as a prior probability estimated from the training microbiome data set or previously published information on disease prevalence. When tested on real-world microbiome data sets, our method, called DMBC (for Dirichlet-multinomial Bayes classifier), shows better classification accuracy than the only existing Bayesian microbiome classifier based on a Dirichlet-multinomial mixture model and the popular random forest method. The advantage of DMBC is its built-in automatic feature selection, capable of identifying a subset of microbial taxa with the best classification accuracy between different classes of samples based on cross-validation. This unique ability enables DMBC to maintain and even improve its accuracy at modeling species-level taxa. The R package for DMBC is freely available at https://github.com/qunfengdong/DMBC. IMPORTANCE By incorporating prior information on disease prevalence, Bayes classifiers have the potential to estimate disease probability better than other common machine-learning methods. Thus, it is important to develop Bayes classifiers specifically tailored for microbiome data. Our method shows higher classification accuracy than the only existing Bayesian classifier and the popular random forest method, and thus provides an alternative option for using microbial compositions for disease diagnosis.

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

Distribution of Marburg virus in Africa: An evolutionary approach.

PubMed

Zehender, Gianguglielmo; Sorrentino, Chiara; Veo, Carla; Fiaschi, Lisa; Gioffrè, Sonia; Ebranati, Erika; Tanzi, Elisabetta; Ciccozzi, Massimo; Lai, Alessia; Galli, Massimo

2016-10-01

The aim of this study was to investigate the origin and geographical dispersion of Marburg virus, the first member of the Filoviridae family to be discovered. Seventy-three complete genome sequences of Marburg virus isolated from animals and humans were retrieved from public databases and analysed using a Bayesian phylogeographical framework. The phylogenetic tree of the Marburg virus data set showed two significant evolutionary lineages: Ravn virus (RAVV) and Marburg virus (MARV). MARV divided into two main clades; clade A included isolates from Uganda (five from the European epidemic in 1967), Kenya (1980) and Angola (from the epidemic of 2004-2005); clade B included most of the isolates obtained during the 1999-2000 epidemic in the Democratic Republic of the Congo (DRC) and a group of Ugandan isolates obtained in 2007-2009. The estimated mean evolutionary rate of the whole genome was 3.3×10(-4) substitutions/site/year (credibility interval 2.0-4.8). The MARV strain had a mean root time of the most recent common ancestor of 177.9years ago (YA) (95% highest posterior density 87-284), thus indicating that it probably originated in the mid-XIX century, whereas the RAVV strain had a later origin dating back to a mean 33.8 YA. The most probable location of the MARV ancestor was Uganda (state posterior probability, spp=0.41), whereas that of the RAVV ancestor was Kenya (spp=0.71). There were significant migration rates from Uganda to the DRC (Bayes Factor, BF=42.0) and in the opposite direction (BF=5.7). Our data suggest that Uganda may have been the cradle of Marburg virus in Africa. Copyright © 2016 Elsevier B.V. All rights reserved.

Top-down estimate of surface flux in the Los Angeles Basin using a mesoscale inverse modeling technique: assessing anthropogenic emissions of CO, NOx and CO2 and their impacts

NASA Astrophysics Data System (ADS)

Brioude, J.; Angevine, W. M.; Ahmadov, R.; Kim, S.-W.; Evan, S.; McKeen, S. A.; Hsie, E.-Y.; Frost, G. J.; Neuman, J. A.; Pollack, I. B.; Peischl, J.; Ryerson, T. B.; Holloway, J.; Brown, S. S.; Nowak, J. B.; Roberts, J. M.; Wofsy, S. C.; Santoni, G. W.; Oda, T.; Trainer, M.

2013-04-01

We present top-down estimates of anthropogenic CO, NOx and CO2 surface fluxes at mesoscale using a Lagrangian model in combination with three different WRF model configurations, driven by data from aircraft flights during the CALNEX campaign in southern California in May-June 2010. The US EPA National Emission Inventory 2005 (NEI 2005) was the prior in the CO and NOx inversion calculations. The flux ratio inversion method, based on linear relationships between chemical species, was used to calculate the CO2 inventory without prior knowledge of CO2 surface fluxes. The inversion was applied to each flight to estimate the variability of single-flight-based flux estimates. In Los Angeles (LA) County, the uncertainties on CO and NOx fluxes were 10% and 15%, respectively. Compared with NEI 2005, the CO posterior emissions were lower by 43% in LA County and by 37% in the South Coast Air Basin (SoCAB). NOx posterior emissions were lower by 32% in LA County and by 27% in the SoCAB. NOx posterior emissions were 40% lower on weekends relative to weekdays. The CO2 posterior estimates were 183 Tg yr-1 in SoCAB. A flight during ITCT (Intercontinental Transport and Chemical Transformation) in 2002 was used to estimate emissions in the LA Basin in 2002. From 2002 to 2010, the CO and NOx posterior emissions decreased by 41% and 37%, respectively, in agreement with previous studies. Over the same time period, CO2 emissions increased by 10% in LA County but decreased by 4% in the SoCAB, a statistically insignificant change. Overall, the posterior estimates were in good agreement with the California Air Resources Board (CARB) inventory, with differences of 15% or less. However, the posterior spatial distribution in the basin was significantly different from CARB for NOx emissions. WRF-Chem mesoscale chemical-transport model simulations allowed an evaluation of differences in chemistry using different inventory assumptions, including NEI 2005, a gridded CARB inventory and the posterior inventories derived in this study. The biases in WRF-Chem ozone were reduced and correlations were increased using the posterior from this study compared with simulations with the two bottom-up inventories, suggesting that improving the spatial distribution of ozone precursor surface emissions is also important in mesoscale chemistry simulations.

Inference of reaction rate parameters based on summary statistics from experiments

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

Khalil, Mohammad; Chowdhary, Kamaljit Singh; Safta, Cosmin

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2/O 2-mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the givenmore » summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.« less

Inference of reaction rate parameters based on summary statistics from experiments

DOE PAGES

Khalil, Mohammad; Chowdhary, Kamaljit Singh; Safta, Cosmin; ...

2016-10-15

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2/O 2-mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the givenmore » summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.« 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

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.

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.

Generative adversarial networks for brain lesion detection

NASA Astrophysics Data System (ADS)

Alex, Varghese; Safwan, K. P. Mohammed; Chennamsetty, Sai Saketh; Krishnamurthi, Ganapathy

2017-02-01

Manual segmentation of brain lesions from Magnetic Resonance Images (MRI) is cumbersome and introduces errors due to inter-rater variability. This paper introduces a semi-supervised technique for detection of brain lesion from MRI using Generative Adversarial Networks (GANs). GANs comprises of a Generator network and a Discriminator network which are trained simultaneously with the objective of one bettering the other. The networks were trained using non lesion patches (n=13,000) from 4 different MR sequences. The network was trained on BraTS dataset and patches were extracted from regions excluding tumor region. The Generator network generates data by modeling the underlying probability distribution of the training data, (PData). The Discriminator learns the posterior probability P (Label Data) by classifying training data and generated data as "Real" or "Fake" respectively. The Generator upon learning the joint distribution, produces images/patches such that the performance of the Discriminator on them are random, i.e. P (Label Data = GeneratedData) = 0.5. During testing, the Discriminator assigns posterior probability values close to 0.5 for patches from non lesion regions, while patches centered on lesion arise from a different distribution (PLesion) and hence are assigned lower posterior probability value by the Discriminator. On the test set (n=14), the proposed technique achieves whole tumor dice score of 0.69, sensitivity of 91% and specificity of 59%. Additionally the generator network was capable of generating non lesion patches from various MR sequences.

Graphical methods for the sensitivity analysis in discriminant analysis

DOE PAGES

Kim, Youngil; Anderson-Cook, Christine M.; Dae-Heung, Jang

2015-09-30

Similar to regression, many measures to detect influential data points in discriminant analysis have been developed. Many follow similar principles as the diagnostic measures used in linear regression in the context of discriminant analysis. Here we focus on the impact on the predicted classification posterior probability when a data point is omitted. The new method is intuitive and easily interpretative compared to existing methods. We also propose a graphical display to show the individual movement of the posterior probability of other data points when a specific data point is omitted. This enables the summaries to capture the overall pattern ofmore » the change.« less

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.

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.

Topics in inference and decision-making with partial knowledge

NASA Technical Reports Server (NTRS)

Safavian, S. Rasoul; Landgrebe, David

1990-01-01

Two essential elements needed in the process of inference and decision-making are prior probabilities and likelihood functions. When both of these components are known accurately and precisely, the Bayesian approach provides a consistent and coherent solution to the problems of inference and decision-making. In many situations, however, either one or both of the above components may not be known, or at least may not be known precisely. This problem of partial knowledge about prior probabilities and likelihood functions is addressed. There are at least two ways to cope with this lack of precise knowledge: robust methods, and interval-valued methods. First, ways of modeling imprecision and indeterminacies in prior probabilities and likelihood functions are examined; then how imprecision in the above components carries over to the posterior probabilities is examined. Finally, the problem of decision making with imprecise posterior probabilities and the consequences of such actions are addressed. Application areas where the above problems may occur are in statistical pattern recognition problems, for example, the problem of classification of high-dimensional multispectral remote sensing image data.

Trans-dimensional inversion of microtremor array dispersion data with hierarchical autoregressive error models

NASA Astrophysics Data System (ADS)

Dettmer, Jan; Molnar, Sheri; Steininger, Gavin; Dosso, Stan E.; Cassidy, John F.

2012-02-01

This paper applies a general trans-dimensional Bayesian inference methodology and hierarchical autoregressive data-error models to the inversion of microtremor array dispersion data for shear wave velocity (vs) structure. This approach accounts for the limited knowledge of the optimal earth model parametrization (e.g. the number of layers in the vs profile) and of the data-error statistics in the resulting vs parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A trans-dimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the indexing parameter) are considered in the results. The earth model is parametrized in terms of a partition model with interfaces given over a depth-range of interest. In this work, the number of interfaces (layers) in the partition model represents the trans-dimensional model indexing. In addition, serial data-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate data-error statistics, and have no requirement for computing the inverse or determinant of a data-error covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the state space that spans multiple subspaces of different dimensionalities. The order of the autoregressive process required to fit the data is determined here by posterior residual-sample examination and statistical tests. Inference for earth model parameters is carried out on the trans-dimensional posterior probability distribution by considering ensembles of parameter vectors. In particular, vs uncertainty estimates are obtained by marginalizing the trans-dimensional posterior distribution in terms of vs-profile marginal distributions. The methodology is applied to microtremor array dispersion data collected at two sites with significantly different geology in British Columbia, Canada. At both sites, results show excellent agreement with estimates from invasive measurements.

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

Bayesian 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

Municipal mortality due to thyroid cancer in Spain

PubMed Central

Lope, Virginia; Pollán, Marina; Pérez-Gómez, Beatriz; Aragonés, Nuria; Ramis, Rebeca; Gómez-Barroso, Diana; López-Abente, Gonzalo

2006-01-01

Background Thyroid cancer is a tumor with a low but growing incidence in Spain. This study sought to depict its spatial municipal mortality pattern, using the classic model proposed by Besag, York and Mollié. Methods It was possible to compile and ascertain the posterior distribution of relative risk on the basis of a single Bayesian spatial model covering all of Spain's 8077 municipal areas. Maps were plotted depicting standardized mortality ratios, smoothed relative risk (RR) estimates, and the posterior probability that RR > 1. Results From 1989 to 1998 a total of 2,538 thyroid cancer deaths were registered in 1,041 municipalities. The highest relative risks were mostly situated in the Canary Islands, the province of Lugo, the east of La Coruña (Corunna) and western areas of Asturias and Orense. Conclusion The observed mortality pattern coincides with areas in Spain where goiter has been declared endemic. The higher frequency in these same areas of undifferentiated, more aggressive carcinomas could be reflected in the mortality figures. Other unknown genetic or environmental factors could also play a role in the etiology of this tumor. PMID:17173668

A Comparison of Grizzly Bear Demographic Parameters Estimated from Non-Spatial and Spatial Open Population Capture-Recapture Models

PubMed Central

Whittington, Jesse; Sawaya, Michael A.

2015-01-01

Capture-recapture studies are frequently used to monitor the status and trends of wildlife populations. Detection histories from individual animals are used to estimate probability of detection and abundance or density. The accuracy of abundance and density estimates depends on the ability to model factors affecting detection probability. Non-spatial capture-recapture models have recently evolved into spatial capture-recapture models that directly include the effect of distances between an animal’s home range centre and trap locations on detection probability. Most studies comparing non-spatial and spatial capture-recapture biases focussed on single year models and no studies have compared the accuracy of demographic parameter estimates from open population models. We applied open population non-spatial and spatial capture-recapture models to three years of grizzly bear DNA-based data from Banff National Park and simulated data sets. The two models produced similar estimates of grizzly bear apparent survival, per capita recruitment, and population growth rates but the spatial capture-recapture models had better fit. Simulations showed that spatial capture-recapture models produced more accurate parameter estimates with better credible interval coverage than non-spatial capture-recapture models. Non-spatial capture-recapture models produced negatively biased estimates of apparent survival and positively biased estimates of per capita recruitment. The spatial capture-recapture grizzly bear population growth rates and 95% highest posterior density averaged across the three years were 0.925 (0.786–1.071) for females, 0.844 (0.703–0.975) for males, and 0.882 (0.779–0.981) for females and males combined. The non-spatial capture-recapture population growth rates were 0.894 (0.758–1.024) for females, 0.825 (0.700–0.948) for males, and 0.863 (0.771–0.957) for both sexes. The combination of low densities, low reproductive rates, and predominantly negative population growth rates suggest that Banff National Park’s population of grizzly bears requires continued conservation-oriented management actions. PMID:26230262

Hidden Markov models and neural networks for fault detection in dynamic systems

NASA Technical Reports Server (NTRS)

Smyth, Padhraic

1994-01-01

Neural networks plus hidden Markov models (HMM) can provide excellent detection and false alarm rate performance in fault detection applications, as shown in this viewgraph presentation. Modified models allow for novelty detection. Key contributions of neural network models are: (1) excellent nonparametric discrimination capability; (2) a good estimator of posterior state probabilities, even in high dimensions, and thus can be embedded within overall probabilistic model (HMM); and (3) simple to implement compared to other nonparametric models. Neural network/HMM monitoring model is currently being integrated with the new Deep Space Network (DSN) antenna controller software and will be on-line monitoring a new DSN 34-m antenna (DSS-24) by July, 1994.

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.

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.

Mineral in skeletal elements of the terrestrial crustacean Porcellio scaber: SRμCT of function related distribution and changes during the moult cycle.

PubMed

Ziegler, Andreas; Neues, Frank; Janáček, Jiří; Beckmann, Felix; Epple, Matthias

2017-01-01

Terrestrial isopods moult first the posterior and then the anterior half of the body, allowing for storage and recycling of CaCO 3 . We used synchrotron-radiation microtomography to estimate mineral content within skeletal segments in sequential moulting stages of Porcellio scaber. The results suggest that all examined cuticular segments contribute to storage and recycling, however, to varying extents. The mineral within the hepatopancreas after moult suggests an uptake of mineral from the ingested exuviae. The total maximum loss of mineral was 46% for the anterior and 43% for the posterior cuticle. The time course of resorption of mineral and mineralisation of the new cuticle suggests storage and recycling of mineral in the posterior and anterior cuticle. The mineral in the anterior pereiopods decreases by 25% only. P. scaber has long legs and can run fast; therefore, a less mineralised and thus lightweight cuticle in pereiopods likely serves to lower energy consumption during escape behaviour. Differential demineralisation occurs in the head cuticle, in which the cornea of the complex eyes remains completely mineralised. The partes incisivae of the mandibles are mineralised before the old cuticle is demineralised and shed. Probably, this enables the animal to ingest the old exuviae after each half moult. Copyright © 2016 Elsevier Ltd. All rights reserved.

Quantifying uncertainty in soot volume fraction estimates using Bayesian inference of auto-correlated laser-induced incandescence measurements

NASA Astrophysics Data System (ADS)

Hadwin, Paul J.; Sipkens, T. A.; Thomson, K. A.; Liu, F.; Daun, K. J.

2016-01-01

Auto-correlated laser-induced incandescence (AC-LII) infers the soot volume fraction (SVF) of soot particles by comparing the spectral incandescence from laser-energized particles to the pyrometrically inferred peak soot temperature. This calculation requires detailed knowledge of model parameters such as the absorption function of soot, which may vary with combustion chemistry, soot age, and the internal structure of the soot. This work presents a Bayesian methodology to quantify such uncertainties. This technique treats the additional "nuisance" model parameters, including the soot absorption function, as stochastic variables and incorporates the current state of knowledge of these parameters into the inference process through maximum entropy priors. While standard AC-LII analysis provides a point estimate of the SVF, Bayesian techniques infer the posterior probability density, which will allow scientists and engineers to better assess the reliability of AC-LII inferred SVFs in the context of environmental regulations and competing diagnostics.

Top-down estimate of surface flux in the Los Angeles Basin using a mesoscale inverse modeling technique: assessing anthropogenic emissions of CO, NOx and CO2 and their impacts

NASA Astrophysics Data System (ADS)

Brioude, Jerome; Angevine, Wayne; Ahmadov, Ravan; Kim, Si Wan; Evan, Stephanie; McKeen, Stuart; Hsie, Eirh Yu; Frost, Greg; Neuman, Andy; Pollack, Ilana; Peischl, Jeff; Ryerson, Tom; Holloway, John; Brown, Steeve; Nowak, John; Roberts, Jim; Wofsy, Steeve; Santoni, Greg; Trainer, Michael

2013-04-01

We present top-down estimates of anthropogenic CO, NOx and CO2 surface fluxes at mesoscale using a Lagrangian model in combination with three different WRF model configurations, driven by data from aircraft flights during the CALNEX campaign in southern California in May-June 2010. The US EPA National Emission Inventory 2005 (NEI 2005) was the prior in the CO and NOx inversion calculations. The flux ratio inversion method, based on linear relationships between chemical species, was used to calculate the CO2 inventory without prior knowledge of CO2 surface fluxes. The inversion was applied to each flight to estimate the variability of single-flight-based flux estimates. In Los Angeles (LA) County, the uncertainties on CO and NOx fluxes were 10% and 15%, respectively. Compared with NEI 2005, the CO posterior emissions were lower by 43% ± 6% in LA County and by 37% ± 10% in the South Coast Air Basin (SoCAB). NOx posterior emissions were lower by 32% ± 10% in LA County and by 27% ± 15% in the SoCAB. NOx posterior emissions were 40% lower on weekends relative to weekdays. The CO2 posterior estimates were 183 ± 18 Tg yr-1 in SoCAB. A flight during ITCT in 2002 was used to estimate emissions in the LA Basin in 2002. From 2002 to 2010, the CO and NOx posterior emissions decreased by 41% and 37%, respectively, in agreement with previous studies. Over the same time period, CO2 emissions increased by 10% ± 14% in LA County but decreased by 4% ± 10% in the SoCAB, a statistically insignificant change. Overall, the posterior estimates were in good agreement with the California Air Resources Board (CARB) inventory, with differences of 15% or less. However, the posterior spatial distribution in the basin was significantly different from CARB for NOx emissions. WRF-Chem mesoscale chemical-transport model simulations allowed an evaluation of differences in chemistry using different inventory assumptions, including NEI 2005, CARB 2010 and the posterior inventories derived in this study. The biases in WRF-Chem ozone were reduced and correlations were increased using the posterior from this study compared with simulations with the two bottom-up inventories, showing that improving the spatial distribution of ozone precursor surface emissions is also important in mesoscale chemistry forecasts.

Top-down estimate of surface flux in the Los Angeles Basin using a mesoscale inverse modeling technique: assessing anthropogenic emissions of CO, NOx and CO2 and their impacts

NASA Astrophysics Data System (ADS)

Brioude, J.; Angevine, W. M.; Ahmadov, R.; Kim, S.-W.; Evan, S.; McKeen, S. A.; Hsie, E.-Y.; Frost, G. J.; Neuman, J. A.; Pollack, I. B.; Peischl, J.; Ryerson, T. B.; Holloway, J.; Brown, S. S.; Nowak, J. B.; Roberts, J. M.; Wofsy, S. C.; Santoni, G. W.; Trainer, M.

2012-12-01

We present top-down estimates of anthropogenic CO, NOx and CO2 surface fluxes at mesoscale using a Lagrangian model in combination with three different WRF model configurations, driven by data from aircraft flights during the CALNEX campaign in southern California in May-June 2010. The US EPA National Emission Inventory 2005 (NEI 2005) was the prior in the CO and NOx inversion calculations. The flux ratio inversion method, based on linear relationships between chemical species, was used to calculate the CO2 inventory without prior knowledge of CO2 surface fluxes. The inversion was applied to each flight to estimate the variability of single-flight-based flux estimates. In Los Angeles (LA) County, the uncertainties on CO and NOx fluxes were 10% and 15%, respectively. Compared with NEI 2005, the CO posterior emissions were lower by 43% ± 6% in LA County and by 37% ± 10% in the South Coast Air Basin (SoCAB). NOx posterior emissions were lower by 32% ± 10% in LA County and by 27% ± 15% in the SoCAB. NOx posterior emissions were 40% lower on weekends relative to weekdays. The CO2 posterior estimates were 183 ± 18 Tg yr-1 in SoCAB. A flight during ITCT in 2002 was used to estimate emissions in the LA Basin in 2002. From 2002 to 2010, the CO and NOx posterior emissions decreased by 41% and 37%, respectively, in agreement with previous studies. Over the same time period, CO2 emissions increased by 10% ± 14% in LA County but decreased by 4% ± 10% in the SoCAB, a statistically insignificant change. Overall, the posterior estimates were in good agreement with the California Air Resources Board (CARB) inventory, with differences of 15% or less. However, the posterior spatial distribution in the basin was significantly different from CARB for NOx emissions. WRF-Chem mesoscale chemical-transport model simulations allowed an evaluation of differences in chemistry using different inventory assumptions, including NEI 2005, CARB 2010 and the posterior inventories derived in this study. The biases in WRF-Chem ozone were reduced and correlations were increased using the posterior from this study compared with simulations with the two bottom-up inventories, showing that improving the spatial distribution of ozone precursor surface emissions is also important in mesoscale chemistry forecasts.

Bayesian averaging over Decision Tree models for trauma severity scoring.

PubMed

Schetinin, V; Jakaite, L; Krzanowski, W

2018-01-01

Health care practitioners analyse possible risks of misleading decisions and need to estimate and quantify uncertainty in predictions. We have examined the "gold" standard of screening a patient's conditions for predicting survival probability, based on logistic regression modelling, which is used in trauma care for clinical purposes and quality audit. This methodology is based on theoretical assumptions about data and uncertainties. Models induced within such an approach have exposed a number of problems, providing unexplained fluctuation of predicted survival and low accuracy of estimating uncertainty intervals within which predictions are made. Bayesian method, which in theory is capable of providing accurate predictions and uncertainty estimates, has been adopted in our study using Decision Tree models. Our approach has been tested on a large set of patients registered in the US National Trauma Data Bank and has outperformed the standard method in terms of prediction accuracy, thereby providing practitioners with accurate estimates of the predictive posterior densities of interest that are required for making risk-aware decisions. Copyright © 2017 Elsevier B.V. All rights reserved.

Automatic threshold selection for multi-class open set recognition

NASA Astrophysics Data System (ADS)

Scherreik, Matthew; Rigling, Brian

2017-05-01

Multi-class open set recognition is the problem of supervised classification with additional unknown classes encountered after a model has been trained. An open set classifer often has two core components. The first component is a base classifier which estimates the most likely class of a given example. The second component consists of open set logic which estimates if the example is truly a member of the candidate class. Such a system is operated in a feed-forward fashion. That is, a candidate label is first estimated by the base classifier, and the true membership of the example to the candidate class is estimated afterward. Previous works have developed an iterative threshold selection algorithm for rejecting examples from classes which were not present at training time. In those studies, a Platt-calibrated SVM was used as the base classifier, and the thresholds were applied to class posterior probabilities for rejection. In this work, we investigate the effectiveness of other base classifiers when paired with the threshold selection algorithm and compare their performance with the original SVM solution.

On the validity of cosmological Fisher matrix forecasts

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

Wolz, Laura; Kilbinger, Martin; Weller, Jochen

2012-09-01

We present a comparison of Fisher matrix forecasts for cosmological probes with Monte Carlo Markov Chain (MCMC) posterior likelihood estimation methods. We analyse the performance of future Dark Energy Task Force (DETF) stage-III and stage-IV dark-energy surveys using supernovae, baryon acoustic oscillations and weak lensing as probes. We concentrate in particular on the dark-energy equation of state parameters w{sub 0} and w{sub a}. For purely geometrical probes, and especially when marginalising over w{sub a}, we find considerable disagreement between the two methods, since in this case the Fisher matrix can not reproduce the highly non-elliptical shape of the likelihood function.more » More quantitatively, the Fisher method underestimates the marginalized errors for purely geometrical probes between 30%-70%. For cases including structure formation such as weak lensing, we find that the posterior probability contours from the Fisher matrix estimation are in good agreement with the MCMC contours and the forecasted errors only changing on the 5% level. We then explore non-linear transformations resulting in physically-motivated parameters and investigate whether these parameterisations exhibit a Gaussian behaviour. We conclude that for the purely geometrical probes and, more generally, in cases where it is not known whether the likelihood is close to Gaussian, the Fisher matrix is not the appropriate tool to produce reliable forecasts.« less

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.

Statistical physics of medical diagnostics: Study of a probabilistic model.

PubMed

Mashaghi, Alireza; Ramezanpour, Abolfazl

2018-03-01

We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses compared to a strategy that is solely based on the direct implications of the initial observations. We demonstrate this by employing the mean-field approximation of statistical physics to compute the posterior disease probabilities for a given subset of observed signs (symptoms) in a probabilistic model of signs and diseases. A Monte Carlo optimization algorithm is then used to maximize an objective function of the sequence of observations, which favors the more decisive observations resulting in more polarized disease probabilities. We see how the observed signs change the nature of the macroscopic (Gibbs) states of the sign and disease probability distributions. The structure of these macroscopic states in the configuration space of the variables affects the quality of any approximate inference algorithm (so the diagnostic performance) which tries to estimate the sign-disease marginal probabilities. In particular, we find that the simulation (or extrapolation) of the diagnostic process is helpful when the disease landscape is not trivial and the system undergoes a phase transition to an ordered phase.

Statistical physics of medical diagnostics: Study of a probabilistic model

NASA Astrophysics Data System (ADS)

Mashaghi, Alireza; Ramezanpour, Abolfazl

2018-03-01

We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses compared to a strategy that is solely based on the direct implications of the initial observations. We demonstrate this by employing the mean-field approximation of statistical physics to compute the posterior disease probabilities for a given subset of observed signs (symptoms) in a probabilistic model of signs and diseases. A Monte Carlo optimization algorithm is then used to maximize an objective function of the sequence of observations, which favors the more decisive observations resulting in more polarized disease probabilities. We see how the observed signs change the nature of the macroscopic (Gibbs) states of the sign and disease probability distributions. The structure of these macroscopic states in the configuration space of the variables affects the quality of any approximate inference algorithm (so the diagnostic performance) which tries to estimate the sign-disease marginal probabilities. In particular, we find that the simulation (or extrapolation) of the diagnostic process is helpful when the disease landscape is not trivial and the system undergoes a phase transition to an ordered phase.

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.

Sexual dimorphism of the tibia in contemporary Greek-Cypriots and Cretans: Forensic applications.

PubMed

Kranioti, E K; García-Donas, J G; Almeida Prado, P S; Kyriakou, X P; Langstaff, H C

2017-02-01

Sex estimation is an essential step in the identification process of unknown heavily decomposed human remains as it eliminates all possible matches of the opposite sex from the missing person's database. Osteometric methods constitute a reliable approach for sex estimation and considering the variation of sexual dimorphism between and within populations; standards for specific populations are required to ensure accurate results. The current study aspires to contribute osteometric data on the tibia from contemporary Greek-Cypriots to assist the identification process. A secondary goal involves osteometric comparison with data from Crete, a Greek island with similar cultural and dietary customs and environmental conditions. Left tibiae from one hundred and thirty-two skeletons (70 males and 62 females) of Greek-Cypriots and one hundred and fifty-seven skeletons (85 males, 72 females) of Cretans were measured. Seven standard metric variables including Maximum length (ML), Upper epiphyseal breadth (UB), Nutrient foramen anteroposterior diameter (NFap), Nutrient Foramen transverse diameter (NFtrsv), Nutrient foramen circumference (NFCirc), Minimum circumference (MinCirc) and Lower epiphyseal breadth (LB) were compared between sexes and populations. Univariate and multivariate discriminant functions were developed and posterior probabilities were calculated for each sample. Results confirmed the existence of sexual dimorphism of the tibia in both samples as well as the pooled sample. Classification accuracy for univariate functions ranged from 78% to 85% for Greek-Cypriots and from 69% to 83% for Cretans. The best multivariate equations after cross-validation resulted in 87% for Greek-Cypriots and 90% accuracy for Cretans. When the samples were pooled accuracy reached 87% with over 95% confidence for about one third of the population. Estimates with over 95% of posterior probability can be considered reliable while any less than 80% should be treated with caution. This work constitutes the initial step towards the creation of an osteometric database for Greek-Cypriots and we hope it can contribute to the biological profiling and identification of the missing and to potential forensic cases of unknown skeletal remains both in Cyprus and Crete. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Statistical Inference in Hidden Markov Models Using k-Segment Constraints

PubMed Central

Titsias, Michalis K.; Holmes, Christopher C.; Yau, Christopher

2016-01-01

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward–backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k-segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k-segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online. PMID:27226674

Elastic K-means using posterior probability.

PubMed

Zheng, Aihua; Jiang, Bo; Li, Yan; Zhang, Xuehan; Ding, Chris

2017-01-01

The widely used K-means clustering is a hard clustering algorithm. Here we propose a Elastic K-means clustering model (EKM) using posterior probability with soft capability where each data point can belong to multiple clusters fractionally and show the benefit of proposed Elastic K-means. Furthermore, in many applications, besides vector attributes information, pairwise relations (graph information) are also available. Thus we integrate EKM with Normalized Cut graph clustering into a single clustering formulation. Finally, we provide several useful matrix inequalities which are useful for matrix formulations of learning models. Based on these results, we prove the correctness and the convergence of EKM algorithms. Experimental results on six benchmark datasets demonstrate the effectiveness of proposed EKM and its integrated model.

Robust Estimation of Electron Density From Anatomic Magnetic Resonance Imaging of the Brain Using a Unifying Multi-Atlas Approach

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

Ren, Shangjie; Department of Radiation Oncology, Stanford University School of Medicine, Palo Alto, California; Hara, Wendy

Purpose: To develop a reliable method to estimate electron density based on anatomic magnetic resonance imaging (MRI) of the brain. Methods and Materials: We proposed a unifying multi-atlas approach for electron density estimation based on standard T1- and T2-weighted MRI. First, a composite atlas was constructed through a voxelwise matching process using multiple atlases, with the goal of mitigating effects of inherent anatomic variations between patients. Next we computed for each voxel 2 kinds of conditional probabilities: (1) electron density given its image intensity on T1- and T2-weighted MR images; and (2) electron density given its spatial location in a referencemore » anatomy, obtained by deformable image registration. These were combined into a unifying posterior probability density function using the Bayesian formalism, which provided the optimal estimates for electron density. We evaluated the method on 10 patients using leave-one-patient-out cross-validation. Receiver operating characteristic analyses for detecting different tissue types were performed. Results: The proposed method significantly reduced the errors in electron density estimation, with a mean absolute Hounsfield unit error of 119, compared with 140 and 144 (P<.0001) using conventional T1-weighted intensity and geometry-based approaches, respectively. For detection of bony anatomy, the proposed method achieved an 89% area under the curve, 86% sensitivity, 88% specificity, and 90% accuracy, which improved upon intensity and geometry-based approaches (area under the curve: 79% and 80%, respectively). Conclusion: The proposed multi-atlas approach provides robust electron density estimation and bone detection based on anatomic MRI. If validated on a larger population, our work could enable the use of MRI as a primary modality for radiation treatment planning.« less

Spatial and temporal Brook Trout density dynamics: Implications for conservation, management, and monitoring

USGS Publications Warehouse

Wagner, Tyler; Jefferson T. Deweber,; Jason Detar,; Kristine, David; John A. Sweka,

2014-01-01

Many potential stressors to aquatic environments operate over large spatial scales, prompting the need to assess and monitor both site-specific and regional dynamics of fish populations. We used hierarchical Bayesian models to evaluate the spatial and temporal variability in density and capture probability of age-1 and older Brook Trout Salvelinus fontinalis from three-pass removal data collected at 291 sites over a 37-year time period (1975–2011) in Pennsylvania streams. There was high between-year variability in density, with annual posterior means ranging from 2.1 to 10.2 fish/100 m2; however, there was no significant long-term linear trend. Brook Trout density was positively correlated with elevation and negatively correlated with percent developed land use in the network catchment. Probability of capture did not vary substantially across sites or years but was negatively correlated with mean stream width. Because of the low spatiotemporal variation in capture probability and a strong correlation between first-pass CPUE (catch/min) and three-pass removal density estimates, the use of an abundance index based on first-pass CPUE could represent a cost-effective alternative to conducting multiple-pass removal sampling for some Brook Trout monitoring and assessment objectives. Single-pass indices may be particularly relevant for monitoring objectives that do not require precise site-specific estimates, such as regional monitoring programs that are designed to detect long-term linear trends in density.

Improving the Rank Precision of Population Health Measures for Small Areas with Longitudinal and Joint Outcome Models

PubMed Central

Athens, Jessica K.; Remington, Patrick L.; Gangnon, Ronald E.

2015-01-01

Objectives The University of Wisconsin Population Health Institute has published the County Health Rankings since 2010. These rankings use population-based data to highlight health outcomes and the multiple determinants of these outcomes and to encourage in-depth health assessment for all United States counties. A significant methodological limitation, however, is the uncertainty of rank estimates, particularly for small counties. To address this challenge, we explore the use of longitudinal and pooled outcome data in hierarchical Bayesian models to generate county ranks with greater precision. Methods In our models we used pooled outcome data for three measure groups: (1) Poor physical and poor mental health days; (2) percent of births with low birth weight and fair or poor health prevalence; and (3) age-specific mortality rates for nine age groups. We used the fixed and random effects components of these models to generate posterior samples of rates for each measure. We also used time-series data in longitudinal random effects models for age-specific mortality. Based on the posterior samples from these models, we estimate ranks and rank quartiles for each measure, as well as the probability of a county ranking in its assigned quartile. Rank quartile probabilities for univariate, joint outcome, and/or longitudinal models were compared to assess improvements in rank precision. Results The joint outcome model for poor physical and poor mental health days resulted in improved rank precision, as did the longitudinal model for age-specific mortality rates. Rank precision for low birth weight births and fair/poor health prevalence based on the univariate and joint outcome models were equivalent. Conclusion Incorporating longitudinal or pooled outcome data may improve rank certainty, depending on characteristics of the measures selected. For measures with different determinants, joint modeling neither improved nor degraded rank precision. This approach suggests a simple way to use existing information to improve the precision of small-area measures of population health. PMID:26098858

QTL fine mapping with Bayes C(π): a simulation study.

PubMed

van den Berg, Irene; Fritz, Sébastien; Boichard, Didier

2013-06-19

Accurate QTL mapping is a prerequisite in the search for causative mutations. Bayesian genomic selection models that analyse many markers simultaneously should provide more accurate QTL detection results than single-marker models. Our objectives were to (a) evaluate by simulation the influence of heritability, number of QTL and number of records on the accuracy of QTL mapping with Bayes Cπ and Bayes C; (b) estimate the QTL status (homozygous vs. heterozygous) of the individuals analysed. This study focussed on the ten largest detected QTL, assuming they are candidates for further characterization. Our simulations were based on a true dairy cattle population genotyped for 38,277 phased markers. Some of these markers were considered biallelic QTL and used to generate corresponding phenotypes. Different numbers of records (4387 and 1500), heritability values (0.1, 0.4 and 0.7) and numbers of QTL (10, 100 and 1000) were studied. QTL detection was based on the posterior inclusion probability for individual markers, or on the sum of the posterior inclusion probabilities for consecutive markers, estimated using Bayes C or Bayes Cπ. The QTL status of the individuals was derived from the contrast between the sums of the SNP allelic effects of their chromosomal segments. The proportion of markers with null effect (π) frequently did not reach convergence, leading to poor results for Bayes Cπ in QTL detection. Fixing π led to better results. Detection of the largest QTL was most accurate for medium to high heritability, for low to moderate numbers of QTL, and with a large number of records. The QTL status was accurately inferred when the distribution of the contrast between chromosomal segment effects was bimodal. QTL detection is feasible with Bayes C. For QTL detection, it is recommended to use a large dataset and to focus on highly heritable traits and on the largest QTL. QTL statuses were inferred based on the distribution of the contrast between chromosomal segment effects.

qPR: An adaptive partial-report procedure based on Bayesian inference.

PubMed

Baek, Jongsoo; Lesmes, Luis Andres; Lu, Zhong-Lin

2016-08-01

Iconic memory is best assessed with the partial report procedure in which an array of letters appears briefly on the screen and a poststimulus cue directs the observer to report the identity of the cued letter(s). Typically, 6-8 cue delays or 600-800 trials are tested to measure the iconic memory decay function. Here we develop a quick partial report, or qPR, procedure based on a Bayesian adaptive framework to estimate the iconic memory decay function with much reduced testing time. The iconic memory decay function is characterized by an exponential function and a joint probability distribution of its three parameters. Starting with a prior of the parameters, the method selects the stimulus to maximize the expected information gain in the next test trial. It then updates the posterior probability distribution of the parameters based on the observer's response using Bayesian inference. The procedure is reiterated until either the total number of trials or the precision of the parameter estimates reaches a certain criterion. Simulation studies showed that only 100 trials were necessary to reach an average absolute bias of 0.026 and a precision of 0.070 (both in terms of probability correct). A psychophysical validation experiment showed that estimates of the iconic memory decay function obtained with 100 qPR trials exhibited good precision (the half width of the 68.2% credible interval = 0.055) and excellent agreement with those obtained with 1,600 trials of the conventional method of constant stimuli procedure (RMSE = 0.063). Quick partial-report relieves the data collection burden in characterizing iconic memory and makes it possible to assess iconic memory in clinical populations.

qPR: An adaptive partial-report procedure based on Bayesian inference

PubMed Central

Baek, Jongsoo; Lesmes, Luis Andres; Lu, Zhong-Lin

2016-01-01

Iconic memory is best assessed with the partial report procedure in which an array of letters appears briefly on the screen and a poststimulus cue directs the observer to report the identity of the cued letter(s). Typically, 6–8 cue delays or 600–800 trials are tested to measure the iconic memory decay function. Here we develop a quick partial report, or qPR, procedure based on a Bayesian adaptive framework to estimate the iconic memory decay function with much reduced testing time. The iconic memory decay function is characterized by an exponential function and a joint probability distribution of its three parameters. Starting with a prior of the parameters, the method selects the stimulus to maximize the expected information gain in the next test trial. It then updates the posterior probability distribution of the parameters based on the observer's response using Bayesian inference. The procedure is reiterated until either the total number of trials or the precision of the parameter estimates reaches a certain criterion. Simulation studies showed that only 100 trials were necessary to reach an average absolute bias of 0.026 and a precision of 0.070 (both in terms of probability correct). A psychophysical validation experiment showed that estimates of the iconic memory decay function obtained with 100 qPR trials exhibited good precision (the half width of the 68.2% credible interval = 0.055) and excellent agreement with those obtained with 1,600 trials of the conventional method of constant stimuli procedure (RMSE = 0.063). Quick partial-report relieves the data collection burden in characterizing iconic memory and makes it possible to assess iconic memory in clinical populations. PMID:27580045

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.

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.

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 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

Estimation of age at death from the pubic symphysis and the auricular surface of the ilium using a smoothing procedure.

PubMed

Martins, Rui; Oliveira, Paulo Eduardo; Schmitt, Aurore

2012-06-10

We discuss here the estimation of age at death from two indicators (pubic symphysis and the sacro-pelvic surface of the ilium) based on four different osteological series from Portugal, Great-Britain, South Africa or USA (European origin). These samples and the scoring system of the two indicators were used by Schmitt et al. (2002), applying the methodology proposed by Lucy et al. (1996). In the present work, the same data was processed using a modification of the empirical method proposed by Lucy et al. (2002). The various probability distributions are estimated from training data by using kernel density procedures and Jackknife methodology. Bayes's theorem is then used to produce the posterior distribution from which point and interval estimates may be made. This statistical approach reduces the bias of the estimates to less than 70% of what was obtained by the initial method. This reduction going up to 52% if knowledge of sex of the individual is available, and produces an age for all the individuals that improves age at death assessment. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Stan : A Probabilistic Programming Language

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

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

Traffic Video Image Segmentation Model Based on Bayesian and Spatio-Temporal Markov Random Field

NASA Astrophysics Data System (ADS)

Zhou, Jun; Bao, Xu; Li, Dawei; Yin, Yongwen

2017-10-01

Traffic video image is a kind of dynamic image and its background and foreground is changed at any time, which results in the occlusion. In this case, using the general method is more difficult to get accurate image segmentation. A segmentation algorithm based on Bayesian and Spatio-Temporal Markov Random Field is put forward, which respectively build the energy function model of observation field and label field to motion sequence image with Markov property, then according to Bayesian' rule, use the interaction of label field and observation field, that is the relationship of label field’s prior probability and observation field’s likelihood probability, get the maximum posterior probability of label field’s estimation parameter, use the ICM model to extract the motion object, consequently the process of segmentation is finished. Finally, the segmentation methods of ST - MRF and the Bayesian combined with ST - MRF were analyzed. Experimental results: the segmentation time in Bayesian combined with ST-MRF algorithm is shorter than in ST-MRF, and the computing workload is small, especially in the heavy traffic dynamic scenes the method also can achieve better segmentation effect.

Stan : A Probabilistic Programming Language

DOE PAGES

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.; ...

2017-01-01

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

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.

Assessing Goodness of Fit in Item Response Theory with Nonparametric Models: A Comparison of Posterior Probabilities and Kernel-Smoothing Approaches

ERIC Educational Resources Information Center

Sueiro, Manuel J.; Abad, Francisco J.

2011-01-01

The distance between nonparametric and parametric item characteristic curves has been proposed as an index of goodness of fit in item response theory in the form of a root integrated squared error index. This article proposes to use the posterior distribution of the latent trait as the nonparametric model and compares the performance of an index…

Elastic K-means using posterior probability

PubMed Central

Zheng, Aihua; Jiang, Bo; Li, Yan; Zhang, Xuehan; Ding, Chris

2017-01-01

The widely used K-means clustering is a hard clustering algorithm. Here we propose a Elastic K-means clustering model (EKM) using posterior probability with soft capability where each data point can belong to multiple clusters fractionally and show the benefit of proposed Elastic K-means. Furthermore, in many applications, besides vector attributes information, pairwise relations (graph information) are also available. Thus we integrate EKM with Normalized Cut graph clustering into a single clustering formulation. Finally, we provide several useful matrix inequalities which are useful for matrix formulations of learning models. Based on these results, we prove the correctness and the convergence of EKM algorithms. Experimental results on six benchmark datasets demonstrate the effectiveness of proposed EKM and its integrated model. PMID:29240756

Item Selection and Ability Estimation Procedures for a Mixed-Format Adaptive Test

ERIC Educational Resources Information Center

Ho, Tsung-Han; Dodd, Barbara G.

2012-01-01

In this study we compared five item selection procedures using three ability estimation methods in the context of a mixed-format adaptive test based on the generalized partial credit model. The item selection procedures used were maximum posterior weighted information, maximum expected information, maximum posterior weighted Kullback-Leibler…

Value of Information Analysis for Time-lapse Seismic Data by Simulation-Regression

NASA Astrophysics Data System (ADS)

Dutta, G.; Mukerji, T.; Eidsvik, J.

2016-12-01

A novel method to estimate the Value of Information (VOI) of time-lapse seismic data in the context of reservoir development is proposed. VOI is a decision analytic metric quantifying the incremental value that would be created by collecting information prior to making a decision under uncertainty. The VOI has to be computed before collecting the information and can be used to justify its collection. Previous work on estimating the VOI of geophysical data has involved explicit approximation of the posterior distribution of reservoir properties given the data and then evaluating the prospect values for that posterior distribution of reservoir properties. Here, we propose to directly estimate the prospect values given the data by building a statistical relationship between them using regression. Various regression techniques such as Partial Least Squares Regression (PLSR), Multivariate Adaptive Regression Splines (MARS) and k-Nearest Neighbors (k-NN) are used to estimate the VOI, and the results compared. For a univariate Gaussian case, the VOI obtained from simulation-regression has been shown to be close to the analytical solution. Estimating VOI by simulation-regression is much less computationally expensive since the posterior distribution of reservoir properties given each possible dataset need not be modeled and the prospect values need not be evaluated for each such posterior distribution of reservoir properties. This method is flexible, since it does not require rigid model specification of posterior but rather fits conditional expectations non-parametrically from samples of values and data.

The Chandra Source Catalog: X-ray Aperture Photometry

NASA Astrophysics Data System (ADS)

Kashyap, Vinay; Primini, F. A.; Glotfelty, K. J.; Anderson, C. S.; Bonaventura, N. R.; Chen, J. C.; Davis, J. E.; Doe, S. M.; Evans, I. N.; Evans, J. D.; Fabbiano, G.; Galle, E. C.; Gibbs, D. G., II; Grier, J. D.; Hain, R.; Hall, D. M.; Harbo, P. N.; He, X.; Houck, J. C.; Karovska, M.; Lauer, J.; McCollough, M. L.; McDowell, J. C.; Miller, J. B.; Mitschang, A. W.; Morgan, D. L.; Nichols, J. S.; Nowak, M. A.; Plummer, D. A.; Refsdal, B. L.; Rots, A. H.; Siemiginowska, A. L.; Sundheim, B. A.; Tibbetts, M. S.; van Stone, D. W.; Winkelman, S. L.; Zografou, P.

2009-09-01

The Chandra Source Catalog (CSC) represents a reanalysis of the entire ACIS and HRC imaging observations over the 9-year Chandra mission. We describe here the method by which fluxes are measured for detected sources. Source detection is carried out on a uniform basis, using the CIAO tool wavdetect. Source fluxes are estimated post-facto using a Bayesian method that accounts for background, spatial resolution effects, and contamination from nearby sources. We use gamma-function prior distributions, which could be either non-informative, or in case there exist previous observations of the same source, strongly informative. The current implementation is however limited to non-informative priors. The resulting posterior probability density functions allow us to report the flux and a robust credible range on it.

Mixture modelling for cluster analysis.

PubMed

McLachlan, G J; Chang, S U

2004-10-01

Cluster analysis via a finite mixture model approach is considered. With this approach to clustering, the data can be partitioned into a specified number of clusters g by first fitting a mixture model with g components. An outright clustering of the data is then obtained by assigning an observation to the component to which it has the highest estimated posterior probability of belonging; that is, the ith cluster consists of those observations assigned to the ith component (i = 1,..., g). The focus is on the use of mixtures of normal components for the cluster analysis of data that can be regarded as being continuous. But attention is also given to the case of mixed data, where the observations consist of both continuous and discrete variables.

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.

Secondary phase validation—Phase classification by polarization

NASA Astrophysics Data System (ADS)

Fedorenko, Yury V.; Matveeva, Tatiana; Beketova, Elena; Husebye, Eystein S.

2008-07-01

A long-standing problem in operational seismology is that of reliable focal depth estimation. Standard analyst practice is to pick and identify a 'phase' in the P-coda. This picking will always produce a depth estimate but without any validation it cannot be trusted. In this article we 'hunt' for standard depth phases like pP, sP and/or PmP but unlike the analyst we use Bayes statistics for classifying the probability that polarization characteristics of pickings belong to one of the mentioned depth phases given preliminary epicenter information. In this regard we describe a general-purpose PC implementation of the Bayesian methodology that can deal with complex nonlinear models in a flexible way. The models are represented by a data-flow diagram that may be manipulated by the analyst through a graphical-programming environment. An analytic signal representation is used with the imaginary part being the Hilbert transform of the signal itself. The pickings are in terms of a plot of posterior probabilities as a function of time for pP, Sp or PmP being within the presumed azimuth and incident angle sectors for given preliminary epicenter locations. We have tested this novel focal depth estimation procedure on explosion and earthquake recordings from Cossack Ranger II stations in Karelia, NW Russia, and with encouraging results. For example, pickings deviating more than 5° off 'true' azimuth are rejected while Pn-incident angle estimate exhibit considerable scatter. A comprehensive test of our approach is not quite easy as recordings from so-called Ground Truth events are elusive.

Chemical Source Localization Fusing Concentration Information in the Presence of Chemical Background Noise.

PubMed

Pomareda, Víctor; Magrans, Rudys; Jiménez-Soto, Juan M; Martínez, Dani; Tresánchez, Marcel; Burgués, Javier; Palacín, Jordi; Marco, Santiago

2017-04-20

We present the estimation of a likelihood map for the location of the source of a chemical plume dispersed under atmospheric turbulence under uniform wind conditions. The main contribution of this work is to extend previous proposals based on Bayesian inference with binary detections to the use of concentration information while at the same time being robust against the presence of background chemical noise. For that, the algorithm builds a background model with robust statistics measurements to assess the posterior probability that a given chemical concentration reading comes from the background or from a source emitting at a distance with a specific release rate. In addition, our algorithm allows multiple mobile gas sensors to be used. Ten realistic simulations and ten real data experiments are used for evaluation purposes. For the simulations, we have supposed that sensors are mounted on cars which do not have among its main tasks navigating toward the source. To collect the real dataset, a special arena with induced wind is built, and an autonomous vehicle equipped with several sensors, including a photo ionization detector (PID) for sensing chemical concentration, is used. Simulation results show that our algorithm, provides a better estimation of the source location even for a low background level that benefits the performance of binary version. The improvement is clear for the synthetic data while for real data the estimation is only slightly better, probably because our exploration arena is not able to provide uniform wind conditions. Finally, an estimation of the computational cost of the algorithmic proposal is presented.

Using spatiotemporal models and distance sampling to map the space use and abundance of newly metamorphosed Western Toads (Anaxyrus boreas)

USGS Publications Warehouse

Chelgren, Nathan D.; Samora, Barbara; Adams, Michael J.; McCreary, Brome

2011-01-01

High variability in abundance, cryptic coloration, and small body size of newly metamorphosed anurans have limited demographic studies of this life-history stage. We used line-transect distance sampling and Bayesian methods to estimate the abundance and spatial distribution of newly metamorphosed Western Toads (Anaxyrus boreas) in terrestrial habitat surrounding a montane lake in central Washington, USA. We completed 154 line-transect surveys from the commencement of metamorphosis (15 September 2009) to the date of first snow accumulation in fall (1 October 2009), and located 543 newly metamorphosed toads. After accounting for variable detection probability associated with the extent of barren habitats, estimates of total surface abundance ranged from a posterior median of 3,880 (95% credible intervals from 2,235 to 12,600) in the first week of sampling to 12,150 (5,543 to 51,670) during the second week of sampling. Numbers of newly metamorphosed toads dropped quickly with increasing distance from the lakeshore in a pattern that differed over the three weeks of the study and contradicted our original hypotheses. Though we hypothesized that the spatial distribution of toads would initially be concentrated near the lake shore and then spread outward from the lake over time, we observed the opposite. Ninety-five percent of individuals occurred within 20, 16, and 15 m of shore during weeks one, two, and three respectively, probably reflecting continued emergence of newly metamorphosed toads from the lake and mortality or burrow use of dispersed individuals. Numbers of toads were highest near the inlet stream of the lake. Distance sampling may provide a useful method for estimating the surface abundance of newly metamorphosed toads and relating their space use to landscape variables despite uncertain and variable probability of detection. We discuss means of improving the precision of estimates of total abundance.

Inverse Modeling Using Markov Chain Monte Carlo Aided by Adaptive Stochastic Collocation Method with Transformation

NASA Astrophysics Data System (ADS)

Zhang, D.; Liao, Q.

2016-12-01

The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of computational efficiency.

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.

Multiple Chronic Conditions and Hospitalizations Among Recipients of Long-Term Services and Supports

PubMed Central

Van Cleave, Janet H.; Egleston, Brian L.; Abbott, Katherine M.; Hirschman, Karen B.; Rao, Aditi; Naylor, Mary D.

2016-01-01

Background Among older adults receiving long term-services and supports (LTSS), debilitating hospitalizations is a pervasive clinical and research problem. Multiple chronic conditions (MCC) are prevalent in LTSS recipients. However, the combination of MCC and diseases associated with hospitalizations of LTSS recipients is unclear. Objective The purpose of this analysis was to determine the association between classes of MCC in newly enrolled LTSS recipients and the number of hospitalizations over a one-year period following enrollment. Methods This report is based on secondary analysis of extant data from a longitudinal cohort study of 470 new recipients of LTSS, ages 60 years and older, receiving services in assisted living facilities, nursing homes, or through home- and community-based services. Using baseline chronic conditions reported in medical records, latent class analysis (LCA) was used to identify classes of MCC and posterior probabilities of membership in each class. Poisson regressions were used to estimate the relative ratio between posterior probabilities of class membership and number of hospitalizations during the 3 month period prior to the start of LTSS (baseline) and then every three months forward through 12 months. Results Three latent MCC-based classes named Cardiopulmonary, Cerebrovascular/Paralysis, and All Other Conditions were identified. The Cardiopulmonary class was associated with elevated numbers of hospitalization compared to the All Other Conditions class (relative ratio [RR] = 1.88, 95% CI [1.33, 2.65], p < .001). Conclusion Older LTSS recipients with a combination of MCCs that includes cardiopulmonary conditions have increased risk for hospitalization. PMID:27801713

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.

Testing founder effect speciation: Divergence population genetics of the Spoonbills Platalea regia and Pl. minor (Threskiornithidae, Aves)

USGS Publications Warehouse

Yeung, Carol K.L.; Tsai, Pi-Wen; Chesser, R. Terry; Lin, Rong-Chien; Yao, Cheng-Te; Tian, Xiu-Hua; Li, Shou-Hsien

2011-01-01

Although founder effect speciation has been a popular theoretical model for the speciation of geographically isolated taxa, its empirical importance has remained difficult to evaluate due to the intractability of past demography, which in a founder effect speciation scenario would involve a speciational bottleneck in the emergent species and the complete cessation of gene flow following divergence. Using regression-weighted approximate Bayesian computation, we tested the validity of these two fundamental conditions of founder effect speciation in a pair of sister species with disjunct distributions: the royal spoonbill Platalea regia in Australasia and the black-faced spoonbill Pl. minor in eastern Asia. When compared with genetic polymorphism observed at 20 nuclear loci in the two species, simulations showed that the founder effect speciation model had an extremely low posterior probability (1.55 × 10-8) of producing the extant genetic pattern. In contrast, speciation models that allowed for postdivergence gene flow were much more probable (posterior probabilities were 0.37 and 0.50 for the bottleneck with gene flow and the gene flow models, respectively) and postdivergence gene flow persisted for a considerable period of time (more than 80% of the divergence history in both models) following initial divergence (median = 197,000 generations, 95% credible interval [CI]: 50,000-478,000, for the bottleneck with gene flow model; and 186,000 generations, 95% CI: 45,000-477,000, for the gene flow model). Furthermore, the estimated population size reduction in Pl. regia to 7,000 individuals (median, 95% CI: 487-12,000, according to the bottleneck with gene flow model) was unlikely to have been severe enough to be considered a bottleneck. Therefore, these results do not support founder effect speciation in Pl. regia but indicate instead that the divergence between Pl. regia and Pl. minor was probably driven by selection despite continuous gene flow. In this light, we discuss the potential importance of evolutionarily labile traits with significant fitness consequences, such as migratory behavior and habitat preference, in facilitating divergence of the spoonbills.

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…

Blending Multiple Nitrogen Dioxide Data Sources for Neighborhood Estimates of Long-Term Exposure for Health Research.

PubMed

Hanigan, Ivan C; Williamson, Grant J; Knibbs, Luke D; Horsley, Joshua; Rolfe, Margaret I; Cope, Martin; Barnett, Adrian G; Cowie, Christine T; Heyworth, Jane S; Serre, Marc L; Jalaludin, Bin; Morgan, Geoffrey G

2017-11-07

Exposure to traffic related nitrogen dioxide (NO 2 ) air pollution is associated with adverse health outcomes. Average pollutant concentrations for fixed monitoring sites are often used to estimate exposures for health studies, however these can be imprecise due to difficulty and cost of spatial modeling at the resolution of neighborhoods (e.g., a scale of tens of meters) rather than at a coarse scale (around several kilometers). The objective of this study was to derive improved estimates of neighborhood NO 2 concentrations by blending measurements with modeled predictions in Sydney, Australia (a low pollution environment). We implemented the Bayesian maximum entropy approach to blend data with uncertainty defined using informative priors. We compiled NO 2 data from fixed-site monitors, chemical transport models, and satellite-based land use regression models to estimate neighborhood annual average NO 2 . The spatial model produced a posterior probability density function of estimated annual average concentrations that spanned an order of magnitude from 3 to 35 ppb. Validation using independent data showed improvement, with root mean squared error improvement of 6% compared with the land use regression model and 16% over the chemical transport model. These estimates will be used in studies of health effects and should minimize misclassification bias.

Multilocus methods for estimating population sizes, migration rates and divergence time, with applications to the divergence of Drosophila pseudoobscura and D. persimilis.

PubMed Central

Hey, Jody; Nielsen, Rasmus

2004-01-01

The genetic study of diverging, closely related populations is required for basic questions on demography and speciation, as well as for biodiversity and conservation research. However, it is often unclear whether divergence is due simply to separation or whether populations have also experienced gene flow. These questions can be addressed with a full model of population separation with gene flow, by applying a Markov chain Monte Carlo method for estimating the posterior probability distribution of model parameters. We have generalized this method and made it applicable to data from multiple unlinked loci. These loci can vary in their modes of inheritance, and inheritance scalars can be implemented either as constants or as parameters to be estimated. By treating inheritance scalars as parameters it is also possible to address variation among loci in the impact via linkage of recurrent selective sweeps or background selection. These methods are applied to a large multilocus data set from Drosophila pseudoobscura and D. persimilis. The species are estimated to have diverged approximately 500,000 years ago. Several loci have nonzero estimates of gene flow since the initial separation of the species, with considerable variation in gene flow estimates among loci, in both directions between the species. PMID:15238526

Estimators of The Magnitude-Squared Spectrum and Methods for Incorporating SNR Uncertainty

PubMed Central

Lu, Yang; Loizou, Philipos C.

2011-01-01

Statistical estimators of the magnitude-squared spectrum are derived based on the assumption that the magnitude-squared spectrum of the noisy speech signal can be computed as the sum of the (clean) signal and noise magnitude-squared spectra. Maximum a posterior (MAP) and minimum mean square error (MMSE) estimators are derived based on a Gaussian statistical model. The gain function of the MAP estimator was found to be identical to the gain function used in the ideal binary mask (IdBM) that is widely used in computational auditory scene analysis (CASA). As such, it was binary and assumed the value of 1 if the local SNR exceeded 0 dB, and assumed the value of 0 otherwise. By modeling the local instantaneous SNR as an F-distributed random variable, soft masking methods were derived incorporating SNR uncertainty. The soft masking method, in particular, which weighted the noisy magnitude-squared spectrum by the a priori probability that the local SNR exceeds 0 dB was shown to be identical to the Wiener gain function. Results indicated that the proposed estimators yielded significantly better speech quality than the conventional MMSE spectral power estimators, in terms of yielding lower residual noise and lower speech distortion. PMID:21886543

An object correlation and maneuver detection approach for space surveillance

NASA Astrophysics Data System (ADS)

Huang, Jian; Hu, Wei-Dong; Xin, Qin; Du, Xiao-Yong

2012-10-01

Object correlation and maneuver detection are persistent problems in space surveillance and maintenance of a space object catalog. We integrate these two problems into one interrelated problem, and consider them simultaneously under a scenario where space objects only perform a single in-track orbital maneuver during the time intervals between observations. We mathematically formulate this integrated scenario as a maximum a posteriori (MAP) estimation. In this work, we propose a novel approach to solve the MAP estimation. More precisely, the corresponding posterior probability of an orbital maneuver and a joint association event can be approximated by the Joint Probabilistic Data Association (JPDA) algorithm. Subsequently, the maneuvering parameters are estimated by optimally solving the constrained non-linear least squares iterative process based on the second-order cone programming (SOCP) algorithm. The desired solution is derived according to the MAP criterions. The performance and advantages of the proposed approach have been shown by both theoretical analysis and simulation results. We hope that our work will stimulate future work on space surveillance and maintenance of a space object catalog.

Combined Estimation of Hydrogeologic Conceptual Model and Parameter Uncertainty

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

Meyer, Philip D.; Ye, Ming; Neuman, Shlomo P.

2004-03-01

The objective of the research described in this report is the development and application of a methodology for comprehensively assessing the hydrogeologic uncertainties involved in dose assessment, including uncertainties associated with conceptual models, parameters, and scenarios. This report describes and applies a statistical method to quantitatively estimate the combined uncertainty in model predictions arising from conceptual model and parameter uncertainties. The method relies on model averaging to combine the predictions of a set of alternative models. Implementation is driven by the available data. When there is minimal site-specific data the method can be carried out with prior parameter estimates basedmore » on generic data and subjective prior model probabilities. For sites with observations of system behavior (and optionally data characterizing model parameters), the method uses model calibration to update the prior parameter estimates and model probabilities based on the correspondence between model predictions and site observations. The set of model alternatives can contain both simplified and complex models, with the requirement that all models be based on the same set of data. The method was applied to the geostatistical modeling of air permeability at a fractured rock site. Seven alternative variogram models of log air permeability were considered to represent data from single-hole pneumatic injection tests in six boreholes at the site. Unbiased maximum likelihood estimates of variogram and drift parameters were obtained for each model. Standard information criteria provided an ambiguous ranking of the models, which would not justify selecting one of them and discarding all others as is commonly done in practice. Instead, some of the models were eliminated based on their negligibly small updated probabilities and the rest were used to project the measured log permeabilities by kriging onto a rock volume containing the six boreholes. These four projections, and associated kriging variances, were averaged using the posterior model probabilities as weights. Finally, cross-validation was conducted by eliminating from consideration all data from one borehole at a time, repeating the above process, and comparing the predictive capability of the model-averaged result with that of each individual model. Using two quantitative measures of comparison, the model-averaged result was superior to any individual geostatistical model of log permeability considered.« less

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

Uncertainty quantification of voice signal production mechanical model and experimental updating

NASA Astrophysics Data System (ADS)

Cataldo, E.; Soize, C.; Sampaio, R.

2013-11-01

The aim of this paper is to analyze the uncertainty quantification in a voice production mechanical model and update the probability density function corresponding to the tension parameter using the Bayes method and experimental data. Three parameters are considered uncertain in the voice production mechanical model used: the tension parameter, the neutral glottal area and the subglottal pressure. The tension parameter of the vocal folds is mainly responsible for the changing of the fundamental frequency of a voice signal, generated by a mechanical/mathematical model for producing voiced sounds. The three uncertain parameters are modeled by random variables. The probability density function related to the tension parameter is considered uniform and the probability density functions related to the neutral glottal area and the subglottal pressure are constructed using the Maximum Entropy Principle. The output of the stochastic computational model is the random voice signal and the Monte Carlo method is used to solve the stochastic equations allowing realizations of the random voice signals to be generated. For each realization of the random voice signal, the corresponding realization of the random fundamental frequency is calculated and the prior pdf of this random fundamental frequency is then estimated. Experimental data are available for the fundamental frequency and the posterior probability density function of the random tension parameter is then estimated using the Bayes method. In addition, an application is performed considering a case with a pathology in the vocal folds. The strategy developed here is important mainly due to two things. The first one is related to the possibility of updating the probability density function of a parameter, the tension parameter of the vocal folds, which cannot be measured direct and the second one is related to the construction of the likelihood function. In general, it is predefined using the known pdf. Here, it is constructed in a new and different manner, using the own system considered.

A model-based approach to wildland fire reconstruction using sediment charcoal records

USGS Publications Warehouse

Itter, Malcolm S.; Finley, Andrew O.; Hooten, Mevin B.; Higuera, Philip E.; Marlon, Jennifer R.; Kelly, Ryan; McLachlan, Jason S.

2017-01-01

Lake sediment charcoal records are used in paleoecological analyses to reconstruct fire history, including the identification of past wildland fires. One challenge of applying sediment charcoal records to infer fire history is the separation of charcoal associated with local fire occurrence and charcoal originating from regional fire activity. Despite a variety of methods to identify local fires from sediment charcoal records, an integrated statistical framework for fire reconstruction is lacking. We develop a Bayesian point process model to estimate the probability of fire associated with charcoal counts from individual-lake sediments and estimate mean fire return intervals. A multivariate extension of the model combines records from multiple lakes to reduce uncertainty in local fire identification and estimate a regional mean fire return interval. The univariate and multivariate models are applied to 13 lakes in the Yukon Flats region of Alaska. Both models resulted in similar mean fire return intervals (100–350 years) with reduced uncertainty under the multivariate model due to improved estimation of regional charcoal deposition. The point process model offers an integrated statistical framework for paleofire reconstruction and extends existing methods to infer regional fire history from multiple lake records with uncertainty following directly from posterior distributions.

The Past Sure is Tense: On Interpreting Phylogenetic Divergence Time Estimates.

PubMed

Brown, Joseph W; Smith, Stephen A

2018-03-01

Divergence time estimation-the calibration of a phylogeny to geological time-is an integral first step in modeling the tempo of biological evolution (traits and lineages). However, despite increasingly sophisticated methods to infer divergence times from molecular genetic sequences, the estimated age of many nodes across the tree of life contrast significantly and consistently with timeframes conveyed by the fossil record. This is perhaps best exemplified by crown angiosperms, where molecular clock (Triassic) estimates predate the oldest (Early Cretaceous) undisputed angiosperm fossils by tens of millions of years or more. While the incompleteness of the fossil record is a common concern, issues of data limitation and model inadequacy are viable (if underexplored) alternative explanations. In this vein, Beaulieu et al. (2015) convincingly demonstrated how methods of divergence time inference can be misled by both (i) extreme state-dependent molecular substitution rate heterogeneity and (ii) biased sampling of representative major lineages. These results demonstrate the impact of (potentially common) model violations. Here, we suggest another potential challenge: that the configuration of the statistical inference problem (i.e., the parameters, their relationships, and associated priors) alone may preclude the reconstruction of the paleontological timeframe for the crown age of angiosperms. We demonstrate, through sampling from the joint prior (formed by combining the tree (diversification) prior with the calibration densities specified for fossil-calibrated nodes) that with no data present at all, that an Early Cretaceous crown angiosperms is rejected (i.e., has essentially zero probability). More worrisome, however, is that for the 24 nodes calibrated by fossils, almost all have indistinguishable marginal prior and posterior age distributions when employing routine lognormal fossil calibration priors. These results indicate that there is inadequate information in the data to over-rule the joint prior. Given that these calibrated nodes are strategically placed in disparate regions of the tree, they act to anchor the tree scaffold, and so the posterior inference for the tree as a whole is largely determined by the pseudodata present in the (often arbitrary) calibration densities. We recommend, as for any Bayesian analysis, that marginal prior and posterior distributions be carefully compared to determine whether signal is coming from the data or prior belief, especially for parameters of direct interest. This recommendation is not novel. However, given how rarely such checks are carried out in evolutionary biology, it bears repeating. Our results demonstrate the fundamental importance of prior/posterior comparisons in any Bayesian analysis, and we hope that they further encourage both researchers and journals to consistently adopt this crucial step as standard practice. Finally, we note that the results presented here do not refute the biological modeling concerns identified by Beaulieu et al. (2015). Both sets of issues remain apposite to the goals of accurate divergence time estimation, and only by considering them in tandem can we move forward more confidently.

Posterior corneal astigmatism in refractive lens exchange surgery.

PubMed

Rydström, Elin; Westin, Oscar; Koskela, Timo; Behndig, Anders

2016-05-01

To assess the anterior, posterior and total corneal spherical and astigmatic powers in patients undergoing refractive lens exchange (RLE) surgery. In 402 consecutive patients planned for RLE at Koskelas Eye Clinic, Luleå, Sweden, right eye data from pre- and postoperative subjective refraction, preoperative IOLMaster(®) biometry and Pentacam HR(®) measurements were collected. Postoperative Pentacam HR(®) data were collected for 54 of the patients. The spherical and astigmatic powers of the anterior and posterior corneal surfaces and for the total cornea were assessed and compared, and surgically, induced astigmatism was calculated using vector analysis. The spherical power of the anterior corneal surface was 48.18 ± 1.69D with an astigmatic power of 0.83 ± 0.54D. The corresponding values for the posterior surface were -6.05 ± 2,52D and 0.26 ± 0.15D, respectively. The total corneal spherical power calculated with ray tracing was 42.47 ± 2.89D with a 0.72 ± 0.48D astigmatic power, and the corresponding figures obtained by estimating the posterior corneal surface were 43.25 ± 1.51D (p < 0.001) with a 0.75 ± 0.49D astigmatic power (p = 0.003). In eyes with anterior astigmatism with-the-rule, the total corneal astigmatism is overestimated if the posterior corneal surface is estimated; in eyes, with against-the-rule astigmatism it is underestimated. Had the posterior corneal surface been measured in this material, 14.7% of the patients would have received a spheric instead of a toric IOL, or vice versa. Estimating the posterior corneal surface in RLE patients leads to systematic measurement errors that can be reduced by measuring the posterior surface. Such an approach can potentially increase the refractive outcome accuracy in RLE surgery. © 2016 Acta Ophthalmologica Scandinavica Foundation. Published by John Wiley & Sons Ltd.

Construction of a Calibrated Probabilistic Classification Catalog: Application to 50k Variable Sources in the All-Sky Automated Survey

NASA Astrophysics Data System (ADS)

Richards, Joseph W.; Starr, Dan L.; Miller, Adam A.; Bloom, Joshua S.; Butler, Nathaniel R.; Brink, Henrik; Crellin-Quick, Arien

2012-12-01

With growing data volumes from synoptic surveys, astronomers necessarily must become more abstracted from the discovery and introspection processes. Given the scarcity of follow-up resources, there is a particularly sharp onus on the frameworks that replace these human roles to provide accurate and well-calibrated probabilistic classification catalogs. Such catalogs inform the subsequent follow-up, allowing consumers to optimize the selection of specific sources for further study and permitting rigorous treatment of classification purities and efficiencies for population studies. Here, we describe a process to produce a probabilistic classification catalog of variability with machine learning from a multi-epoch photometric survey. In addition to producing accurate classifications, we show how to estimate calibrated class probabilities and motivate the importance of probability calibration. We also introduce a methodology for feature-based anomaly detection, which allows discovery of objects in the survey that do not fit within the predefined class taxonomy. Finally, we apply these methods to sources observed by the All-Sky Automated Survey (ASAS), and release the Machine-learned ASAS Classification Catalog (MACC), a 28 class probabilistic classification catalog of 50,124 ASAS sources in the ASAS Catalog of Variable Stars. We estimate that MACC achieves a sub-20% classification error rate and demonstrate that the class posterior probabilities are reasonably calibrated. MACC classifications compare favorably to the classifications of several previous domain-specific ASAS papers and to the ASAS Catalog of Variable Stars, which had classified only 24% of those sources into one of 12 science classes.

CONSTRUCTION OF A CALIBRATED PROBABILISTIC CLASSIFICATION CATALOG: APPLICATION TO 50k VARIABLE SOURCES IN THE ALL-SKY AUTOMATED SURVEY

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

Richards, Joseph W.; Starr, Dan L.; Miller, Adam A.

2012-12-15

With growing data volumes from synoptic surveys, astronomers necessarily must become more abstracted from the discovery and introspection processes. Given the scarcity of follow-up resources, there is a particularly sharp onus on the frameworks that replace these human roles to provide accurate and well-calibrated probabilistic classification catalogs. Such catalogs inform the subsequent follow-up, allowing consumers to optimize the selection of specific sources for further study and permitting rigorous treatment of classification purities and efficiencies for population studies. Here, we describe a process to produce a probabilistic classification catalog of variability with machine learning from a multi-epoch photometric survey. In additionmore » to producing accurate classifications, we show how to estimate calibrated class probabilities and motivate the importance of probability calibration. We also introduce a methodology for feature-based anomaly detection, which allows discovery of objects in the survey that do not fit within the predefined class taxonomy. Finally, we apply these methods to sources observed by the All-Sky Automated Survey (ASAS), and release the Machine-learned ASAS Classification Catalog (MACC), a 28 class probabilistic classification catalog of 50,124 ASAS sources in the ASAS Catalog of Variable Stars. We estimate that MACC achieves a sub-20% classification error rate and demonstrate that the class posterior probabilities are reasonably calibrated. MACC classifications compare favorably to the classifications of several previous domain-specific ASAS papers and to the ASAS Catalog of Variable Stars, which had classified only 24% of those sources into one of 12 science classes.« less

Robust Bayesian Algorithm for Targeted Compound Screening in Forensic Toxicology.

PubMed

Woldegebriel, Michael; Gonsalves, John; van Asten, Arian; Vivó-Truyols, Gabriel

2016-02-16

As part of forensic toxicological investigation of cases involving unexpected death of an individual, targeted or untargeted xenobiotic screening of post-mortem samples is normally conducted. To this end, liquid chromatography (LC) coupled to high-resolution mass spectrometry (MS) is typically employed. For data analysis, almost all commonly applied algorithms are threshold-based (frequentist). These algorithms examine the value of a certain measurement (e.g., peak height) to decide whether a certain xenobiotic of interest (XOI) is present/absent, yielding a binary output. Frequentist methods pose a problem when several sources of information [e.g., shape of the chromatographic peak, isotopic distribution, estimated mass-to-charge ratio (m/z), adduct, etc.] need to be combined, requiring the approach to make arbitrary decisions at substep levels of data analysis. We hereby introduce a novel Bayesian probabilistic algorithm for toxicological screening. The method tackles the problem with a different strategy. It is not aimed at reaching a final conclusion regarding the presence of the XOI, but it estimates its probability. The algorithm effectively and efficiently combines all possible pieces of evidence from the chromatogram and calculates the posterior probability of the presence/absence of XOI features. This way, the model can accommodate more information by updating the probability if extra evidence is acquired. The final probabilistic result assists the end user to make a final decision with respect to the presence/absence of the xenobiotic. The Bayesian method was validated and found to perform better (in terms of false positives and false negatives) than the vendor-supplied software package.

The known unknowns: neural representation of second-order uncertainty, and ambiguity

PubMed Central

Bach, Dominik R.; Hulme, Oliver; Penny, William D.; Dolan, Raymond J.

2011-01-01

Predictions provided by action-outcome probabilities entail a degree of (first-order) uncertainty. However, these probabilities themselves can be imprecise and embody second-order uncertainty. Tracking second-order uncertainty is important for optimal decision making and reinforcement learning. Previous functional magnetic resonance imaging investigations of second-order uncertainty in humans have drawn on an economic concept of ambiguity, where action-outcome associations in a gamble are either known (unambiguous) or completely unknown (ambiguous). Here, we relaxed the constraints associated with a purely categorical concept of ambiguity and varied the second-order uncertainty of gambles continuously, quantified as entropy over second-order probabilities. We show that second-order uncertainty influences decisions in a pessimistic way by biasing second-order probabilities, and that second-order uncertainty is negatively correlated with posterior cingulate cortex activity. The category of ambiguous (compared to non-ambiguous) gambles also biased choice in a similar direction, but was associated with distinct activation of a posterior parietal cortical area; an activation that we show reflects a different computational mechanism. Our findings indicate that behavioural and neural responses to second-order uncertainty are distinct from those associated with ambiguity and may call for a reappraisal of previous data. PMID:21451019

Image segmentation using hidden Markov Gauss mixture models.

PubMed

Pyun, Kyungsuk; Lim, Johan; Won, Chee Sun; Gray, Robert M

2007-07-01

Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.

Multi-Target State Extraction for the SMC-PHD Filter

PubMed Central

Si, Weijian; Wang, Liwei; Qu, Zhiyu

2016-01-01

The sequential Monte Carlo probability hypothesis density (SMC-PHD) filter has been demonstrated to be a favorable method for multi-target tracking. However, the time-varying target states need to be extracted from the particle approximation of the posterior PHD, which is difficult to implement due to the unknown relations between the large amount of particles and the PHD peaks representing potential target locations. To address this problem, a novel multi-target state extraction algorithm is proposed in this paper. By exploiting the information of measurements and particle likelihoods in the filtering stage, we propose a validation mechanism which aims at selecting effective measurements and particles corresponding to detected targets. Subsequently, the state estimates of the detected and undetected targets are performed separately: the former are obtained from the particle clusters directed by effective measurements, while the latter are obtained from the particles corresponding to undetected targets via clustering method. Simulation results demonstrate that the proposed method yields better estimation accuracy and reliability compared to existing methods. PMID:27322274

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.

Efficient Learning of Continuous-Time Hidden Markov Models for Disease Progression

PubMed Central

Liu, Yu-Ying; Li, Shuang; Li, Fuxin; Song, Le; Rehg, James M.

2016-01-01

The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer’s disease dataset. PMID:27019571

Quantifying Transmission Heterogeneity Using Both Pathogen Phylogenies and Incidence Time Series

PubMed Central

Li, Lucy M.; Grassly, Nicholas C.; Fraser, Christophe

2017-01-01

Abstract Heterogeneity in individual-level transmissibility can be quantified by the dispersion parameter k of the offspring distribution. Quantifying heterogeneity is important as it affects other parameter estimates, it modulates the degree of unpredictability of an epidemic, and it needs to be accounted for in models of infection control. Aggregated data such as incidence time series are often not sufficiently informative to estimate k. Incorporating phylogenetic analysis can help to estimate k concurrently with other epidemiological parameters. We have developed an inference framework that uses particle Markov Chain Monte Carlo to estimate k and other epidemiological parameters using both incidence time series and the pathogen phylogeny. Using the framework to fit a modified compartmental transmission model that includes the parameter k to simulated data, we found that more accurate and less biased estimates of the reproductive number were obtained by combining epidemiological and phylogenetic analyses. However, k was most accurately estimated using pathogen phylogeny alone. Accurately estimating k was necessary for unbiased estimates of the reproductive number, but it did not affect the accuracy of reporting probability and epidemic start date estimates. We further demonstrated that inference was possible in the presence of phylogenetic uncertainty by sampling from the posterior distribution of phylogenies. Finally, we used the inference framework to estimate transmission parameters from epidemiological and genetic data collected during a poliovirus outbreak. Despite the large degree of phylogenetic uncertainty, we demonstrated that incorporating phylogenetic data in parameter inference improved the accuracy and precision of estimates. PMID:28981709

Fast Bayesian approach for modal identification using free vibration data, Part I - Most probable value

NASA Astrophysics Data System (ADS)

Zhang, Feng-Liang; Ni, Yan-Chun; Au, Siu-Kui; Lam, Heung-Fai

2016-03-01

The identification of modal properties from field testing of civil engineering structures is becoming economically viable, thanks to the advent of modern sensor and data acquisition technology. Its demand is driven by innovative structural designs and increased performance requirements of dynamic-prone structures that call for a close cross-checking or monitoring of their dynamic properties and responses. Existing instrumentation capabilities and modal identification techniques allow structures to be tested under free vibration, forced vibration (known input) or ambient vibration (unknown broadband loading). These tests can be considered complementary rather than competing as they are based on different modeling assumptions in the identification model and have different implications on costs and benefits. Uncertainty arises naturally in the dynamic testing of structures due to measurement noise, sensor alignment error, modeling error, etc. This is especially relevant in field vibration tests because the test condition in the field environment can hardly be controlled. In this work, a Bayesian statistical approach is developed for modal identification using the free vibration response of structures. A frequency domain formulation is proposed that makes statistical inference based on the Fast Fourier Transform (FFT) of the data in a selected frequency band. This significantly simplifies the identification model because only the modes dominating the frequency band need to be included. It also legitimately ignores the information in the excluded frequency bands that are either irrelevant or difficult to model, thereby significantly reducing modeling error risk. The posterior probability density function (PDF) of the modal parameters is derived rigorously from modeling assumptions and Bayesian probability logic. Computational difficulties associated with calculating the posterior statistics, including the most probable value (MPV) and the posterior covariance matrix, are addressed. Fast computational algorithms for determining the MPV are proposed so that the method can be practically implemented. In the companion paper (Part II), analytical formulae are derived for the posterior covariance matrix so that it can be evaluated without resorting to finite difference method. The proposed method is verified using synthetic data. It is also applied to modal identification of full-scale field structures.

A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks

PubMed Central

Zaikin, Alexey; Míguez, Joaquín

2017-01-01

We compare three state-of-the-art Bayesian inference methods for the estimation of the unknown parameters in a stochastic model of a genetic network. In particular, we introduce a stochastic version of the paradigmatic synthetic multicellular clock model proposed by Ullner et al., 2007. By introducing dynamical noise in the model and assuming that the partial observations of the system are contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we tackle the Bayesian estimation of a subset of the model parameters. Specifically, we compare three Monte Carlo based numerical methods for the approximation of the posterior probability density function of the unknown parameters given a set of partial and noisy observations of the system. The schemes we assess are the particle Metropolis-Hastings (PMH) algorithm, the nonlinear population Monte Carlo (NPMC) method and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) scheme. We present an extensive numerical simulation study, which shows that while the three techniques can effectively solve the problem there are significant differences both in estimation accuracy and computational efficiency. PMID:28797087

Hydraulic Conductivity Estimation using Bayesian Model Averaging and Generalized Parameterization

NASA Astrophysics Data System (ADS)

Tsai, F. T.; Li, X.

2006-12-01

Non-uniqueness in parameterization scheme is an inherent problem in groundwater inverse modeling due to limited data. To cope with the non-uniqueness problem of parameterization, we introduce a Bayesian Model Averaging (BMA) method to integrate a set of selected parameterization methods. The estimation uncertainty in BMA includes the uncertainty in individual parameterization methods as the within-parameterization variance and the uncertainty from using different parameterization methods as the between-parameterization variance. Moreover, the generalized parameterization (GP) method is considered in the geostatistical framework in this study. The GP method aims at increasing the flexibility of parameterization through the combination of a zonation structure and an interpolation method. The use of BMP with GP avoids over-confidence in a single parameterization method. A normalized least-squares estimation (NLSE) is adopted to calculate the posterior probability for each GP. We employee the adjoint state method for the sensitivity analysis on the weighting coefficients in the GP method. The adjoint state method is also applied to the NLSE problem. The proposed methodology is implemented to the Alamitos Barrier Project (ABP) in California, where the spatially distributed hydraulic conductivity is estimated. The optimal weighting coefficients embedded in GP are identified through the maximum likelihood estimation (MLE) where the misfits between the observed and calculated groundwater heads are minimized. The conditional mean and conditional variance of the estimated hydraulic conductivity distribution using BMA are obtained to assess the estimation uncertainty.

Credible occurrence probabilities for extreme geophysical events: earthquakes, volcanic eruptions, magnetic storms

USGS Publications Warehouse

Love, Jeffrey J.

2012-01-01

Statistical analysis is made of rare, extreme geophysical events recorded in historical data -- counting the number of events $k$ with sizes that exceed chosen thresholds during specific durations of time $\\tau$. Under transformations that stabilize data and model-parameter variances, the most likely Poisson-event occurrence rate, $k/\\tau$, applies for frequentist inference and, also, for Bayesian inference with a Jeffreys prior that ensures posterior invariance under changes of variables. Frequentist confidence intervals and Bayesian (Jeffreys) credibility intervals are approximately the same and easy to calculate: $(1/\\tau)[(\\sqrt{k} - z/2)^{2},(\\sqrt{k} + z/2)^{2}]$, where $z$ is a parameter that specifies the width, $z=1$ ($z=2$) corresponding to $1\\sigma$, $68.3\\%$ ($2\\sigma$, $95.4\\%$). If only a few events have been observed, as is usually the case for extreme events, then these "error-bar" intervals might be considered to be relatively wide. From historical records, we estimate most likely long-term occurrence rates, 10-yr occurrence probabilities, and intervals of frequentist confidence and Bayesian credibility for large earthquakes, explosive volcanic eruptions, and magnetic storms.

[Research on engine remaining useful life prediction based on oil spectrum analysis and particle filtering].

PubMed

Sun, Lei; Jia, Yun-xian; Cai, Li-ying; Lin, Guo-yu; Zhao, Jin-song

2013-09-01

The spectrometric oil analysis(SOA) is an important technique for machine state monitoring, fault diagnosis and prognosis, and SOA based remaining useful life(RUL) prediction has an advantage of finding out the optimal maintenance strategy for machine system. Because the complexity of machine system, its health state degradation process can't be simply characterized by linear model, while particle filtering(PF) possesses obvious advantages over traditional Kalman filtering for dealing nonlinear and non-Gaussian system, the PF approach was applied to state forecasting by SOA, and the RUL prediction technique based on SOA and PF algorithm is proposed. In the prediction model, according to the estimating result of system's posterior probability, its prior probability distribution is realized, and the multi-step ahead prediction model based on PF algorithm is established. Finally, the practical SOA data of some engine was analyzed and forecasted by the above method, and the forecasting result was compared with that of traditional Kalman filtering method. The result fully shows the superiority and effectivity of the

Uncertainty quantification of crustal scale thermo-chemical properties in Southeast Australia

NASA Astrophysics Data System (ADS)

Mather, B.; Moresi, L. N.; Rayner, P. J.

2017-12-01

The thermo-chemical properties of the crust are essential to understanding the mechanical and thermal state of the lithosphere. The uncertainties associated with these parameters are connected to the available geophysical observations and a priori information to constrain the objective function. Often, it is computationally efficient to reduce the parameter space by mapping large portions of the crust into lithologies that have assumed homogeneity. However, the boundaries of these lithologies are, in themselves, uncertain and should also be included in the inverse problem. We assimilate geological uncertainties from an a priori geological model of Southeast Australia with geophysical uncertainties from S-wave tomography and 174 heat flow observations within an adjoint inversion framework. This reduces the computational cost of inverting high dimensional probability spaces, compared to probabilistic inversion techniques that operate in the `forward' mode, but at the sacrifice of uncertainty and covariance information. We overcome this restriction using a sensitivity analysis, that perturbs our observations and a priori information within their probability distributions, to estimate the posterior uncertainty of thermo-chemical parameters in the crust.

Efficient pairwise RNA structure prediction using probabilistic alignment constraints in Dynalign

PubMed Central

2007-01-01

Background Joint alignment and secondary structure prediction of two RNA sequences can significantly improve the accuracy of the structural predictions. Methods addressing this problem, however, are forced to employ constraints that reduce computation by restricting the alignments and/or structures (i.e. folds) that are permissible. In this paper, a new methodology is presented for the purpose of establishing alignment constraints based on nucleotide alignment and insertion posterior probabilities. Using a hidden Markov model, posterior probabilities of alignment and insertion are computed for all possible pairings of nucleotide positions from the two sequences. These alignment and insertion posterior probabilities are additively combined to obtain probabilities of co-incidence for nucleotide position pairs. A suitable alignment constraint is obtained by thresholding the co-incidence probabilities. The constraint is integrated with Dynalign, a free energy minimization algorithm for joint alignment and secondary structure prediction. The resulting method is benchmarked against the previous version of Dynalign and against other programs for pairwise RNA structure prediction. Results The proposed technique eliminates manual parameter selection in Dynalign and provides significant computational time savings in comparison to prior constraints in Dynalign while simultaneously providing a small improvement in the structural prediction accuracy. Savings are also realized in memory. In experiments over a 5S RNA dataset with average sequence length of approximately 120 nucleotides, the method reduces computation by a factor of 2. The method performs favorably in comparison to other programs for pairwise RNA structure prediction: yielding better accuracy, on average, and requiring significantly lesser computational resources. Conclusion Probabilistic analysis can be utilized in order to automate the determination of alignment constraints for pairwise RNA structure prediction methods in a principled fashion. These constraints can reduce the computational and memory requirements of these methods while maintaining or improving their accuracy of structural prediction. This extends the practical reach of these methods to longer length sequences. The revised Dynalign code is freely available for download. PMID:17445273

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.

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

Functional mechanisms of probabilistic inference in feature- and space-based attentional systems.

PubMed

Dombert, Pascasie L; Kuhns, Anna; Mengotti, Paola; Fink, Gereon R; Vossel, Simone

2016-11-15

Humans flexibly attend to features or locations and these processes are influenced by the probability of sensory events. We combined computational modeling of response times with fMRI to compare the functional correlates of (re-)orienting, and the modulation by probabilistic inference in spatial and feature-based attention systems. Twenty-four volunteers performed two task versions with spatial or color cues. Percentage of cue validity changed unpredictably. A hierarchical Bayesian model was used to derive trial-wise estimates of probability-dependent attention, entering the fMRI analysis as parametric regressors. Attentional orienting activated a dorsal frontoparietal network in both tasks, without significant parametric modulation. Spatially invalid trials activated a bilateral frontoparietal network and the precuneus, while invalid feature trials activated the left intraparietal sulcus (IPS). Probability-dependent attention modulated activity in the precuneus, left posterior IPS, middle occipital gyrus, and right temporoparietal junction for spatial attention, and in the left anterior IPS for feature-based and spatial attention. These findings provide novel insights into the generality and specificity of the functional basis of attentional control. They suggest that probabilistic inference can distinctively affect each attentional subsystem, but that there is an overlap in the left IPS, which responds to both spatial and feature-based expectancy violations. Copyright © 2016 Elsevier Inc. All rights reserved.

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

The Chandra Source Catalog: X-ray Aperture Photometry

NASA Astrophysics Data System (ADS)

Kashyap, Vinay; Primini, F. A.; Glotfelty, K. J.; Anderson, C. S.; Bonaventura, N. R.; Chen, J. C.; Davis, J. E.; Doe, S. M.; Evans, I. N.; Evans, J. D.; Fabbiano, G.; Galle, E.; Gibbs, D. G.; Grier, J. D.; Hain, R.; Hall, D. M.; Harbo, P. N.; He, X.; Houck, J. C.; Karovska, M.; Lauer, J.; McCollough, M. L.; McDowell, J. C.; Miller, J. B.; Mitschang, A. W.; Morgan, D. L.; Nichols, J. S.; Nowak, M. A.; Plummer, D. A.; Refsdal, B. L.; Rots, A. H.; Siemiginowska, A. L.; Sundheim, B. A.; Tibbetts, M. S.; Van Stone, D. W.; Winkelman, S. L.; Zografou, P.

2009-01-01

The Chandra Source Catalog represents a reanalysis of the entire ACIS and HRC imaging observations over the 9-year Chandra mission. Source detection is carried out on a uniform basis, using the CIAO tool wavdetect, and source fluxes are estimated post-facto using a Bayesian method that accounts for background, spatial resolution effects, and contamination from nearby sources. We use gamma-function prior distributions, which could be either non-informative, or in case there exist previous observations of the same source, strongly informative. The resulting posterior probability density functions allow us to report the flux and a robust credible range on it. We also determine limiting sensitivities at arbitrary locations in the field using the same formulation. This work was supported by CXC NASA contracts NAS8-39073 (VK) and NAS8-03060 (CSC).

eDNAoccupancy: An R package for multi-scale occupancy modeling of environmental DNA data

USGS Publications Warehouse

Dorazio, Robert; Erickson, Richard A.

2017-01-01

In this article we describe eDNAoccupancy, an R package for fitting Bayesian, multi-scale occupancy models. These models are appropriate for occupancy surveys that include three, nested levels of sampling: primary sample units within a study area, secondary sample units collected from each primary unit, and replicates of each secondary sample unit. This design is commonly used in occupancy surveys of environmental DNA (eDNA). eDNAoccupancy allows users to specify and fit multi-scale occupancy models with or without covariates, to estimate posterior summaries of occurrence and detection probabilities, and to compare different models using Bayesian model-selection criteria. We illustrate these features by analyzing two published data sets: eDNA surveys of a fungal pathogen of amphibians and eDNA surveys of an endangered fish species.

Uncertainty quantification in LES of channel flow

DOE PAGES

Safta, Cosmin; Blaylock, Myra; Templeton, Jeremy; ...

2016-07-12

Here, in this paper, we present a Bayesian framework for estimating joint densities for large eddy simulation (LES) sub-grid scale model parameters based on canonical forced isotropic turbulence direct numerical simulation (DNS) data. The framework accounts for noise in the independent variables, and we present alternative formulations for accounting for discrepancies between model and data. To generate probability densities for flow characteristics, posterior densities for sub-grid scale model parameters are propagated forward through LES of channel flow and compared with DNS data. Synthesis of the calibration and prediction results demonstrates that model parameters have an explicit filter width dependence andmore » are highly correlated. Discrepancies between DNS and calibrated LES results point to additional model form inadequacies that need to be accounted for.« less

Applications of quantum entropy to statistics

NASA Astrophysics Data System (ADS)

Silver, R. N.; Martz, H. F.

This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to hierarchical Bayes methods.

Soft sensor modeling based on variable partition ensemble method for nonlinear batch processes

NASA Astrophysics Data System (ADS)

Wang, Li; Chen, Xiangguang; Yang, Kai; Jin, Huaiping

2017-01-01

Batch processes are always characterized by nonlinear and system uncertain properties, therefore, the conventional single model may be ill-suited. A local learning strategy soft sensor based on variable partition ensemble method is developed for the quality prediction of nonlinear and non-Gaussian batch processes. A set of input variable sets are obtained by bootstrapping and PMI criterion. Then, multiple local GPR models are developed based on each local input variable set. When a new test data is coming, the posterior probability of each best performance local model is estimated based on Bayesian inference and used to combine these local GPR models to get the final prediction result. The proposed soft sensor is demonstrated by applying to an industrial fed-batch chlortetracycline fermentation process.

A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays.

PubMed

McLachlan, G J; Bean, R W; Jones, L Ben-Tovim

2006-07-01

An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets.

Automated reliability assessment for spectroscopic redshift measurements

NASA Astrophysics Data System (ADS)

Jamal, S.; Le Brun, V.; Le Fèvre, O.; Vibert, D.; Schmitt, A.; Surace, C.; Copin, Y.; Garilli, B.; Moresco, M.; Pozzetti, L.

2018-03-01

Context. Future large-scale surveys, such as the ESA Euclid mission, will produce a large set of galaxy redshifts (≥106) that will require fully automated data-processing pipelines to analyze the data, extract crucial information and ensure that all requirements are met. A fundamental element in these pipelines is to associate to each galaxy redshift measurement a quality, or reliability, estimate. Aim. In this work, we introduce a new approach to automate the spectroscopic redshift reliability assessment based on machine learning (ML) and characteristics of the redshift probability density function. Methods: We propose to rephrase the spectroscopic redshift estimation into a Bayesian framework, in order to incorporate all sources of information and uncertainties related to the redshift estimation process and produce a redshift posterior probability density function (PDF). To automate the assessment of a reliability flag, we exploit key features in the redshift posterior PDF and machine learning algorithms. Results: As a working example, public data from the VIMOS VLT Deep Survey is exploited to present and test this new methodology. We first tried to reproduce the existing reliability flags using supervised classification in order to describe different types of redshift PDFs, but due to the subjective definition of these flags (classification accuracy 58%), we soon opted for a new homogeneous partitioning of the data into distinct clusters via unsupervised classification. After assessing the accuracy of the new clusters via resubstitution and test predictions (classification accuracy 98%), we projected unlabeled data from preliminary mock simulations for the Euclid space mission into this mapping to predict their redshift reliability labels. Conclusions: Through the development of a methodology in which a system can build its own experience to assess the quality of a parameter, we are able to set a preliminary basis of an automated reliability assessment for spectroscopic redshift measurements. This newly-defined method is very promising for next-generation large spectroscopic surveys from the ground and in space, such as Euclid and WFIRST. A table of the reclassified VVDS redshifts and reliability is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/611/A53

Evaluating multi-level models to test occupancy state responses of Plethodontid salamanders

USGS Publications Warehouse

Kroll, Andrew J.; Garcia, Tiffany S.; Jones, Jay E.; Dugger, Catherine; Murden, Blake; Johnson, Josh; Peerman, Summer; Brintz, Ben; Rochelle, Michael

2015-01-01

Plethodontid salamanders are diverse and widely distributed taxa and play critical roles in ecosystem processes. Due to salamander use of structurally complex habitats, and because only a portion of a population is available for sampling, evaluation of sampling designs and estimators is critical to provide strong inference about Plethodontid ecology and responses to conservation and management activities. We conducted a simulation study to evaluate the effectiveness of multi-scale and hierarchical single-scale occupancy models in the context of a Before-After Control-Impact (BACI) experimental design with multiple levels of sampling. Also, we fit the hierarchical single-scale model to empirical data collected for Oregon slender and Ensatina salamanders across two years on 66 forest stands in the Cascade Range, Oregon, USA. All models were fit within a Bayesian framework. Estimator precision in both models improved with increasing numbers of primary and secondary sampling units, underscoring the potential gains accrued when adding secondary sampling units. Both models showed evidence of estimator bias at low detection probabilities and low sample sizes; this problem was particularly acute for the multi-scale model. Our results suggested that sufficient sample sizes at both the primary and secondary sampling levels could ameliorate this issue. Empirical data indicated Oregon slender salamander occupancy was associated strongly with the amount of coarse woody debris (posterior mean = 0.74; SD = 0.24); Ensatina occupancy was not associated with amount of coarse woody debris (posterior mean = -0.01; SD = 0.29). Our simulation results indicate that either model is suitable for use in an experimental study of Plethodontid salamanders provided that sample sizes are sufficiently large. However, hierarchical single-scale and multi-scale models describe different processes and estimate different parameters. As a result, we recommend careful consideration of study questions and objectives prior to sampling data and fitting models.

Estimation of Community Land Model parameters for an improved assessment of net carbon fluxes at European sites

NASA Astrophysics Data System (ADS)

Post, Hanna; Vrugt, Jasper A.; Fox, Andrew; Vereecken, Harry; Hendricks Franssen, Harrie-Jan

2017-03-01

The Community Land Model (CLM) contains many parameters whose values are uncertain and thus require careful estimation for model application at individual sites. Here we used Bayesian inference with the DiffeRential Evolution Adaptive Metropolis (DREAM(zs)) algorithm to estimate eight CLM v.4.5 ecosystem parameters using 1 year records of half-hourly net ecosystem CO2 exchange (NEE) observations of four central European sites with different plant functional types (PFTs). The posterior CLM parameter distributions of each site were estimated per individual season and on a yearly basis. These estimates were then evaluated using NEE data from an independent evaluation period and data from "nearby" FLUXNET sites at 600 km distance to the original sites. Latent variables (multipliers) were used to treat explicitly uncertainty in the initial carbon-nitrogen pools. The posterior parameter estimates were superior to their default values in their ability to track and explain the measured NEE data of each site. The seasonal parameter values reduced with more than 50% (averaged over all sites) the bias in the simulated NEE values. The most consistent performance of CLM during the evaluation period was found for the posterior parameter values of the forest PFTs, and contrary to the C3-grass and C3-crop sites, the latent variables of the initial pools further enhanced the quality-of-fit. The carbon sink function of the forest PFTs significantly increased with the posterior parameter estimates. We thus conclude that land surface model predictions of carbon stocks and fluxes require careful consideration of uncertain ecological parameters and initial states.

Estimating Bayesian Phylogenetic Information Content

PubMed Central

Lewis, Paul O.; Chen, Ming-Hui; Kuo, Lynn; Lewis, Louise A.; Fučíková, Karolina; Neupane, Suman; Wang, Yu-Bo; Shi, Daoyuan

2016-01-01

Measuring the phylogenetic information content of data has a long history in systematics. Here we explore a Bayesian approach to information content estimation. The entropy of the posterior distribution compared with the entropy of the prior distribution provides a natural way to measure information content. If the data have no information relevant to ranking tree topologies beyond the information supplied by the prior, the posterior and prior will be identical. Information in data discourages consideration of some hypotheses allowed by the prior, resulting in a posterior distribution that is more concentrated (has lower entropy) than the prior. We focus on measuring information about tree topology using marginal posterior distributions of tree topologies. We show that both the accuracy and the computational efficiency of topological information content estimation improve with use of the conditional clade distribution, which also allows topological information content to be partitioned by clade. We explore two important applications of our method: providing a compelling definition of saturation and detecting conflict among data partitions that can negatively affect analyses of concatenated data. [Bayesian; concatenation; conditional clade distribution; entropy; information; phylogenetics; saturation.] PMID:27155008

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.

Inferring probabilistic stellar rotation periods using Gaussian processes

NASA Astrophysics Data System (ADS)

Angus, Ruth; Morton, Timothy; Aigrain, Suzanne; Foreman-Mackey, Daniel; Rajpaul, Vinesh

2018-02-01

Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic - spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly periodic sinusoid therefore cannot accurately model a rotationally modulated stellar light curve. Physical models of stellar surfaces have many drawbacks preventing effective inference, such as highly degenerate or high-dimensional parameter spaces. In this work, we test an appropriate effective model: a Gaussian Process with a quasi-periodic covariance kernel function. This highly flexible model allows sampling of the posterior probability density function of the periodic parameter, marginalizing over the other kernel hyperparameters using a Markov Chain Monte Carlo approach. To test the effectiveness of this method, we infer rotation periods from 333 simulated stellar light curves, demonstrating that the Gaussian process method produces periods that are more accurate than both a sine-fitting periodogram and an autocorrelation function method. We also demonstrate that it works well on real data, by inferring rotation periods for 275 Kepler stars with previously measured periods. We provide a table of rotation periods for these and many more, altogether 1102 Kepler objects of interest, and their posterior probability density function samples. Because this method delivers posterior probability density functions, it will enable hierarchical studies involving stellar rotation, particularly those involving population modelling, such as inferring stellar ages, obliquities in exoplanet systems, or characterizing star-planet interactions. The code used to implement this method is available online.

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.

Reversible posterior leucoencephalopathy syndrome associated with bone marrow transplantation.

PubMed

Teive, H A; Brandi, I V; Camargo, C H; Bittencourt, M A; Bonfim, C M; Friedrich, M L; de Medeiros, C R; Werneck, L C; Pasquini, R

2001-09-01

Reversible posterior leucoencephalopathy syndrome (RPLS) has previously been described in patients who have renal insufficiency, eclampsia, hypertensive encephalopathy and patients receiving immunosuppressive therapy. The mechanism by which immunosuppressive agents can cause this syndrome is not clear, but it is probably related with cytotoxic effects of these agents on the vascular endothelium. We report eight patients who received cyclosporine A (CSA) after allogeneic bone marrow transplantation or as treatment for severe aplastic anemia (SSA) who developed posterior leucoencephalopathy. The most common signs and symptoms were seizures and headache. Neurological dysfunction occurred preceded by or concomitant with high blood pressure and some degree of acute renal failure in six patients. Computerized tomography studies showed low-density white matter lesions involving the posterior areas of cerebral hemispheres. Symptoms and neuroimaging abnormalities were reversible and improvement occurred in all patients when given lower doses of CSA or when the drug was withdrawn. RPLS may be considered an expression of CSA neurotoxicity.

Posterior semicircular canal dehiscence: value of VEMP and multidetector CT.

PubMed

Vanspauwen, R; Salembier, L; Van den Hauwe, L; Parizel, P; Wuyts, F L; Van de Heyning, P H

2006-01-01

To illustrate that posterior semicircular canal dehiscence can present similarly to superior semicircular canal dehiscence. The symptomatology initially presented as probable Menière's disease evolving into a mixed conductive hearing loss with a Carhart notch-type perceptive component suggestive of otosclerosis-type stapes fixation. A small hole stapedotomy resulted in a dead ear and a horizontal semicircular canal hypofunction. Recurrent incapacitating vertigo attacks developed. Vestibular evoked myogenic potential (VEMP) testing demonstrated intact vestibulocollic reflexes. Additional evaluation with high resolution multidetector computed tomography (MDCT) of the temporal bone showed a dehiscence of the left posterior semicircular canal. Besides superior semicircular canal dehiscence, posterior semicircular canal dehiscence has to be included in the differential diagnosis of atypical Menière's disease and/or low tone conductive hearing loss. The value of performing MDCT before otosclerosis-type surgery is stressed. VEMP might contribute to establishing the differential diagnosis.

Reliability-based design optimization using a generalized subset simulation method and posterior approximation

NASA Astrophysics Data System (ADS)

Ma, Yuan-Zhuo; Li, Hong-Shuang; Yao, Wei-Xing

2018-05-01

The evaluation of the probabilistic constraints in reliability-based design optimization (RBDO) problems has always been significant and challenging work, which strongly affects the performance of RBDO methods. This article deals with RBDO problems using a recently developed generalized subset simulation (GSS) method and a posterior approximation approach. The posterior approximation approach is used to transform all the probabilistic constraints into ordinary constraints as in deterministic optimization. The assessment of multiple failure probabilities required by the posterior approximation approach is achieved by GSS in a single run at all supporting points, which are selected by a proper experimental design scheme combining Sobol' sequences and Bucher's design. Sequentially, the transformed deterministic design optimization problem can be solved by optimization algorithms, for example, the sequential quadratic programming method. Three optimization problems are used to demonstrate the efficiency and accuracy of the proposed method.

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.

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.

Morphological and molecular data reveal a new species of Neoechinorhynchus (Acanthocephala: Neoechinorhynchidae) from Dormitator maculatus in the Gulf of Mexico.

PubMed

Pinacho-Pinacho, Carlos Daniel; Sereno-Uribe, Ana L; García-Varela, Martín

2014-12-01

Neoechinorhynchus (Neoechinorhynchus) mexicoensis sp. n. is described from the intestine of Dormitator maculatus (Bloch 1792) collected in 5 coastal localities from the Gulf of Mexico. The new species is mainly distinguished from the other 33 described species of Neoechinorhynchus from the Americas associated with freshwater, marine and brackish fishes by having smaller middle and posterior hooks and possessing a small proboscis with three rows of six hooks each, apical hooks longer than other hooks and extending to the same level as the posterior hooks, 1 giant nucleus in the ventral body wall and females with eggs longer than other congeneric species. Sequences of the internal transcribed spacer (ITS) and the large subunit (LSU) of ribosomal DNA including the domain D2+D3 were used independently to corroborate the morphological distinction among the new species and other congeneric species associated with freshwater and brackish water fish from Mexico. The genetic divergence estimated among congeneric species ranged from 7.34 to 44% for ITS and from 1.65 to 32.9% for LSU. Maximum likelihood and Bayesian inference analyses with each dataset showed that the 25 specimens analyzed from 5 localities of the coast of the Gulf of Mexico parasitizing D. maculatus represent an independent clade with strong bootstrap support and posterior probabilities. The morphological evidence, plus the monophyly in the phylogenetic analyses, indicates that the acanthocephalans collected from intestine of D. maculatus from the Gulf of Mexico represent a new species, herein named N. (N.) mexicoensis sp. n. Copyright © 2014. Published by Elsevier Ireland Ltd.

Birth/birth-death processes and their computable transition probabilities with biological applications.

PubMed

Ho, Lam Si Tung; Xu, Jason; Crawford, Forrest W; Minin, Vladimir N; Suchard, Marc A

2018-03-01

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.

Modulation of cognitive control levels via manipulation of saccade trial-type probability assessed with event-related BOLD fMRI.

PubMed

Pierce, Jordan E; McDowell, Jennifer E

2016-02-01

Cognitive control supports flexible behavior adapted to meet current goals and can be modeled through investigation of saccade tasks with varying cognitive demands. Basic prosaccades (rapid glances toward a newly appearing stimulus) are supported by neural circuitry, including occipital and posterior parietal cortex, frontal and supplementary eye fields, and basal ganglia. These trials can be contrasted with complex antisaccades (glances toward the mirror image location of a stimulus), which are characterized by greater functional magnetic resonance imaging (MRI) blood oxygenation level-dependent (BOLD) signal in the aforementioned regions and recruitment of additional regions such as dorsolateral prefrontal cortex. The current study manipulated the cognitive demands of these saccade tasks by presenting three rapid event-related runs of mixed saccades with a varying probability of antisaccade vs. prosaccade trials (25, 50, or 75%). Behavioral results showed an effect of trial-type probability on reaction time, with slower responses in runs with a high antisaccade probability. Imaging results exhibited an effect of probability in bilateral pre- and postcentral gyrus, bilateral superior temporal gyrus, and medial frontal gyrus. Additionally, the interaction between saccade trial type and probability revealed a strong probability effect for prosaccade trials, showing a linear increase in activation parallel to antisaccade probability in bilateral temporal/occipital, posterior parietal, medial frontal, and lateral prefrontal cortex. In contrast, antisaccade trials showed elevated activation across all runs. Overall, this study demonstrated that improbable performance of a typically simple prosaccade task led to augmented BOLD signal to support changing cognitive control demands, resulting in activation levels similar to the more complex antisaccade task. Copyright © 2016 the American Physiological Society.

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

NASA Astrophysics Data System (ADS)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity in the forward problem. We show that using only a limited number of forward solves, the resulting subspaces lead to an efficient method to explore the high-dimensional posterior.

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

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.

Confident difference criterion: a new Bayesian differentially expressed gene selection algorithm with applications.

PubMed

Yu, Fang; Chen, Ming-Hui; Kuo, Lynn; Talbott, Heather; Davis, John S

2015-08-07

Recently, the Bayesian method becomes more popular for analyzing high dimensional gene expression data as it allows us to borrow information across different genes and provides powerful estimators for evaluating gene expression levels. It is crucial to develop a simple but efficient gene selection algorithm for detecting differentially expressed (DE) genes based on the Bayesian estimators. In this paper, by extending the two-criterion idea of Chen et al. (Chen M-H, Ibrahim JG, Chi Y-Y. A new class of mixture models for differential gene expression in DNA microarray data. J Stat Plan Inference. 2008;138:387-404), we propose two new gene selection algorithms for general Bayesian models and name these new methods as the confident difference criterion methods. One is based on the standardized differences between two mean expression values among genes; the other adds the differences between two variances to it. The proposed confident difference criterion methods first evaluate the posterior probability of a gene having different gene expressions between competitive samples and then declare a gene to be DE if the posterior probability is large. The theoretical connection between the proposed first method based on the means and the Bayes factor approach proposed by Yu et al. (Yu F, Chen M-H, Kuo L. Detecting differentially expressed genes using alibrated Bayes factors. Statistica Sinica. 2008;18:783-802) is established under the normal-normal-model with equal variances between two samples. The empirical performance of the proposed methods is examined and compared to those of several existing methods via several simulations. The results from these simulation studies show that the proposed confident difference criterion methods outperform the existing methods when comparing gene expressions across different conditions for both microarray studies and sequence-based high-throughput studies. A real dataset is used to further demonstrate the proposed methodology. In the real data application, the confident difference criterion methods successfully identified more clinically important DE genes than the other methods. The confident difference criterion method proposed in this paper provides a new efficient approach for both microarray studies and sequence-based high-throughput studies to identify differentially expressed genes.

A Bayesian method to rank different model forecasts of the same volcanic ash cloud: Chapter 24

USGS Publications Warehouse

Denlinger, Roger P.; Webley, P.; Mastin, Larry G.; Schwaiger, Hans F.

2012-01-01

Volcanic eruptions often spew fine ash high into the atmosphere, where it is carried downwind, forming long ash clouds that disrupt air traffic and pose a hazard to air travel. To mitigate such hazards, the community studying ash hazards must assess risk of ash ingestion for any flight path and provide robust and accurate forecasts of volcanic ash dispersal. We provide a quantitative and objective method to evaluate the efficacy of ash dispersal estimates from different models, using Bayes theorem to assess the predictions that each model makes about ash dispersal. We incorporate model and measurement uncertainty and produce a posterior probability for model input parameters. The integral of the posterior over all possible combinations of model inputs determines the evidence for each model and is used to compare models. We compare two different types of transport models, an Eulerian model (Ash3d) and a Langrangian model (PUFF), as applied to the 2010 eruptions of Eyjafjallajökull volcano in Iceland. The evidence for each model benefits from common physical characteristics of ash dispersal from an eruption column and provides a measure of how well each model forecasts cloud transport. Given the complexity of the wind fields, we find that the differences between these models depend upon the differences in the way the models disperse ash into the wind from the source plume. With continued observation, the accuracy of the estimates made by each model increases, increasing the efficacy of each model’s ability to simulate ash dispersal.

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

Otake, M.; Schull, W.J.

The occurrence of lenticular opacities among atomic bomb survivors in Hiroshima and Nagasaki detected in 1963-1964 has been examined in reference to their ..gamma.. and neutron doses. A lenticular opacity in this context implies an ophthalmoscopic and slit lamp biomicroscopic defect in the axial posterior aspect of the lens which may or may not interfere measureably with visual acuity. Several different dose-response models were fitted to the data after the effects of age at time of bombing (ATB) were examined. Some postulate the existence of a threshold(s), others do not. All models assume a ''background'' exists, that is, that somemore » number of posterior lenticular opacities are ascribable to events other than radiation exposure. Among these alternatives we can show that a simple linear ..gamma..-neutron relationship which assumes no threshold does not fit the data adequately under the T65 dosimetry, but does fit the recent Oak Ridge and Lawrence Livermore estimates. Other models which envisage quadratic terms in gamma and which may or may not assume a threshold are compatible with the data. The ''best'' fit, that is, the one with the smallest X/sup 2/ and largest tail probability, is with a ''linear gamma:linear neutron'' model which postulates a ..gamma.. threshold but no threshold for neutrons. It should be noted that the greatest difference in the dose-response models associated with the three different sets of doses involves the neutron component, as is, of course, to be expected. No effect of neutrons on the occurrence of lenticular opacities is demonstrable with either the Lawrence Livermore or Oak Ridge estimates.« less

Detection of multiple airborne targets from multisensor data

NASA Astrophysics Data System (ADS)

Foltz, Mark A.; Srivastava, Anuj; Miller, Michael I.; Grenander, Ulf

1995-08-01

Previously we presented a jump-diffusion based random sampling algorithm for generating conditional mean estimates of scene representations for the tracking and recongition of maneuvering airborne targets. These representations include target positions and orientations along their trajectories and the target type associated with each trajectory. Taking a Bayesian approach, a posterior measure is defined on the parameter space by combining sensor models with a sophisticated prior based on nonlinear airplane dynamics. The jump-diffusion algorithm constructs a Markov process which visits the elements of the parameter space with frequencies proportional to the posterior probability. It consititutes both the infinitesimal, local search via a sample path continuous diffusion transform and the larger, global steps through discrete jump moves. The jump moves involve the addition and deletion of elements from the scene configuration or changes in the target type assoviated with each target trajectory. One such move results in target detection by the addition of a track seed to the inference set. This provides initial track data for the tracking/recognition algorithm to estimate linear graph structures representing tracks using the other jump moves and the diffusion process, as described in our earlier work. Target detection ideally involves a continuous research over a continuum of the observation space. In this work we conclude that for practical implemenations the search space must be discretized with lattice granularity comparable to sensor resolution, and discuss how fast Fourier transforms are utilized for efficient calcuation of sufficient statistics given our array models. Some results are also presented from our implementation on a networked system including a massively parallel machine architecture and a silicon graphics onyx workstation.

An application of change-point recursive models to the relationship between litter size and number of stillborns in pigs.

PubMed

Ibáñez-Escriche, N; López de Maturana, E; Noguera, J L; Varona, L

2010-11-01

We developed and implemented change-point recursive models and compared them with a linear recursive model and a standard mixed model (SMM), in the scope of the relationship between litter size (LS) and number of stillborns (NSB) in pigs. The proposed approach allows us to estimate the point of change in multiple-segment modeling of a nonlinear relationship between phenotypes. We applied the procedure to a data set provided by a commercial Large White selection nucleus. The data file consisted of LS and NSB records of 4,462 parities. The results of the analysis clearly identified the location of the change points between different structural regression coefficients. The magnitude of these coefficients increased with LS, indicating an increasing incidence of LS on the NSB ratio. However, posterior distributions of correlations were similar across subpopulations (defined by the change points on LS), except for those between residuals. The heritability estimates of NSB did not present differences between recursive models. Nevertheless, these heritabilities were greater than those obtained for SMM (0.05) with a posterior probability of 85%. These results suggest a nonlinear relationship between LS and NSB, which supports the adequacy of a change-point recursive model for its analysis. Furthermore, the results from model comparisons support the use of recursive models. However, the adequacy of the different recursive models depended on the criteria used: the linear recursive model was preferred on account of its smallest deviance value, whereas nonlinear recursive models provided a better fit and predictive ability based on the cross-validation approach.

Downregulation of the posterior medial frontal cortex prevents social conformity.

PubMed

Klucharev, Vasily; Munneke, Moniek A M; Smidts, Ale; Fernández, Guillén

2011-08-17

We often change our behavior to conform to real or imagined group pressure. Social influence on our behavior has been extensively studied in social psychology, but its neural mechanisms have remained largely unknown. Here we demonstrate that the transient downregulation of the posterior medial frontal cortex by theta-burst transcranial magnetic stimulation reduces conformity, as indicated by reduced conformal adjustments in line with group opinion. Both the extent and probability of conformal behavioral adjustments decreased significantly relative to a sham and a control stimulation over another brain area. The posterior part of the medial frontal cortex has previously been implicated in behavioral and attitudinal adjustments. Here, we provide the first interventional evidence of its critical role in social influence on human behavior.

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.

Digital map of posterior cerebral artery infarcts associated with posterior cerebral artery trunk and branch occlusion.

PubMed

Phan, Thanh G; Fong, Ashley C; Donnan, Geoffrey; Reutens, David C

2007-06-01

Knowledge of the extent and distribution of infarcts of the posterior cerebral artery (PCA) may give insight into the limits of the arterial territory and infarct mechanism. We describe the creation of a digital atlas of PCA infarcts associated with PCA branch and trunk occlusion by magnetic resonance imaging techniques. Infarcts were manually segmented on T(2)-weighted magnetic resonance images obtained >24 hours after stroke onset. The images were linearly registered into a common stereotaxic coordinate space. The segmented images were averaged to yield the probability of involvement by infarction at each voxel. Comparisons were made with existing maps of the PCA territory. Thirty patients with a median age of 61 years (range, 22 to 86 years) were studied. In the digital atlas of the PCA, the highest frequency of infarction was within the medial temporal lobe and lingual gyrus (probability=0.60 to 0.70). The mean and maximal PCA infarct volumes were 55.1 and 128.9 cm(3), respectively. Comparison with published maps showed greater agreement in the anterior and medial boundaries of the PCA territory compared with its posterior and lateral boundaries. We have created a probabilistic digital atlas of the PCA based on subacute magnetic resonance scans. This approach is useful for establishing the spatial distribution of strokes in a given cerebral arterial territory and determining the regions within the arterial territory that are at greatest risk of infarction.

Efficient estimation of abundance for patchily distributed populations via two-phase, adaptive sampling.

USGS Publications Warehouse

Conroy, M.J.; Runge, J.P.; Barker, R.J.; Schofield, M.R.; Fonnesbeck, C.J.

2008-01-01

Many organisms are patchily distributed, with some patches occupied at high density, others at lower densities, and others not occupied. Estimation of overall abundance can be difficult and is inefficient via intensive approaches such as capture-mark-recapture (CMR) or distance sampling. We propose a two-phase sampling scheme and model in a Bayesian framework to estimate abundance for patchily distributed populations. In the first phase, occupancy is estimated by binomial detection samples taken on all selected sites, where selection may be of all sites available, or a random sample of sites. Detection can be by visual surveys, detection of sign, physical captures, or other approach. At the second phase, if a detection threshold is achieved, CMR or other intensive sampling is conducted via standard procedures (grids or webs) to estimate abundance. Detection and CMR data are then used in a joint likelihood to model probability of detection in the occupancy sample via an abundance-detection model. CMR modeling is used to estimate abundance for the abundance-detection relationship, which in turn is used to predict abundance at the remaining sites, where only detection data are collected. We present a full Bayesian modeling treatment of this problem, in which posterior inference on abundance and other parameters (detection, capture probability) is obtained under a variety of assumptions about spatial and individual sources of heterogeneity. We apply the approach to abundance estimation for two species of voles (Microtus spp.) in Montana, USA. We also use a simulation study to evaluate the frequentist properties of our procedure given known patterns in abundance and detection among sites as well as design criteria. For most population characteristics and designs considered, bias and mean-square error (MSE) were low, and coverage of true parameter values by Bayesian credibility intervals was near nominal. Our two-phase, adaptive approach allows efficient estimation of abundance of rare and patchily distributed species and is particularly appropriate when sampling in all patches is impossible, but a global estimate of abundance is required.

Assessment of source-specific health effects associated with an unknown number of major sources of multiple air pollutants: a unified Bayesian approach.

PubMed

Park, Eun Sug; Hopke, Philip K; Oh, Man-Suk; Symanski, Elaine; Han, Daikwon; Spiegelman, Clifford H

2014-07-01

There has been increasing interest in assessing health effects associated with multiple air pollutants emitted by specific sources. A major difficulty with achieving this goal is that the pollution source profiles are unknown and source-specific exposures cannot be measured directly; rather, they need to be estimated by decomposing ambient measurements of multiple air pollutants. This estimation process, called multivariate receptor modeling, is challenging because of the unknown number of sources and unknown identifiability conditions (model uncertainty). The uncertainty in source-specific exposures (source contributions) as well as uncertainty in the number of major pollution sources and identifiability conditions have been largely ignored in previous studies. A multipollutant approach that can deal with model uncertainty in multivariate receptor models while simultaneously accounting for parameter uncertainty in estimated source-specific exposures in assessment of source-specific health effects is presented in this paper. The methods are applied to daily ambient air measurements of the chemical composition of fine particulate matter ([Formula: see text]), weather data, and counts of cardiovascular deaths from 1995 to 1997 for Phoenix, AZ, USA. Our approach for evaluating source-specific health effects yields not only estimates of source contributions along with their uncertainties and associated health effects estimates but also estimates of model uncertainty (posterior model probabilities) that have been ignored in previous studies. The results from our methods agreed in general with those from the previously conducted workshop/studies on the source apportionment of PM health effects in terms of number of major contributing sources, estimated source profiles, and contributions. However, some of the adverse source-specific health effects identified in the previous studies were not statistically significant in our analysis, which probably resulted because we incorporated parameter uncertainty in estimated source contributions that has been ignored in the previous studies into the estimation of health effects parameters. © The Author 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Geochemical Characterization Using Geophysical Data and Markov Chain Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Chen, J.; Hubbard, S.; Rubin, Y.; Murray, C.; Roden, E.; Majer, E.

2002-12-01

Although the spatial distribution of geochemical parameters is extremely important for many subsurface remediation approaches, traditional characterization of those parameters is invasive and laborious, and thus is rarely performed sufficiently to describe natural hydrogeological variability at the field-scale. This study is an effort to jointly use multiple sources of information, including noninvasive geophysical data, for geochemical characterization of the saturated and anaerobic portion of the DOE South Oyster Bacterial Transport Site in Virginia. Our data set includes hydrogeological and geochemical measurements from five boreholes and ground-penetrating radar (GPR) and seismic tomographic data along two profiles that traverse the boreholes. The primary geochemical parameters are the concentrations of extractable ferrous iron Fe(II) and ferric iron Fe(III). Since iron-reducing bacteria can reduce Fe(III) to Fe(II) under certain conditions, information about the spatial distributions of Fe(II) and Fe(III) may indicate both where microbial iron reduction has occurred and in which zone it is likely to occur in the future. In addition, as geochemical heterogeneity influences bacterial transport and activity, estimates of the geochemical parameters provide important input to numerical flow and contaminant transport models geared toward bioremediation. Motivated by our previous research, which demonstrated that crosshole geophysical data could be very useful for estimating hydrogeological parameters, we hypothesize in this study that geochemical and geophysical parameters may be linked through their mutual dependence on hydrogeological parameters such as lithofacies. We attempt to estimate geochemical parameters using both hydrogeological and geophysical measurements in a Bayesian framework. Within the two-dimensional study domain (12m x 6m vertical cross section divided into 0.25m x 0.25m pixels), geochemical and hydrogeological parameters were considered as data if they were available from direct measurements or as variables otherwise. To estimate the geochemical parameters, we first assigned a prior model for each variable and a likelihood model for each type of data, which together define posterior probability distributions for each variable on the domain. Since the posterior probability distribution may involve hundreds of variables, we used a Markov Chain Monte Carlo (MCMC) method to explore each variable by generating and subsequently evaluating hundreds of realizations. Results from this case study showed that although geophysical attributes are not necessarily directly related to geochemical parameters, geophysical data could be very useful for providing accurate and high-resolution information about geochemical parameter distribution through their joint and indirect connections with hydrogeological properties such as lithofacies. This case study also demonstrated that MCMC methods were particularly useful for geochemical parameter estimation using geophysical data because they allow incorporation into the procedure of spatial correlation information, measurement errors, and cross correlations among different types of parameters.

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

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

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

2013-02-12

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

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

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

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

2013-02-22

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

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.

Retinoic acid signaling acts via Hox1 to establish the posterior limit of the pharynx in the chordate amphioxus.

PubMed

Schubert, Michael; Yu, Jr-Kai; Holland, Nicholas D; Escriva, Hector; Laudet, Vincent; Holland, Linda Z

2005-01-01

In the invertebrate chordate amphioxus, as in vertebrates, retinoic acid (RA) specifies position along the anterior/posterior axis with elevated RA signaling in the middle third of the endoderm setting the posterior limit of the pharynx. Here we show that AmphiHox1 is also expressed in the middle third of the developing amphioxus endoderm and is activated by RA signaling. Knockdown of AmphiHox1 function with an antisense morpholino oligonucleotide shows that AmphiHox1 mediates the role of RA signaling in setting the posterior limit of the pharynx by repressing expression of pharyngeal markers in the posterior foregut/midgut endoderm. The spatiotemporal expression of these endodermal genes in embryos treated with RA or the RA antagonist BMS009 indicates that Pax1/9, Pitx and Notch are probably more upstream than Otx and Nodal in the hierarchy of genes repressed by RA signaling. This work highlights the potential of amphioxus, a genomically simple, vertebrate-like invertebrate chordate, as a paradigm for understanding gene hierarchies similar to the more complex ones of vertebrates.

Annular and central heavy pigment deposition on the posterior lens capsule in the pigment dispersion syndrome: pigment deposition on the posterior lens capsule in the pigment dispersion syndrome.

PubMed

Turgut, Burak; Türkçüoğlu, Peykan; Deniz, Nurettin; Catak, Onur

2008-12-01

To report annular and central heavy pigment deposition on the posterior lens capsule in a case of pigment dispersion syndrome. Case report. A 36-year-old female with bilateral pigment dispersion syndrome presented with progressive decrease in visual acuity in the right eye over the past 1-2 years. Clinical examination revealed the typical findings of pigment dispersion syndrome including bilateral Krunkenberg spindles, iris transillumination defects, and dense trabecular meshwork pigmentation. Remarkably, annular and central dense pigmentation of the posterior lens capsule was noted in the right eye. Annular pigment deposition on the posterior lens capsule may be a rare finding associated with pigment dispersion syndrome. Such a finding suggests that there may be aqueous flow into the retrolental space in some patients with this condition. The way of central pigmentation is the entrance of aqueous to Berger's space. In our case, it is probable that spontaneous detachment of the anterior hyaloid membrane aided this entrance.

Joint Inference of Population Assignment and Demographic History

PubMed Central

Choi, Sang Chul; Hey, Jody

2011-01-01

A new approach to assigning individuals to populations using genetic data is described. Most existing methods work by maximizing Hardy–Weinberg and linkage equilibrium within populations, neither of which will apply for many demographic histories. By including a demographic model, within a likelihood framework based on coalescent theory, we can jointly study demographic history and population assignment. Genealogies and population assignments are sampled from a posterior distribution using a general isolation-with-migration model for multiple populations. A measure of partition distance between assignments facilitates not only the summary of a posterior sample of assignments, but also the estimation of the posterior density for the demographic history. It is shown that joint estimates of assignment and demographic history are possible, including estimation of population phylogeny for samples from three populations. The new method is compared to results of a widely used assignment method, using simulated and published empirical data sets. PMID:21775468

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.

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.

Leveraging probabilistic peak detection to estimate baseline drift in complex chromatographic samples.

PubMed

Lopatka, Martin; Barcaru, Andrei; Sjerps, Marjan J; Vivó-Truyols, Gabriel

2016-01-29

Accurate analysis of chromatographic data often requires the removal of baseline drift. A frequently employed strategy strives to determine asymmetric weights in order to fit a baseline model by regression. Unfortunately, chromatograms characterized by a very high peak saturation pose a significant challenge to such algorithms. In addition, a low signal-to-noise ratio (i.e. s/n<40) also adversely affects accurate baseline correction by asymmetrically weighted regression. We present a baseline estimation method that leverages a probabilistic peak detection algorithm. A posterior probability of being affected by a peak is computed for each point in the chromatogram, leading to a set of weights that allow non-iterative calculation of a baseline estimate. For extremely saturated chromatograms, the peak weighted (PW) method demonstrates notable improvement compared to the other methods examined. However, in chromatograms characterized by low-noise and well-resolved peaks, the asymmetric least squares (ALS) and the more sophisticated Mixture Model (MM) approaches achieve superior results in significantly less time. We evaluate the performance of these three baseline correction methods over a range of chromatographic conditions to demonstrate the cases in which each method is most appropriate. Copyright © 2016 Elsevier B.V. All rights reserved.

Empty sella syndrome secondary to intrasellar cyst in adolescence.

PubMed

Raiti, S; Albrink, M J; Maclaren, N K; Chadduck, W M; Gabriele, O F; Chou, S M

1976-09-01

A 15-year-old boy had growth failure and failure of sexual development. The probable onset was at age 10. Endocrine studies showed hypopituitarism with deficiency of growth hormone and follicle-stimulating hormone, an abnormal response to metyrapone, and deficiency of thyroid function. Luteinizing hormone level was in the low-normal range. Posterior pituitary function was normal. Roentgenogram showed a large sella with some destruction of the posterior clinoids. Transsphenoidal exploration was carried out. The sella was empty except for a whitish membrane; no pituitary tissue was seen. The sella was packed with muscle. Recovery was uneventful, and the patient was given replacement therapy. On histologic examination,the cyst wall showed low pseudostratified cuboidal epithelium and occasional squamous metaplasia. Hemosiderin-filled phagocytes and acinar structures were also seen. The diagnosis was probable rupture of an intrasellar epithelial cyst, leading to empty sella syndrome.

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

Not that neglected! Base rates influence related and unrelated judgments.

PubMed

Białek, Michał

2017-06-01

It is claimed that people are unable (or unwilling) to incorporate prior probabilities into posterior assessments, such as their estimation of the likelihood of a person with characteristics typical of an engineer actually being an engineer given that they are drawn from a sample including a very small number of engineers. This paper shows that base rates are incorporated in classifications (Experiment 1) and, moreover, that base rates also affect unrelated judgments, such as how well a provided description of a person fits a stereotypical engineer (Experiment 2). Finally, Experiment 3 shows that individuals who make both types of assessments - though using base rates to the same extent in the former judgments - are able to decrease the extent to which they incorporate base rates in the latter judgments. Copyright © 2017 Elsevier B.V. All rights reserved.

Stochastic Inversion of 2D Magnetotelluric Data

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

Chen, Jinsong

2010-07-01

The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, itmore » provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows« less

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.

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 feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

A Novel Methodology to Estimate the Treatment Effect in Presence of Highly Variable Placebo Response

PubMed Central

Gomeni, Roberto; Goyal, Navin; Bressolle, Françoise; Fava, Maurizio

2015-01-01

One of the main reasons for the inefficiency of multicenter randomized clinical trials (RCTs) in depression is the excessively high level of placebo response. The aim of this work was to propose a novel methodology to analyze RCTs based on the assumption that centers with high placebo response are less informative than the other centers for estimating the ‘true' treatment effect (TE). A linear mixed-effect modeling approach for repeated measures (MMRM) was used as a reference approach. The new method for estimating TE was based on a nonlinear longitudinal modeling of clinical scores (NLMMRM). NLMMRM estimates TE by associating a weighting factor to the data collected in each center. The weight was defined by the posterior probability of detecting a clinically relevant difference between active treatment and placebo at that center. Data from five RCTs in depression were used to compare the performance of MMRM with NLMMRM. The results of the analyses showed an average improvement of ~15% in the TE estimated with NLMMRM when the center effect was included in the analyses. Opposite results were observed with MMRM: TE estimate was reduced by ~4% when the center effect was considered as covariate in the analysis. The novel NLMMRM approach provides a tool for controlling the confounding effect of high placebo response, to increase signal detection and to provide a more reliable estimate of the ‘true' TE by controlling false negative results associated with excessively high placebo response. PMID:25895454

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.

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.

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

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.

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.

Optimal interpolation schemes to constrain pmPM2.5 in regional modeling over the United States

NASA Astrophysics Data System (ADS)

Sousan, Sinan Dhia Jameel

This thesis presents the use of data assimilation with optimal interpolation (OI) to develop atmospheric aerosol concentration estimates for the United States at high spatial and temporal resolutions. Concentration estimates are highly desirable for a wide range of applications, including visibility, climate, and human health. OI is a viable data assimilation method that can be used to improve Community Multiscale Air Quality (CMAQ) model fine particulate matter (PM2.5) estimates. PM2.5 is the mass of solid and liquid particles with diameters less than or equal to 2.5 µm suspended in the gas phase. OI was employed by combining model estimates with satellite and surface measurements. The satellite data assimilation combined 36 x 36 km aerosol concentrations from CMAQ with aerosol optical depth (AOD) measured by MODIS and AERONET over the continental United States for 2002. Posterior model concentrations generated by the OI algorithm were compared with surface PM2.5 measurements to evaluate a number of possible data assimilation parameters, including model error, observation error, and temporal averaging assumptions. Evaluation was conducted separately for six geographic U.S. regions in 2002. Variability in model error and MODIS biases limited the effectiveness of a single data assimilation system for the entire continental domain. The best combinations of four settings and three averaging schemes led to a domain-averaged improvement in fractional error from 1.2 to 0.97 and from 0.99 to 0.89 at respective IMPROVE and STN monitoring sites. For 38% of OI results, MODIS OI degraded the forward model skill due to biases and outliers in MODIS AOD. Surface data assimilation combined 36 × 36 km aerosol concentrations from the CMAQ model with surface PM2.5 measurements over the continental United States for 2002. The model error covariance matrix was constructed by using the observational method. The observation error covariance matrix included site representation that scaled the observation error by land use (i.e. urban or rural locations). In theory, urban locations should have less effect on surrounding areas than rural sites, which can be controlled using site representation error. The annual evaluations showed substantial improvements in model performance with increases in the correlation coefficient from 0.36 (prior) to 0.76 (posterior), and decreases in the fractional error from 0.43 (prior) to 0.15 (posterior). In addition, the normalized mean error decreased from 0.36 (prior) to 0.13 (posterior), and the RMSE decreased from 5.39 µg m-3 (prior) to 2.32 µg m-3 (posterior). OI decreased model bias for both large spatial areas and point locations, and could be extended to more advanced data assimilation methods. The current work will be applied to a five year (2000-2004) CMAQ simulation aimed at improving aerosol model estimates. The posterior model concentrations will be used to inform exposure studies over the U.S. that relate aerosol exposure to mortality and morbidity rates. Future improvements for the OI techniques used in the current study will include combining both surface and satellite data to improve posterior model estimates. Satellite data have high spatial and temporal resolutions in comparison to surface measurements, which are scarce but more accurate than model estimates. The satellite data are subject to noise affected by location and season of retrieval. The implementation of OI to combine satellite and surface data sets has the potential to improve posterior model estimates for locations that have no direct measurements.

Understanding seasonal variability of uncertainty in hydrological prediction

NASA Astrophysics Data System (ADS)

Li, M.; Wang, Q. J.

2012-04-01

Understanding uncertainty in hydrological prediction can be highly valuable for improving the reliability of streamflow prediction. In this study, a monthly water balance model, WAPABA, in a Bayesian joint probability with error models are presented to investigate the seasonal dependency of prediction error structure. A seasonal invariant error model, analogous to traditional time series analysis, uses constant parameters for model error and account for no seasonal variations. In contrast, a seasonal variant error model uses a different set of parameters for bias, variance and autocorrelation for each individual calendar month. Potential connection amongst model parameters from similar months is not considered within the seasonal variant model and could result in over-fitting and over-parameterization. A hierarchical error model further applies some distributional restrictions on model parameters within a Bayesian hierarchical framework. An iterative algorithm is implemented to expedite the maximum a posterior (MAP) estimation of a hierarchical error model. Three error models are applied to forecasting streamflow at a catchment in southeast Australia in a cross-validation analysis. This study also presents a number of statistical measures and graphical tools to compare the predictive skills of different error models. From probability integral transform histograms and other diagnostic graphs, the hierarchical error model conforms better to reliability when compared to the seasonal invariant error model. The hierarchical error model also generally provides the most accurate mean prediction in terms of the Nash-Sutcliffe model efficiency coefficient and the best probabilistic prediction in terms of the continuous ranked probability score (CRPS). The model parameters of the seasonal variant error model are very sensitive to each cross validation, while the hierarchical error model produces much more robust and reliable model parameters. Furthermore, the result of the hierarchical error model shows that most of model parameters are not seasonal variant except for error bias. The seasonal variant error model is likely to use more parameters than necessary to maximize the posterior likelihood. The model flexibility and robustness indicates that the hierarchical error model has great potential for future streamflow predictions.

Surgical options for lumbosacral fusion: biomechanical stability, advantage, disadvantage and affecting factors in selecting options.

PubMed

Yoshihara, Hiroyuki

2014-07-01

Numerous surgical procedures and instrumentation techniques for lumbosacral fusion (LSF) have been developed. This is probably because of its high mechanical demand and unique anatomy. Surgical options include anterior column support (ACS) and posterior stabilization procedures. Biomechanical studies have been performed to verify the stability of those options. The options have their own advantage but also disadvantage aspects. This review article reports the surgical options for lumbosacral fusion, their biomechanical stability, advantages/disadvantages, and affecting factors in option selection. Review of literature. LSF has lots of options both for ACS and posterior stabilization procedures. Combination of posterior stabilization procedures is an option. Furthermore, combinations of ACS and posterior stabilization procedures are other options. It is difficult to make a recommendation or treatment algorithm of LSF from the current literature. However, it is important to know all aspects of the options and decision-making of surgical options for LSF needs to be tailored for each patient, considering factors such as biomechanical stress and osteoporosis.

Identification of treatment responders based on multiple longitudinal outcomes with applications to multiple sclerosis patients.

PubMed

Kondo, Yumi; Zhao, Yinshan; Petkau, John

2017-05-30

Identification of treatment responders is a challenge in comparative studies where treatment efficacy is measured by multiple longitudinally collected continuous and count outcomes. Existing procedures often identify responders on the basis of only a single outcome. We propose a novel multiple longitudinal outcome mixture model that assumes that, conditionally on a cluster label, each longitudinal outcome is from a generalized linear mixed effect model. We utilize a Monte Carlo expectation-maximization algorithm to obtain the maximum likelihood estimates of our high-dimensional model and classify patients according to their estimated posterior probability of being a responder. We demonstrate the flexibility of our novel procedure on two multiple sclerosis clinical trial datasets with distinct data structures. Our simulation study shows that incorporating multiple outcomes improves the responder identification performance; this can occur even if some of the outcomes are ineffective. Our general procedure facilitates the identification of responders who are comprehensively defined by multiple outcomes from various distributions. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Multi-Target Tracking Using an Improved Gaussian Mixture CPHD Filter.

PubMed

Si, Weijian; Wang, Liwei; Qu, Zhiyu

2016-11-23

The cardinalized probability hypothesis density (CPHD) filter is an alternative approximation to the full multi-target Bayesian filter for tracking multiple targets. However, although the joint propagation of the posterior intensity and cardinality distribution in its recursion allows more reliable estimates of the target number than the PHD filter, the CPHD filter suffers from the spooky effect where there exists arbitrary PHD mass shifting in the presence of missed detections. To address this issue in the Gaussian mixture (GM) implementation of the CPHD filter, this paper presents an improved GM-CPHD filter, which incorporates a weight redistribution scheme into the filtering process to modify the updated weights of the Gaussian components when missed detections occur. In addition, an efficient gating strategy that can adaptively adjust the gate sizes according to the number of missed detections of each Gaussian component is also presented to further improve the computational efficiency of the proposed filter. Simulation results demonstrate that the proposed method offers favorable performance in terms of both estimation accuracy and robustness to clutter and detection uncertainty over the existing methods.

Estimating the Attack Ratio of Dengue Epidemics under Time-varying Force of Infection using Aggregated Notification Data

NASA Astrophysics Data System (ADS)

Coelho, Flavio Codeço; Carvalho, Luiz Max De

2015-12-01

Quantifying the attack ratio of disease is key to epidemiological inference and public health planning. For multi-serotype pathogens, however, different levels of serotype-specific immunity make it difficult to assess the population at risk. In this paper we propose a Bayesian method for estimation of the attack ratio of an epidemic and the initial fraction of susceptibles using aggregated incidence data. We derive the probability distribution of the effective reproductive number, Rt, and use MCMC to obtain posterior distributions of the parameters of a single-strain SIR transmission model with time-varying force of infection. Our method is showcased in a data set consisting of 18 years of dengue incidence in the city of Rio de Janeiro, Brazil. We demonstrate that it is possible to learn about the initial fraction of susceptibles and the attack ratio even in the absence of serotype specific data. On the other hand, the information provided by this approach is limited, stressing the need for detailed serological surveys to characterise the distribution of serotype-specific immunity in the population.

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.

Posterior uncertainty of GEOS-5 L-band radiative transfer model parameters and brightness temperatures after calibration with SMOS observations

NASA Astrophysics Data System (ADS)

De Lannoy, G. J.; Reichle, R. H.; Vrugt, J. A.

2012-12-01

Simulated L-band (1.4 GHz) brightness temperatures are very sensitive to the values of the parameters in the radiative transfer model (RTM). We assess the optimum RTM parameter values and their (posterior) uncertainty in the Goddard Earth Observing System (GEOS-5) land surface model using observations of multi-angular brightness temperature over North America from the Soil Moisture Ocean Salinity (SMOS) mission. Two different parameter estimation methods are being compared: (i) a particle swarm optimization (PSO) approach, and (ii) an MCMC simulation procedure using the differential evolution adaptive Metropolis (DREAM) algorithm. Our results demonstrate that both methods provide similar "optimal" parameter values. Yet, DREAM exhibits better convergence properties, resulting in a reduced spread of the posterior ensemble. The posterior parameter distributions derived with both methods are used for predictive uncertainty estimation of brightness temperature. This presentation will highlight our model-data synthesis framework and summarize our initial findings.

Poster error probability in the Mu-11 Sequential Ranging System

NASA Technical Reports Server (NTRS)

Coyle, C. W.

1981-01-01

An expression is derived for the posterior error probability in the Mu-2 Sequential Ranging System. An algorithm is developed which closely bounds the exact answer and can be implemented in the machine software. A computer simulation is provided to illustrate the improved level of confidence in a ranging acquisition using this figure of merit as compared to that using only the prior probabilities. In a simulation of 20,000 acquisitions with an experimentally determined threshold setting, the algorithm detected 90% of the actual errors and made false indication of errors on 0.2% of the acquisitions.

Vertebral artery ostium atherosclerotic plaque as a potential source of posterior circulation ischemic stroke: result from borgess medical center vertebral artery ostium stenting registry.

PubMed

Al-Ali, Firas; Barrow, Tom; Duan, Li; Jefferson, Anne; Louis, Susan; Luke, Kim; Major, Kevin; Smoker, Sandy; Walker, Sarah; Yacobozzi, Margaret

2011-09-01

Although atherosclerotic plaque in the carotid and coronary arteries is accepted as a cause of ischemia, vertebral artery ostium (VAO) atherosclerotic plaque is not widely recognized as a source of ischemic stroke. We seek to demonstrate its implication in some posterior circulation ischemia. This is a nonrandomized, prospective, single-center registry on consecutive patients presenting with posterior circulation ischemia who underwent VAO stenting for significant atherosclerotic stenosis. Diagnostic evaluation and imaging studies determined the likelihood of this lesion as the symptom source (highly likely, probable, or highly unlikely). Patients were divided into 4 groups in decreasing order of severity of clinical presentation (ischemic stroke, TIA then stroke, TIA, asymptomatic), which were compared with the morphological and hemodynamic characteristics of the VAO plaque. Clinical follow-up 1 year after stenting assessed symptom recurrence. One hundred fourteen patients underwent stenting of 127 lesions; 35% of the lesions were highly likely the source of symptoms, 53% were probable, and 12% were highly unlikely. Clinical presentation correlated directly with plaque irregularity and presence of clot at the VAO, as did bilateral lesions and presence of tandem lesions. Symptom recurrence at 1 year was 2%. Thirty-five percent of the lesions were highly likely the source of the symptoms. A direct relationship between some morphological/hemodynamic characteristics and the severity of clinical presentation was also found. Finally, patients had a very low rate of symptom recurrence after treatment. These 3 observations point strongly to VAO plaque as a potential source of some posterior circulation stroke.

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.

Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model

USGS Publications Warehouse

Ellefsen, Karl J.; Smith, David

2016-01-01

Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples.

MSblender: A probabilistic approach for integrating peptide identifications from multiple database search engines.

PubMed

Kwon, Taejoon; Choi, Hyungwon; Vogel, Christine; Nesvizhskii, Alexey I; Marcotte, Edward M

2011-07-01

Shotgun proteomics using mass spectrometry is a powerful method for protein identification but suffers limited sensitivity in complex samples. Integrating peptide identifications from multiple database search engines is a promising strategy to increase the number of peptide identifications and reduce the volume of unassigned tandem mass spectra. Existing methods pool statistical significance scores such as p-values or posterior probabilities of peptide-spectrum matches (PSMs) from multiple search engines after high scoring peptides have been assigned to spectra, but these methods lack reliable control of identification error rates as data are integrated from different search engines. We developed a statistically coherent method for integrative analysis, termed MSblender. MSblender converts raw search scores from search engines into a probability score for every possible PSM and properly accounts for the correlation between search scores. The method reliably estimates false discovery rates and identifies more PSMs than any single search engine at the same false discovery rate. Increased identifications increment spectral counts for most proteins and allow quantification of proteins that would not have been quantified by individual search engines. We also demonstrate that enhanced quantification contributes to improve sensitivity in differential expression analyses.

MSblender: a probabilistic approach for integrating peptide identifications from multiple database search engines

PubMed Central

Kwon, Taejoon; Choi, Hyungwon; Vogel, Christine; Nesvizhskii, Alexey I.; Marcotte, Edward M.

2011-01-01

Shotgun proteomics using mass spectrometry is a powerful method for protein identification but suffers limited sensitivity in complex samples. Integrating peptide identifications from multiple database search engines is a promising strategy to increase the number of peptide identifications and reduce the volume of unassigned tandem mass spectra. Existing methods pool statistical significance scores such as p-values or posterior probabilities of peptide-spectrum matches (PSMs) from multiple search engines after high scoring peptides have been assigned to spectra, but these methods lack reliable control of identification error rates as data are integrated from different search engines. We developed a statistically coherent method for integrative analysis, termed MSblender. MSblender converts raw search scores from search engines into a probability score for all possible PSMs and properly accounts for the correlation between search scores. The method reliably estimates false discovery rates and identifies more PSMs than any single search engine at the same false discovery rate. Increased identifications increment spectral counts for all detected proteins and allow quantification of proteins that would not have been quantified by individual search engines. We also demonstrate that enhanced quantification contributes to improve sensitivity in differential expression analyses. PMID:21488652

Inferring genealogical processes from patterns of Bronze-Age and modern DNA variation in Sardinia.

PubMed

Ghirotto, Silvia; Mona, Stefano; Benazzo, Andrea; Paparazzo, Francesco; Caramelli, David; Barbujani, Guido

2010-04-01

The ancient inhabitants of a region are often regarded as ancestral, and hence genetically related, to the modern dwellers (for instance, in studies of admixture), but so far, this assumption has not been tested empirically using ancient DNA data. We studied mitochondrial DNA (mtDNA) variation in Sardinia, across a time span of 2,500 years, comparing 23 Bronze-Age (nuragic) mtDNA sequences with those of 254 modern individuals from two regions, Ogliastra (a likely genetic isolate) and Gallura, and considering the possible impact of gene flow from mainland Italy. To understand the genealogical relationships between past and present populations, we developed seven explicit demographic models; we tested whether these models can account for the levels and patterns of genetic diversity in the data and which one does it best. Extensive simulation based on a serial coalescent algorithm allowed us to compare the posterior probability of each model and estimate the relevant evolutionary (mutation and migration rates) and demographic (effective population sizes, times since population splits) parameters, by approximate Bayesian computations. We then validated the analyses by investigating how well parameters estimated from the simulated data can reproduce the observed data set. We show that a direct genealogical continuity between Bronze-Age Sardinians and the current people of Ogliastra, but not Gallura, has a much higher probability than any alternative scenarios and that genetic diversity in Gallura evolved largely independently, owing in part to gene flow from the mainland.

Identifying Causal Variants at Loci with Multiple Signals of Association

PubMed Central

Hormozdiari, Farhad; Kostem, Emrah; Kang, Eun Yong; Pasaniuc, Bogdan; Eskin, Eleazar

2014-01-01

Although genome-wide association studies have successfully identified thousands of risk loci for complex traits, only a handful of the biologically causal variants, responsible for association at these loci, have been successfully identified. Current statistical methods for identifying causal variants at risk loci either use the strength of the association signal in an iterative conditioning framework or estimate probabilities for variants to be causal. A main drawback of existing methods is that they rely on the simplifying assumption of a single causal variant at each risk locus, which is typically invalid at many risk loci. In this work, we propose a new statistical framework that allows for the possibility of an arbitrary number of causal variants when estimating the posterior probability of a variant being causal. A direct benefit of our approach is that we predict a set of variants for each locus that under reasonable assumptions will contain all of the true causal variants with a high confidence level (e.g., 95%) even when the locus contains multiple causal variants. We use simulations to show that our approach provides 20–50% improvement in our ability to identify the causal variants compared to the existing methods at loci harboring multiple causal variants. We validate our approach using empirical data from an expression QTL study of CHI3L2 to identify new causal variants that affect gene expression at this locus. CAVIAR is publicly available online at http://genetics.cs.ucla.edu/caviar/. PMID:25104515

Identifying causal variants at loci with multiple signals of association.

PubMed

Hormozdiari, Farhad; Kostem, Emrah; Kang, Eun Yong; Pasaniuc, Bogdan; Eskin, Eleazar

2014-10-01

Although genome-wide association studies have successfully identified thousands of risk loci for complex traits, only a handful of the biologically causal variants, responsible for association at these loci, have been successfully identified. Current statistical methods for identifying causal variants at risk loci either use the strength of the association signal in an iterative conditioning framework or estimate probabilities for variants to be causal. A main drawback of existing methods is that they rely on the simplifying assumption of a single causal variant at each risk locus, which is typically invalid at many risk loci. In this work, we propose a new statistical framework that allows for the possibility of an arbitrary number of causal variants when estimating the posterior probability of a variant being causal. A direct benefit of our approach is that we predict a set of variants for each locus that under reasonable assumptions will contain all of the true causal variants with a high confidence level (e.g., 95%) even when the locus contains multiple causal variants. We use simulations to show that our approach provides 20-50% improvement in our ability to identify the causal variants compared to the existing methods at loci harboring multiple causal variants. We validate our approach using empirical data from an expression QTL study of CHI3L2 to identify new causal variants that affect gene expression at this locus. CAVIAR is publicly available online at http://genetics.cs.ucla.edu/caviar/. Copyright © 2014 by the Genetics Society of America.

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.

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

Deep convolutional networks for automated detection of posterior-element fractures on spine CT

NASA Astrophysics Data System (ADS)

Roth, Holger R.; Wang, Yinong; Yao, Jianhua; Lu, Le; Burns, Joseph E.; Summers, Ronald M.

2016-03-01

Injuries of the spine, and its posterior elements in particular, are a common occurrence in trauma patients, with potentially devastating consequences. Computer-aided detection (CADe) could assist in the detection and classification of spine fractures. Furthermore, CAD could help assess the stability and chronicity of fractures, as well as facilitate research into optimization of treatment paradigms. In this work, we apply deep convolutional networks (ConvNets) for the automated detection of posterior element fractures of the spine. First, the vertebra bodies of the spine with its posterior elements are segmented in spine CT using multi-atlas label fusion. Then, edge maps of the posterior elements are computed. These edge maps serve as candidate regions for predicting a set of probabilities for fractures along the image edges using ConvNets in a 2.5D fashion (three orthogonal patches in axial, coronal and sagittal planes). We explore three different methods for training the ConvNet using 2.5D patches along the edge maps of `positive', i.e. fractured posterior-elements and `negative', i.e. non-fractured elements. An experienced radiologist retrospectively marked the location of 55 displaced posterior-element fractures in 18 trauma patients. We randomly split the data into training and testing cases. In testing, we achieve an area-under-the-curve of 0.857. This corresponds to 71% or 81% sensitivities at 5 or 10 false-positives per patient, respectively. Analysis of our set of trauma patients demonstrates the feasibility of detecting posterior-element fractures in spine CT images using computer vision techniques such as deep convolutional networks.

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.

Asymmetry and anisotropy of surface effects of mining induced seismic events

NASA Astrophysics Data System (ADS)

Lasocki, Stanislaw; Orlecka-Sikora, Beata

2013-04-01

Long-lasting exploitation in underground mines and the complex system of goaf - unmined areas - excavation may cause the occurrence of seismic events, whose influence in the excavation and on the free surface is untypical. We present here the analysis of surface effects of a series of ten seismic events that occurred in one panel of a copper-ore mine. The analysis bases on a comparison of the observed ground motion due to the studied events with the estimates from Ground Motion Prediction Equations for peak horizontal (PHA) and vertical (PVA) acceleration of motion in the frequency band up to 10Hz, local for that mining area. The GMPE-s take into account also relative site amplification factors. The posterior probabilities that the observed PHA-s are not attained according to GMPE-s are calculated and mapped. Although all ten considered events had comparable magnitudes and were located close one to another their ground effects were very diverse. The analysis of anomalies of surface effects shows strong asymmetry of ground motion propagation and anisotropy of surface effects of the studied tremors. Based on similarities of surface effects anomalies, expressed in terms of the posterior probabilities, the events are split into distinct groups. In case of four events the actual PHA-s on most of the stations are greater than the respective estimated medians, especially in the sector N-SE. The PHA values of the second group are at short epicentral distances mostly on the same level as the predicted estimates from GMPE. The observed effects, however, become abnormally strong with the increase of epicentral distances in the sector NE-SE. The effects of events from next groups abnormally increase either in NE or NE - SE direction and the maximum anomalies appear about 3km from the epicenter. The extreme discrepancies can be attributed neither to local site effects nor to preferential propagation conditions along some wavepaths. Therefore it is concluded that the observed anomalies of ground motion result from sources properties. Integrated analysis of source mechanism of these events indicates that their untypical and diverse surface effects result from complexity of their sources expressed by tensile source mechanisms, finite sources, directivity of ruptures and nearly horizontal rupture planes. The above features seem to be implied by a superposition of coseismic alterations of stress field and stress changes due to mining. This work has been done in the framework of the research project No. NN525393539, financed by the National Science Centre of Poland for the period 2010-2013.

Ensemble-type numerical uncertainty information from single model integrations

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

Rauser, Florian, E-mail: florian.rauser@mpimet.mpg.de; Marotzke, Jochem; Korn, Peter

2015-07-01

We suggest an algorithm that quantifies the discretization error of time-dependent physical quantities of interest (goals) for numerical models of geophysical fluid dynamics. The goal discretization error is estimated using a sum of weighted local discretization errors. The key feature of our algorithm is that these local discretization errors are interpreted as realizations of a random process. The random process is determined by the model and the flow state. From a class of local error random processes we select a suitable specific random process by integrating the model over a short time interval at different resolutions. The weights of themore » influences of the local discretization errors on the goal are modeled as goal sensitivities, which are calculated via automatic differentiation. The integration of the weighted realizations of local error random processes yields a posterior ensemble of goal approximations from a single run of the numerical model. From the posterior ensemble we derive the uncertainty information of the goal discretization error. This algorithm bypasses the requirement of detailed knowledge about the models discretization to generate numerical error estimates. The algorithm is evaluated for the spherical shallow-water equations. For two standard test cases we successfully estimate the error of regional potential energy, track its evolution, and compare it to standard ensemble techniques. The posterior ensemble shares linear-error-growth properties with ensembles of multiple model integrations when comparably perturbed. The posterior ensemble numerical error estimates are of comparable size as those of a stochastic physics ensemble.« less

A Comparison of Item Selection Techniques for Testlets

ERIC Educational Resources Information Center

Murphy, Daniel L.; Dodd, Barbara G.; Vaughn, Brandon K.

2010-01-01

This study examined the performance of the maximum Fisher's information, the maximum posterior weighted information, and the minimum expected posterior variance methods for selecting items in a computerized adaptive testing system when the items were grouped in testlets. A simulation study compared the efficiency of ability estimation among the…

Damage evaluation by a guided wave-hidden Markov model based method

NASA Astrophysics Data System (ADS)

Mei, Hanfei; Yuan, Shenfang; Qiu, Lei; Zhang, Jinjin

2016-02-01

Guided wave based structural health monitoring has shown great potential in aerospace applications. However, one of the key challenges of practical engineering applications is the accurate interpretation of the guided wave signals under time-varying environmental and operational conditions. This paper presents a guided wave-hidden Markov model based method to improve the damage evaluation reliability of real aircraft structures under time-varying conditions. In the proposed approach, an HMM based unweighted moving average trend estimation method, which can capture the trend of damage propagation from the posterior probability obtained by HMM modeling is used to achieve a probabilistic evaluation of the structural damage. To validate the developed method, experiments are performed on a hole-edge crack specimen under fatigue loading condition and a real aircraft wing spar under changing structural boundary conditions. Experimental results show the advantage of the proposed method.

Ensemble-Based Parameter Estimation in a Coupled GCM Using the Adaptive Spatial Average Method

DOE PAGES

Liu, Y.; Liu, Z.; Zhang, S.; ...

2014-05-29

Ensemble-based parameter estimation for a climate model is emerging as an important topic in climate research. And for a complex system such as a coupled ocean–atmosphere general circulation model, the sensitivity and response of a model variable to a model parameter could vary spatially and temporally. An adaptive spatial average (ASA) algorithm is proposed to increase the efficiency of parameter estimation. Refined from a previous spatial average method, the ASA uses the ensemble spread as the criterion for selecting “good” values from the spatially varying posterior estimated parameter values; these good values are then averaged to give the final globalmore » uniform posterior parameter. In comparison with existing methods, the ASA parameter estimation has a superior performance: faster convergence and enhanced signal-to-noise ratio.« less

Statistical properties of alternative national forest inventory area estimators

Treesearch

Francis Roesch; John Coulston; Andrew D. Hill

2012-01-01

The statistical properties of potential estimators of forest area for the USDA Forest Service's Forest Inventory and Analysis (FIA) program are presented and discussed. The current FIA area estimator is compared and contrasted with a weighted mean estimator and an estimator based on the Polya posterior, in the presence of nonresponse. Estimator optimality is...

Estimating regional CO2 and CH4 fluxes using GOSAT XCO2 and XCH4 observations

NASA Astrophysics Data System (ADS)

Fraser, A. C.; Palmer, P. I.; Feng, L.; Parker, R.; Boesch, H.; Cogan, A. J.

2012-12-01

We infer regional monthly surface flux estimates for CO2 and CH4, June 2009-December 2010, from proxy dry-air column-averaged mole fractions of CO2 and CH4 from the Greenhouse gases Observing SATellite (GOSAT) using an ensemble Kalman Filter combined with the GEOS-Chem chemistry transport model. We compare these flux estimates with estimates inferred from in situ surface mole fraction measurements and from combining in situ and GOSAT measurements in order to quantify the added value of GOSAT data above the conventional surface measurement network. We find that the error reduction, a measure of how much the posterior fluxes are being informed by the assimilated data, at least doubles when GOSAT measurements are used versus the surface only inversions, with the exception of regions that are well covered by the surface network at the spatial and temporal resolution of our flux estimation calculation. We have incorporated a new online bias correction scheme to account for GOSAT biases. We report global and regional flux estimates inferred from GOSAT and/or in situ measurements. While the global posterior fluxes from GOSAT and in situ measurements agree, we find significant differences in the regional fluxes, particularly over the tropics. We evaluate the posterior fluxes by comparing them against independent surface mole fraction, column, and aircraft measurements using the GEOS-Chem model as an intermediary.

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.

The effect of business improvement districts on the incidence of violent crimes

PubMed Central

Golinelli, Daniela; Stokes, Robert J; Bluthenthal, Ricky

2010-01-01

Objective To examine whether business improvement districts (BID) contributed to greater than expected declines in the incidence of violent crimes in affected neighbourhoods. Method A Bayesian hierarchical model was used to assess the changes in the incidence of violent crimes between 1994 and 2005 and the implementation of 30 BID in Los Angeles neighbourhoods. Results The implementation of BID was associated with a 12% reduction in the incidence of robbery (95% posterior probability interval −2 to 24) and an 8% reduction in the total incidence of violent crimes (95% posterior probability interval −5 to 21). The strength of the effect of BID on robbery crimes varied by location. Conclusion These findings indicate that the implementation of BID can reduce the incidence of violent crimes likely to result in injury to individuals. The findings also indicate that the establishment of a BID by itself is not a panacea, and highlight the importance of targeting BID efforts to crime prevention interventions that reduce violence exposure associated with criminal behaviours. PMID:20587814

The effect of business improvement districts on the incidence of violent crimes.

PubMed

MacDonald, John; Golinelli, Daniela; Stokes, Robert J; Bluthenthal, Ricky

2010-10-01

To examine whether business improvement districts (BID) contributed to greater than expected declines in the incidence of violent crimes in affected neighbourhoods. A Bayesian hierarchical model was used to assess the changes in the incidence of violent crimes between 1994 and 2005 and the implementation of 30 BID in Los Angeles neighbourhoods. The implementation of BID was associated with a 12% reduction in the incidence of robbery (95% posterior probability interval -2 to 24) and an 8% reduction in the total incidence of violent crimes (95% posterior probability interval -5 to 21). The strength of the effect of BID on robbery crimes varied by location. These findings indicate that the implementation of BID can reduce the incidence of violent crimes likely to result in injury to individuals. The findings also indicate that the establishment of a BID by itself is not a panacea, and highlight the importance of targeting BID efforts to crime prevention interventions that reduce violence exposure associated with criminal behaviours.

Divergence time, historical biogeography and evolutionary rate estimation of the order Bangiales (Rhodophyta) inferred from multilocus data

NASA Astrophysics Data System (ADS)

Xu, Kuipeng; Tang, Xianghai; Wang, Lu; Yu, Xinzi; Sun, Peipei; Mao, Yunxiang

2017-08-01

Bangiales is the only order of the Bangiophyceae and has been suggested to be monophyletic. This order contains approximately 190 species and is distributed worldwide. Previous molecular studies have produced robust phylogenies among the red algae, but the divergence times, historical biogeography and evolutionary rates of Bangiales have rarely been studied. Phylogenetic relationships within the Bangiales were examined using the concatenated gene sets from all available organellar genomes. This analysis has revealed the topology ((( Bangia, Porphyra ) Pyropia ) Wildemania ). Molecular dating indicates that Bangiales diversified approximately 246.40 million years ago (95% highest posterior density (HPD)= 194.78u2013318.24 Ma, posterior probability (PP)=0.99) in the Late Permian and Early Triassic, and that the ancestral species most likely originated from eastern Gondwanaland (currently New Zealand and Australia) and subsequently began to spread and evolve worldwide. Based on pairwise comparisons, we found a slower rate of nucleotide substitutions and lower rates of diversification in Bangiales relative to Florideophyceae. Compared with Viridiplantae (green algae and land plants), the evolutionary rates of Bangiales and other Rhodophyte groups were found to be dramatically faster, by more than 3-fold for plastid genome (ptDNA) and 15-fold for mitochondrial genome (mtDNA). In addition, an average 2.5-fold lower dN/dS was found for the algae than for the land plants, which indicates purifying selection of the algae.

Probabilistic parameter estimation of activated sludge processes using Markov Chain Monte Carlo.

PubMed

Sharifi, Soroosh; Murthy, Sudhir; Takács, Imre; Massoudieh, Arash

2014-03-01

One of the most important challenges in making activated sludge models (ASMs) applicable to design problems is identifying the values of its many stoichiometric and kinetic parameters. When wastewater characteristics data from full-scale biological treatment systems are used for parameter estimation, several sources of uncertainty, including uncertainty in measured data, external forcing (e.g. influent characteristics), and model structural errors influence the value of the estimated parameters. This paper presents a Bayesian hierarchical modeling framework for the probabilistic estimation of activated sludge process parameters. The method provides the joint probability density functions (JPDFs) of stoichiometric and kinetic parameters by updating prior information regarding the parameters obtained from expert knowledge and literature. The method also provides the posterior correlations between the parameters, as well as a measure of sensitivity of the different constituents with respect to the parameters. This information can be used to design experiments to provide higher information content regarding certain parameters. The method is illustrated using the ASM1 model to describe synthetically generated data from a hypothetical biological treatment system. The results indicate that data from full-scale systems can narrow down the ranges of some parameters substantially whereas the amount of information they provide regarding other parameters is small, due to either large correlations between some of the parameters or a lack of sensitivity with respect to the parameters. Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

Estimation of distances to stars with stellar parameters from LAMOST

DOE PAGES

Carlin, Jeffrey L.; Liu, Chao; Newberg, Heidi Jo; ...

2015-06-05

Here, we present a method to estimate distances to stars with spectroscopically derived stellar parameters. The technique is a Bayesian approach with likelihood estimated via comparison of measured parameters to a grid of stellar isochrones, and returns a posterior probability density function for each star's absolute magnitude. We tailor this technique specifically to data from the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST) survey. Because LAMOST obtains roughly 3000 stellar spectra simultaneously within each ~5-degree diameter "plate" that is observed, we can use the stellar parameters of the observed stars to account for the stellar luminosity function and targetmore » selection effects. This removes biasing assumptions about the underlying populations, both due to predictions of the luminosity function from stellar evolution modeling, and from Galactic models of stellar populations along each line of sight. Using calibration data of stars with known distances and stellar parameters, we show that our method recovers distances for most stars within ~20%, but with some systematic overestimation of distances to halo giants. We apply our code to the LAMOST database, and show that the current precision of LAMOST stellar parameters permits measurements of distances with ~40% error bars. This precision should improve as the LAMOST data pipelines continue to be refined.« less

Estimation of distances to stars with stellar parameters from LAMOST

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

Carlin, Jeffrey L.; Liu, Chao; Newberg, Heidi Jo

Here, we present a method to estimate distances to stars with spectroscopically derived stellar parameters. The technique is a Bayesian approach with likelihood estimated via comparison of measured parameters to a grid of stellar isochrones, and returns a posterior probability density function for each star's absolute magnitude. We tailor this technique specifically to data from the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST) survey. Because LAMOST obtains roughly 3000 stellar spectra simultaneously within each ~5-degree diameter "plate" that is observed, we can use the stellar parameters of the observed stars to account for the stellar luminosity function and targetmore » selection effects. This removes biasing assumptions about the underlying populations, both due to predictions of the luminosity function from stellar evolution modeling, and from Galactic models of stellar populations along each line of sight. Using calibration data of stars with known distances and stellar parameters, we show that our method recovers distances for most stars within ~20%, but with some systematic overestimation of distances to halo giants. We apply our code to the LAMOST database, and show that the current precision of LAMOST stellar parameters permits measurements of distances with ~40% error bars. This precision should improve as the LAMOST data pipelines continue to be refined.« less

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.

Measurement of Posterior Corneal Astigmatism by the IOLMaster 700.

PubMed

LaHood, Benjamin R; Goggin, Michael

2018-05-01

To provide the first description of posterior corneal astigmatism as measured by the IOLMaster 700 (Carl Zeiss Meditec, Jena, Germany) and assess how its characteristics compare to previous measurements from other devices. A total of 1,098 routine IOLMaster 700 biometric measurements were analyzed to provide magnitudes and orientation of steep and flat axes of anterior and posterior corneal astigmatism. Subgroup analysis was conducted to assess correlation of posterior corneal astigmatism characteristics to anterior corneal astigmatism and describe the distribution of posterior corneal astigmatism with age. Mean posterior corneal astigmatism was 0.24 ± 0.15 diopters (D). The steep axis of posterior corneal astigmatism was vertically oriented in 73.32% of measurements. Correlation between the magnitude of anterior and posterior corneal astigmatism was greatest when the steep axis of the anterior corneal astigmatism was oriented vertically (r = 0.68, P < .0001). Vertical orientation of the steep axis of anterior corneal astigmatism became less common as age increased, whereas for posterior corneal astigmatism it remained by far the most common orientation. This first description of posterior corneal astigmatism measurement by the IOLMaster 700 found the average magnitude of posterior corneal astigmatism and proportion of vertical orientation of steep axis was lower than previous estimates. The IOLMaster 700 appears capable of providing enhanced biometric measurement for individualized surgical planning. [J Refract Surg. 2018;34(5):331-336.]. Copyright 2018, SLACK Incorporated.

Interhemispheric Effective and Functional Cortical Connectivity Signatures of Spina Bifida Are Consistent with Callosal Anomaly

PubMed Central

Malekpour, Sheida; Li, Zhimin; Cheung, Bing Leung Patrick; Castillo, Eduardo M.; Papanicolaou, Andrew C.; Kramer, Larry A.; Fletcher, Jack M.

2012-01-01

Abstract The impact of the posterior callosal anomalies associated with spina bifida on interhemispheric cortical connectivity is studied using a method for estimating cortical multivariable autoregressive models from scalp magnetoencephalography data. Interhemispheric effective and functional connectivity, measured using conditional Granger causality and coherence, respectively, is determined for the anterior and posterior cortical regions in a population of five spina bifida and five control subjects during a resting eyes-closed state. The estimated connectivity is shown to be consistent over the randomly selected subsets of the data for each subject. The posterior interhemispheric effective and functional connectivity and cortical power are significantly lower in the spina bifida group, a result that is consistent with posterior callosal anomalies. The anterior interhemispheric effective and functional connectivity are elevated in the spina bifida group, a result that may reflect compensatory mechanisms. In contrast, the intrahemispheric effective connectivity is comparable in the two groups. The differences between the spina bifida and control groups are most significant in the θ and α bands. PMID:22571349

Factors influencing reporting and harvest probabilities in North American geese

USGS Publications Warehouse

Zimmerman, G.S.; Moser, T.J.; Kendall, W.L.; Doherty, P.F.; White, Gary C.; Caswell, D.F.

2009-01-01

We assessed variation in reporting probabilities of standard bands among species, populations, harvest locations, and size classes of North American geese to enable estimation of unbiased harvest probabilities. We included reward (US10,20,30,50, or100) and control (0) banded geese from 16 recognized goose populations of 4 species: Canada (Branta canadensis), cackling (B. hutchinsii), Ross's (Chen rossii), and snow geese (C. caerulescens). We incorporated spatially explicit direct recoveries and live recaptures into a multinomial model to estimate reporting, harvest, and band-retention probabilities. We compared various models for estimating harvest probabilities at country (United States vs. Canada), flyway (5 administrative regions), and harvest area (i.e., flyways divided into northern and southern sections) scales. Mean reporting probability of standard bands was 0.73 (95 CI 0.690.77). Point estimates of reporting probabilities for goose populations or spatial units varied from 0.52 to 0.93, but confidence intervals for individual estimates overlapped and model selection indicated that models with species, population, or spatial effects were less parsimonious than those without these effects. Our estimates were similar to recently reported estimates for mallards (Anas platyrhynchos). We provide current harvest probability estimates for these populations using our direct measures of reporting probability, improving the accuracy of previous estimates obtained from recovery probabilities alone. Goose managers and researchers throughout North America can use our reporting probabilities to correct recovery probabilities estimated from standard banding operations for deriving spatially explicit harvest probabilities.

Progression of Brain Network Alterations in Cerebral Amyloid Angiopathy.

PubMed

Reijmer, Yael D; Fotiadis, Panagiotis; Riley, Grace A; Xiong, Li; Charidimou, Andreas; Boulouis, Gregoire; Ayres, Alison M; Schwab, Kristin; Rosand, Jonathan; Gurol, M Edip; Viswanathan, Anand; Greenberg, Steven M

2016-10-01

We recently showed that cerebral amyloid angiopathy (CAA) is associated with functionally relevant brain network impairments, in particular affecting posterior white matter connections. Here we examined how these brain network impairments progress over time. Thirty-three patients with probable CAA underwent multimodal brain magnetic resonance imaging at 2 time points (mean follow-up time: 1.3±0.4 years). Brain networks of the hemisphere free of intracerebral hemorrhages were reconstructed using fiber tractography and graph theory. The global efficiency of the network and mean fractional anisotropies of posterior-posterior, frontal-frontal, and posterior-frontal network connections were calculated. Patients with moderate versus severe CAA were defined based on microbleed count, dichotomized at the median (median=35). Global efficiency of the intracerebral hemorrhage-free hemispheric network declined from baseline to follow-up (-0.008±0.003; P=0.029). The decline in global efficiency was most pronounced for patients with severe CAA (group×time interaction P=0.03). The decline in global network efficiency was associated with worse executive functioning (β=0.46; P=0.03). Examination of subgroups of network connections revealed a decline in fractional anisotropies of posterior-posterior connections at both levels of CAA severity (-0.006±0.002; P=0.017; group×time interaction P=0.16). The fractional anisotropies of posterior-frontal and frontal-frontal connections declined in patients with severe but not moderate CAA (group×time interaction P=0.007 and P=0.005). Associations were independent of change in white matter hyperintensity volume. Brain network impairment in patients with CAA worsens measurably over just 1.3-year follow-up and seem to progress from posterior to frontal connections with increasing disease severity. © 2016 American Heart Association, Inc.

Full Bayes Poisson gamma, Poisson lognormal, and zero inflated random effects models: Comparing the precision of crash frequency estimates.

PubMed

Aguero-Valverde, Jonathan

2013-01-01

In recent years, complex statistical modeling approaches have being proposed to handle the unobserved heterogeneity and the excess of zeros frequently found in crash data, including random effects and zero inflated models. This research compares random effects, zero inflated, and zero inflated random effects models using a full Bayes hierarchical approach. The models are compared not just in terms of goodness-of-fit measures but also in terms of precision of posterior crash frequency estimates since the precision of these estimates is vital for ranking of sites for engineering improvement. Fixed-over-time random effects models are also compared to independent-over-time random effects models. For the crash dataset being analyzed, it was found that once the random effects are included in the zero inflated models, the probability of being in the zero state is drastically reduced, and the zero inflated models degenerate to their non zero inflated counterparts. Also by fixing the random effects over time the fit of the models and the precision of the crash frequency estimates are significantly increased. It was found that the rankings of the fixed-over-time random effects models are very consistent among them. In addition, the results show that by fixing the random effects over time, the standard errors of the crash frequency estimates are significantly reduced for the majority of the segments on the top of the ranking. Copyright © 2012 Elsevier Ltd. All rights reserved.

Differential alpha coherence hemispheric patterns in men and women during pleasant and unpleasant musical emotions.

PubMed

Flores-Gutiérrez, Enrique O; Díaz, José-Luis; Barrios, Fernando A; Guevara, Miguel Angel; Del Río-Portilla, Yolanda; Corsi-Cabrera, María; Del Flores-Gutiérrez, Enrique O

2009-01-01

Potential sex differences in EEG coherent activity during pleasant and unpleasant musical emotions were investigated. Musical excerpts by Mahler, Bach, and Prodromidès were played to seven men and seven women and their subjective emotions were evaluated in relation to alpha band intracortical coherence. Different brain links in specific frequencies were associated to pleasant and unpleasant emotions. Pleasant emotions (Mahler, Bach) increased upper alpha couplings linking left anterior and posterior regions. Unpleasant emotions (Prodromidès) were sustained by posterior midline coherence exclusively in the right hemisphere in men and bilateral in women. Combined music induced bilateral oscillations among posterior sensory and predominantly left association areas in women. Consistent with their greater positive attributions to music, the coherent network is larger in women, both for musical emotion and for unspecific musical effects. Musical emotion entails specific coupling among cortical regions and involves coherent upper alpha activity between posterior association areas and frontal regions probably mediating emotional and perceptual integration. Linked regions by combined music suggest more working memory contribution in women and attention in men.

VizieR Online Data Catalog: Wide binaries in Tycho-Gaia: search method (Andrews+, 2017)

NASA Astrophysics Data System (ADS)

Andrews, J. J.; Chaname, J.; Agueros, M. A.

2017-11-01

Our catalogue of wide binaries identified in the Tycho-Gaia Astrometric Solution catalogue. The Gaia source IDs, Tycho IDs, astrometry, posterior probabilities for both the log-flat prior and power-law prior models, and angular separation are presented. (1 data file).

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.

Inverse Problems in Complex Models and Applications to Earth Sciences

NASA Astrophysics Data System (ADS)

Bosch, M. E.

2015-12-01

The inference of the subsurface earth structure and properties requires the integration of different types of data, information and knowledge, by combined processes of analysis and synthesis. To support the process of integrating information, the regular concept of data inversion is evolving to expand its application to models with multiple inner components (properties, scales, structural parameters) that explain multiple data (geophysical survey data, well-logs, core data). The probabilistic inference methods provide the natural framework for the formulation of these problems, considering a posterior probability density function (PDF) that combines the information from a prior information PDF and the new sets of observations. To formulate the posterior PDF in the context of multiple datasets, the data likelihood functions are factorized assuming independence of uncertainties for data originating across different surveys. A realistic description of the earth medium requires modeling several properties and structural parameters, which relate to each other according to dependency and independency notions. Thus, conditional probabilities across model components also factorize. A common setting proceeds by structuring the model parameter space in hierarchical layers. A primary layer (e.g. lithology) conditions a secondary layer (e.g. physical medium properties), which conditions a third layer (e.g. geophysical data). In general, less structured relations within model components and data emerge from the analysis of other inverse problems. They can be described with flexibility via direct acyclic graphs, which are graphs that map dependency relations between the model components. Examples of inverse problems in complex models can be shown at various scales. At local scale, for example, the distribution of gas saturation is inferred from pre-stack seismic data and a calibrated rock-physics model. At regional scale, joint inversion of gravity and magnetic data is applied for the estimation of lithological structure of the crust, with the lithotype body regions conditioning the mass density and magnetic susceptibility fields. At planetary scale, the Earth mantle temperature and element composition is inferred from seismic travel-time and geodetic data.

The effect of deacetylated gellan gum on aesculin distribution in the posterior segment of the eye after topical administration.

PubMed

Chen, Qiuhong; Zheng, Yu; Li, Ye; Zeng, Ying; Kuang, Jianchao; Hou, Shixiang; Li, Xiaohui

2012-05-01

The aim of the present work was to evaluate the effect of deacetylated gellan gum on delivering hydrophilic drug to the posterior segment of the eye. An aesculin-containing in situ gel based on deacetylated gellan gum (AG) was prepared and characterized. In vitro corneal permeation across isolated rabbit cornea of aesculin between AG and aesculin solution (AS) was compared. The results showed that deacetylated gellan gum promotes corneal penetration of aesculin. Pharmacokinetics and ocular tissue distribution of aesculin after topical administration in rabbit eye showed that AG greatly improved aesculin accumulation in posterior segmentsrelative to AS, which was probably attributed to conjunctivital/sclera pathway. The area-under-the-curve (AUC) for AG in aqueous humor, choroid-retina, sclera and iris-ciliary body were significantly larger than those of AS. AG can be used as a potential carrier for broading the application of aesculin.

CKS knee prosthesis: biomechanics and clinical results in 42 cases.

PubMed

Martucci, E; Verni, E; Del Prete, G; Stulberg, S D

1996-01-01

From 1991 to 1993 a total of 42 CKS prostheses were implanted for the following reasons: osteoarthrosis (34 cases), rheumatoid arthritis (7 cases) tibial necrosis (1 case). At follow-up obtained after 17 to 41 months the results were: excellent or good: 41; the only poor result was probably related to excessive tension of the posterior cruciate ligament. 94% of the patients reported complete regression of pain, 85% was capable of going up and down stairs without support. Mean joint flexion was 105 degrees. Radiologically the anatomical axis of the knee had a mean valgus of anatomical axis of the knee had a mean valgus of 6 degrees. The prosthetic components were always cemented. The posterior cruciate ligament was removed in 7 knees, so that the prosthesis with "posterior stability" was used. The patella was never prosthetized. One patient complained of peri-patellar pain two months after surgery which then regressed completely.

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

Estimation of post-test probabilities by residents: Bayesian reasoning versus heuristics?

PubMed

Hall, Stacey; Phang, Sen Han; Schaefer, Jeffrey P; Ghali, William; Wright, Bruce; McLaughlin, Kevin

2014-08-01

Although the process of diagnosing invariably begins with a heuristic, we encourage our learners to support their diagnoses by analytical cognitive processes, such as Bayesian reasoning, in an attempt to mitigate the effects of heuristics on diagnosing. There are, however, limited data on the use ± impact of Bayesian reasoning on the accuracy of disease probability estimates. In this study our objective was to explore whether Internal Medicine residents use a Bayesian process to estimate disease probabilities by comparing their disease probability estimates to literature-derived Bayesian post-test probabilities. We gave 35 Internal Medicine residents four clinical vignettes in the form of a referral letter and asked them to estimate the post-test probability of the target condition in each case. We then compared these to literature-derived probabilities. For each vignette the estimated probability was significantly different from the literature-derived probability. For the two cases with low literature-derived probability our participants significantly overestimated the probability of these target conditions being the correct diagnosis, whereas for the two cases with high literature-derived probability the estimated probability was significantly lower than the calculated value. Our results suggest that residents generate inaccurate post-test probability estimates. Possible explanations for this include ineffective application of Bayesian reasoning, attribute substitution whereby a complex cognitive task is replaced by an easier one (e.g., a heuristic), or systematic rater bias, such as central tendency bias. Further studies are needed to identify the reasons for inaccuracy of disease probability estimates and to explore ways of improving accuracy.

Star Cluster Properties in Two LEGUS Galaxies Computed with Stochastic Stellar Population Synthesis Models

NASA Astrophysics Data System (ADS)

Krumholz, Mark R.; Adamo, Angela; Fumagalli, Michele; Wofford, Aida; Calzetti, Daniela; Lee, Janice C.; Whitmore, Bradley C.; Bright, Stacey N.; Grasha, Kathryn; Gouliermis, Dimitrios A.; Kim, Hwihyun; Nair, Preethi; Ryon, Jenna E.; Smith, Linda J.; Thilker, David; Ubeda, Leonardo; Zackrisson, Erik

2015-10-01

We investigate a novel Bayesian analysis method, based on the Stochastically Lighting Up Galaxies (slug) code, to derive the masses, ages, and extinctions of star clusters from integrated light photometry. Unlike many analysis methods, slug correctly accounts for incomplete initial mass function (IMF) sampling, and returns full posterior probability distributions rather than simply probability maxima. We apply our technique to 621 visually confirmed clusters in two nearby galaxies, NGC 628 and NGC 7793, that are part of the Legacy Extragalactic UV Survey (LEGUS). LEGUS provides Hubble Space Telescope photometry in the NUV, U, B, V, and I bands. We analyze the sensitivity of the derived cluster properties to choices of prior probability distribution, evolutionary tracks, IMF, metallicity, treatment of nebular emission, and extinction curve. We find that slug's results for individual clusters are insensitive to most of these choices, but that the posterior probability distributions we derive are often quite broad, and sometimes multi-peaked and quite sensitive to the choice of priors. In contrast, the properties of the cluster population as a whole are relatively robust against all of these choices. We also compare our results from slug to those derived with a conventional non-stochastic fitting code, Yggdrasil. We show that slug's stochastic models are generally a better fit to the observations than the deterministic ones used by Yggdrasil. However, the overall properties of the cluster populations recovered by both codes are qualitatively similar.

Probability modeling of the number of positive cores in a prostate cancer biopsy session, with applications.

PubMed

Serfling, Robert; Ogola, Gerald

2016-02-10

Among men, prostate cancer (CaP) is the most common newly diagnosed cancer and the second leading cause of death from cancer. A major issue of very large scale is avoiding both over-treatment and under-treatment of CaP cases. The central challenge is deciding clinical significance or insignificance when the CaP biopsy results are positive but only marginally so. A related concern is deciding how to increase the number of biopsy cores for larger prostates. As a foundation for improved choice of number of cores and improved interpretation of biopsy results, we develop a probability model for the number of positive cores found in a biopsy, given the total number of cores, the volumes of the tumor nodules, and - very importantly - the prostate volume. Also, three applications are carried out: guidelines for the number of cores as a function of prostate volume, decision rules for insignificant versus significant CaP using number of positive cores, and, using prior distributions on total tumor size, Bayesian posterior probabilities for insignificant CaP and posterior median CaP. The model-based results have generality of application, take prostate volume into account, and provide attractive tradeoffs of specificity versus sensitivity. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Robust Bayesian Experimental Design for Conceptual Model Discrimination

NASA Astrophysics Data System (ADS)

Pham, H. V.; Tsai, F. T. C.

2015-12-01

A robust Bayesian optimal experimental design under uncertainty is presented to provide firm information for model discrimination, given the least number of pumping wells and observation wells. Firm information is the maximum information of a system can be guaranteed from an experimental design. The design is based on the Box-Hill expected entropy decrease (EED) before and after the experiment design and the Bayesian model averaging (BMA) framework. A max-min programming is introduced to choose the robust design that maximizes the minimal Box-Hill EED subject to that the highest expected posterior model probability satisfies a desired probability threshold. The EED is calculated by the Gauss-Hermite quadrature. The BMA method is used to predict future observations and to quantify future observation uncertainty arising from conceptual and parametric uncertainties in calculating EED. Monte Carlo approach is adopted to quantify the uncertainty in the posterior model probabilities. The optimal experimental design is tested by a synthetic 5-layer anisotropic confined aquifer. Nine conceptual groundwater models are constructed due to uncertain geological architecture and boundary condition. High-performance computing is used to enumerate all possible design solutions in order to identify the most plausible groundwater model. Results highlight the impacts of scedasticity in future observation data as well as uncertainty sources on potential pumping and observation locations.

Neural substrates of the impaired effort expenditure decision making in schizophrenia.

PubMed

Huang, Jia; Yang, Xin-Hua; Lan, Yong; Zhu, Cui-Ying; Liu, Xiao-Qun; Wang, Ye-Fei; Cheung, Eric F C; Xie, Guang-Rong; Chan, Raymond C K

2016-09-01

Unwillingness to expend more effort to pursue high value rewards has been associated with motivational anhedonia in schizophrenia (SCZ) and abnormal dopamine activity in the nucleus accumbens (NAcc). The authors hypothesized that dysfunction of the NAcc and the associated forebrain regions are involved in the impaired effort expenditure decision-making of SCZ. A 2 (reward magnitude: low vs. high) × 3 (probability: 20% vs. 50% vs. 80%) event-related fMRI design in the effort-expenditure for reward task (EEfRT) was used to examine the neural response of 23 SCZ patients and 23 demographically matched control participants when the participants made effort expenditure decisions to pursue uncertain rewards. SCZ patients were significantly less likely to expend high level of effort in the medium (50%) and high (80%) probability conditions than healthy controls. The neural response in the NAcc, the posterior cingulate gyrus and the left medial frontal gyrus in SCZ patients were weaker than healthy controls and did not linearly increase with an increase in reward magnitude and probability. Moreover, NAcc activity was positively correlated with the willingness to expend high-level effort and concrete consummatory pleasure experience. NAcc and posterior cingulate dysfunctions in SCZ patients may be involved in their impaired effort expenditure decision-making. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Effect of Therapeutic Hypothermia Initiated After 6 Hours of Age on Death or Disability Among Newborns With Hypoxic-Ischemic Encephalopathy: A Randomized Clinical Trial.

PubMed

Laptook, Abbot R; Shankaran, Seetha; Tyson, Jon E; Munoz, Breda; Bell, Edward F; Goldberg, Ronald N; Parikh, Nehal A; Ambalavanan, Namasivayam; Pedroza, Claudia; Pappas, Athina; Das, Abhik; Chaudhary, Aasma S; Ehrenkranz, Richard A; Hensman, Angelita M; Van Meurs, Krisa P; Chalak, Lina F; Khan, Amir M; Hamrick, Shannon E G; Sokol, Gregory M; Walsh, Michele C; Poindexter, Brenda B; Faix, Roger G; Watterberg, Kristi L; Frantz, Ivan D; Guillet, Ronnie; Devaskar, Uday; Truog, William E; Chock, Valerie Y; Wyckoff, Myra H; McGowan, Elisabeth C; Carlton, David P; Harmon, Heidi M; Brumbaugh, Jane E; Cotten, C Michael; Sánchez, Pablo J; Hibbs, Anna Maria; Higgins, Rosemary D

2017-10-24

Hypothermia initiated at less than 6 hours after birth reduces death or disability for infants with hypoxic-ischemic encephalopathy at 36 weeks' or later gestation. To our knowledge, hypothermia trials have not been performed in infants presenting after 6 hours. To estimate the probability that hypothermia initiated at 6 to 24 hours after birth reduces the risk of death or disability at 18 months among infants with hypoxic-ischemic encephalopathy. A randomized clinical trial was conducted between April 2008 and June 2016 among infants at 36 weeks' or later gestation with moderate or severe hypoxic-ischemic encephalopathy enrolled at 6 to 24 hours after birth. Twenty-one US Neonatal Research Network centers participated. Bayesian analyses were prespecified given the anticipated limited sample size. Targeted esophageal temperature was used in 168 infants. Eighty-three hypothermic infants were maintained at 33.5°C (acceptable range, 33°C-34°C) for 96 hours and then rewarmed. Eighty-five noncooled infants were maintained at 37.0°C (acceptable range, 36.5°C-37.3°C). The composite of death or disability (moderate or severe) at 18 to 22 months adjusted for level of encephalopathy and age at randomization. Hypothermic and noncooled infants were term (mean [SD], 39 [2] and 39 [1] weeks' gestation, respectively), and 47 of 83 (57%) and 55 of 85 (65%) were male, respectively. Both groups were acidemic at birth, predominantly transferred to the treating center with moderate encephalopathy, and were randomized at a mean (SD) of 16 (5) and 15 (5) hours for hypothermic and noncooled groups, respectively. The primary outcome occurred in 19 of 78 hypothermic infants (24.4%) and 22 of 79 noncooled infants (27.9%) (absolute difference, 3.5%; 95% CI, -1% to 17%). Bayesian analysis using a neutral prior indicated a 76% posterior probability of reduced death or disability with hypothermia relative to the noncooled group (adjusted posterior risk ratio, 0.86; 95% credible interval, 0.58-1.29). The probability that death or disability in cooled infants was at least 1%, 2%, or 3% less than noncooled infants was 71%, 64%, and 56%, respectively. Among term infants with hypoxic-ischemic encephalopathy, hypothermia initiated at 6 to 24 hours after birth compared with noncooling resulted in a 76% probability of any reduction in death or disability, and a 64% probability of at least 2% less death or disability at 18 to 22 months. Hypothermia initiated at 6 to 24 hours after birth may have benefit but there is uncertainty in its effectiveness. clinicaltrials.gov Identifier: NCT00614744.

Effect of Therapeutic Hypothermia Initiated After 6 Hours of Age on Death or Disability Among Newborns With Hypoxic-Ischemic Encephalopathy

PubMed Central

Laptook, Abbot R.; Shankaran, Seetha; Tyson, Jon E.; Munoz, Breda; Bell, Edward F.; Goldberg, Ronald N.; Parikh, Nehal A.; Ambalavanan, Namasivayam; Pedroza, Claudia; Pappas, Athina; Das, Abhik; Chaudhary, Aasma S.; Ehrenkranz, Richard A.; Hensman, Angelita M.; Van Meurs, Krisa P.; Chalak, Lina F.; Hamrick, Shannon E. G.; Sokol, Gregory M.; Walsh, Michele C.; Poindexter, Brenda B.; Faix, Roger G.; Watterberg, Kristi L.; Frantz, Ivan D.; Guillet, Ronnie; Devaskar, Uday; Truog, William E.; Chock, Valerie Y.; Wyckoff, Myra H.; McGowan, Elisabeth C.; Carlton, David P.; Harmon, Heidi M.; Brumbaugh, Jane E.; Cotten, C. Michael; Sánchez, Pablo J.; Hibbs, Anna Maria; Higgins, Rosemary D.

2018-01-01

IMPORTANCE Hypothermia initiated at less than 6 hours after birth reduces death or disability for infants with hypoxic-ischemic encephalopathy at 36 weeks’ or later gestation. To our knowledge, hypothermia trials have not been performed in infants presenting after 6 hours. OBJECTIVE To estimate the probability that hypothermia initiated at 6 to 24 hours after birth reduces the risk of death or disability at 18 months among infants with hypoxic-ischemic encephalopathy. DESIGN, SETTING, AND PARTICIPANTS A randomized clinical trial was conducted between April 2008 and June 2016 among infants at 36 weeks’ or later gestation with moderate or severe hypoxic-ischemic encephalopathy enrolled at 6 to 24 hours after birth. Twenty-one US Neonatal Research Network centers participated. Bayesian analyses were prespecified given the anticipated limited sample size. INTERVENTIONS Targeted esophageal temperature was used in 168 infants. Eighty-three hypothermic infants were maintained at 33.5°C (acceptable range, 33°C–34°C) for 96 hours and then rewarmed. Eighty-five noncooled infants were maintained at 37.0°C (acceptable range, 36.5°C–37.3°C). MAIN OUTCOMES AND MEASURES The composite of death or disability (moderate or severe) at 18 to 22 months adjusted for level of encephalopathy and age at randomization. RESULTS Hypothermic and noncooled infants were term (mean [SD], 39 [2] and 39 [1] weeks’ gestation, respectively), and 47 of 83 (57%) and 55 of 85 (65%) were male, respectively. Both groups were acidemic at birth, predominantly transferred to the treating center with moderate encephalopathy, and were randomized at a mean (SD) of 16 (5) and 15 (5) hours for hypothermic and noncooled groups, respectively. The primary outcome occurred in 19 of 78 hypothermic infants (24.4%) and 22 of 79 noncooled infants (27.9%) (absolute difference, 3.5%; 95% CI, −1% to 17%). Bayesian analysis using a neutral prior indicated a 76% posterior probability of reduced death or disability with hypothermia relative to the noncooled group (adjusted posterior risk ratio, 0.86; 95% credible interval, 0.58–1.29). The probability that death or disability in cooled infants was at least 1%, 2%, or 3% less than noncooled infants was 71%, 64%, and 56%, respectively. CONCLUSIONS AND RELEVANCE Among term infants with hypoxic-ischemic encephalopathy, hypothermia initiated at 6 to 24 hours after birth compared with noncooling resulted in a 76% probability of any reduction in death or disability, and a 64% probability of at least 2% less death or disability at 18 to 22 months. Hypothermia initiated at 6 to 24 hours after birth may have benefit but there is uncertainty in its effectiveness. TRIAL REGISTRATION clinicaltrials.gov Identifier: NCT00614744 PMID:29067428

The digestive system of the "stick bug" Cladomorphus phyllinus (Phasmida, Phasmatidae): a morphological, physiological and biochemical analysis.

PubMed

Monteiro, Emiliano C; Tamaki, Fábio K; Terra, Walter R; Ribeiro, Alberto F

2014-03-01

This work presents a detailed morphofunctional study of the digestive system of a phasmid representative, Cladomorphus phyllinus. Cells from anterior midgut exhibit a merocrine secretion, whereas posterior midgut cells show a microapocrine secretion. A complex system of midgut tubules is observed in the posterior midgut which is probably related to the luminal alkalization of this region. Amaranth dye injection into the haemolymph and orally feeding insects with dye indicated that the anterior midgut is water-absorbing, whereas the Malpighian tubules are the main site of water secretion. Thus, a putative counter-current flux of fluid from posterior to anterior midgut may propel enzyme digestive recycling, confirmed by the low rate of enzyme excretion. The foregut and anterior midgut present an acidic pH (5.3 and 5.6, respectively), whereas the posterior midgut is highly alkaline (9.1) which may be related to the digestion of hemicelluloses. Most amylase, trypsin and chymotrypsin activities occur in the foregut and anterior midgut. Maltase is found along the midgut associated with the microvillar glycocalix, while aminopeptidase occurs in the middle and posterior midgut in membrane bound forms. Both amylase and trypsin are secreted mainly by the anterior midgut through an exocytic process as revealed by immunocytochemical data. Copyright © 2013 Elsevier Ltd. All rights reserved.

Coupling Self-Organizing Maps with a Naïve Bayesian classifier: A case study for classifying Vermont streams using geomorphic, habitat and biological assessment data

NASA Astrophysics Data System (ADS)

Fytilis, N.; Rizzo, D. M.

2012-12-01

Environmental managers are increasingly required to forecast the long-term effects and the resilience or vulnerability of biophysical systems to human-generated stresses. Mitigation strategies for hydrological and environmental systems need to be assessed in the presence of uncertainty. An important aspect of such complex systems is the assessment of variable uncertainty on the model response outputs. We develop a new classification tool that couples a Naïve Bayesian Classifier with a modified Kohonen Self-Organizing Map to tackle this challenge. For proof-of-concept, we use rapid geomorphic and reach-scale habitat assessments data from over 2500 Vermont stream reaches (~1371 stream miles) assessed by the Vermont Agency of Natural Resources (VTANR). In addition, the Vermont Department of Environmental Conservation (VTDEC) estimates stream habitat biodiversity indices (macro-invertebrates and fish) and a variety of water quality data. Our approach fully utilizes the existing VTANR and VTDEC data sets to improve classification of stream-reach habitat and biological integrity. The combined SOM-Naïve Bayesian architecture is sufficiently flexible to allow for continual updates and increased accuracy associated with acquiring new data. The Kohonen Self-Organizing Map (SOM) is an unsupervised artificial neural network that autonomously analyzes properties inherent in a given a set of data. It is typically used to cluster data vectors into similar categories when a priori classes do not exist. The ability of the SOM to convert nonlinear, high dimensional data to some user-defined lower dimension and mine large amounts of data types (i.e., discrete or continuous, biological or geomorphic data) makes it ideal for characterizing the sensitivity of river networks in a variety of contexts. The procedure is data-driven, and therefore does not require the development of site-specific, process-based classification stream models, or sets of if-then-else rules associated with expert systems. This has the potential to save time and resources, while enabling a truly adaptive management approach using existing knowledge (expressed as prior probabilities) and new information (expressed as likelihood functions) to update estimates (i.e., in this case, improved stream classifications expressed as posterior probabilities). The distribution parameters of these posterior probabilities are used to quantify uncertainty associated with environmental data. Since classification plays a leading role in the future development of data-enabled science and engineering, such a computational tool is applicable to a variety of engineering applications. The ability of the new classification neural network to characterize streams with high environmental risk is essential for a proactive adaptive watershed management approach.

Probabilistic distance-based quantizer design for distributed estimation

NASA Astrophysics Data System (ADS)

Kim, Yoon Hak

2016-12-01

We consider an iterative design of independently operating local quantizers at nodes that should cooperate without interaction to achieve application objectives for distributed estimation systems. We suggest as a new cost function a probabilistic distance between the posterior distribution and its quantized one expressed as the Kullback Leibler (KL) divergence. We first present the analysis that minimizing the KL divergence in the cyclic generalized Lloyd design framework is equivalent to maximizing the logarithmic quantized posterior distribution on the average which can be further computationally reduced in our iterative design. We propose an iterative design algorithm that seeks to maximize the simplified version of the posterior quantized distribution and discuss that our algorithm converges to a global optimum due to the convexity of the cost function and generates the most informative quantized measurements. We also provide an independent encoding technique that enables minimization of the cost function and can be efficiently simplified for a practical use of power-constrained nodes. We finally demonstrate through extensive experiments an obvious advantage of improved estimation performance as compared with the typical designs and the novel design techniques previously published.

Hierarchical Bayesian sparse image reconstruction with application to MRFM.

PubMed

Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves

2009-09-01

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

The relationship between species detection probability and local extinction probability

USGS Publications Warehouse

Alpizar-Jara, R.; Nichols, J.D.; Hines, J.E.; Sauer, J.R.; Pollock, K.H.; Rosenberry, C.S.

2004-01-01

In community-level ecological studies, generally not all species present in sampled areas are detected. Many authors have proposed the use of estimation methods that allow detection probabilities that are < 1 and that are heterogeneous among species. These methods can also be used to estimate community-dynamic parameters such as species local extinction probability and turnover rates (Nichols et al. Ecol Appl 8:1213-1225; Conserv Biol 12:1390-1398). Here, we present an ad hoc approach to estimating community-level vital rates in the presence of joint heterogeneity of detection probabilities and vital rates. The method consists of partitioning the number of species into two groups using the detection frequencies and then estimating vital rates (e.g., local extinction probabilities) for each group. Estimators from each group are combined in a weighted estimator of vital rates that accounts for the effect of heterogeneity. Using data from the North American Breeding Bird Survey, we computed such estimates and tested the hypothesis that detection probabilities and local extinction probabilities were negatively related. Our analyses support the hypothesis that species detection probability covaries negatively with local probability of extinction and turnover rates. A simulation study was conducted to assess the performance of vital parameter estimators as well as other estimators relevant to questions about heterogeneity, such as coefficient of variation of detection probabilities and proportion of species in each group. Both the weighted estimator suggested in this paper and the original unweighted estimator for local extinction probability performed fairly well and provided no basis for preferring one to the other.

Bayesian estimation of true prevalence, sensitivity and specificity of three diagnostic tests for detection of Escherichia coli O157 in cattle feces.

PubMed

Ekong, Pius S; Sanderson, Michael W; Bello, Nora M; Noll, Lance W; Cernicchiaro, Natalia; Renter, David G; Bai, Jianfa; Nagaraja, T G

2017-12-01

Cattle are a reservoir for Escherichia coli O157 and they shed the pathogen in their feces. Fecal contaminants on the hides can be transferred onto carcasses during processing at slaughter plants, thereby serving as a source of foodborne infection in humans. The detection of E. coli O157 in cattle feces is based on culture, immunological, and molecular methods We evaluated the diagnostic sensitivity and specificity of one culture- and two PCR-based tests for the detection of E. coli O157 in cattle feces, and its true prevalence using a Bayesian implementation of latent class models. A total of 576 fecal samples were collected from the floor of pens of finishing feedlot cattle in the central United States during summer 2013. Samples were enriched and subjected to detection of E. coli O157 by culture (immunomagnetic separation, plating on a selective medium, latex agglutination, and indole testing), conventional PCR (cPCR), and multiplex quantitative PCR (mqPCR). The statistical models assumed conditional dependence of the PCR tests and high specificity for culture (mode=99%; 5th percentile=97%). Prior estimates of test parameters were elicited from three experts. Estimated posterior sensitivity (posterior median and 95% highest posterior density intervals) of culture, cPCR, and mqPCR was 49.1% (44.8-53.4%), 59.7% (55.3-63.9%), and 97.3% (95.1-99.0%), respectively. Estimated posterior specificity of culture, cPCR, and mqPCR were 98.7% (96.8-99.8%), 94.1% (87.4-99.1%), and 94.8% (84.1-99.9%), respectively. True prevalence was estimated at 91.3% (88.1-94.2%). There was evidence of a weak conditional dependence between cPCR and mqPCR amongst test positive samples, but no evidence of conditional dependence amongst test negative samples. Sensitivity analyses showed that overall our posterior inference was rather robust to the choice of priors, except for inference on specificity of mqPCR, which was estimated with considerable uncertainty. Our study evaluates performance of three diagnostic tests for detection of E. coli O157 in feces of feedlot cattle which is important for quantifying true fecal prevalence and adjusting for test error in risk modeling. Copyright © 2017 Elsevier B.V. All rights reserved.

Active contour configuration model for estimating the posterior ablative margin in image fusion of real-time ultrasound and 3D ultrasound or magnetic resonance images for radiofrequency ablation: an experimental study.

PubMed

Lee, Junkyo; Lee, Min Woo; Choi, Dongil; Cha, Dong Ik; Lee, Sunyoung; Kang, Tae Wook; Yang, Jehoon; Jo, Jaemoon; Bang, Won-Chul; Kim, Jongsik; Shin, Dongkuk

2017-12-21

The purpose of this study was to evaluate the accuracy of an active contour model for estimating the posterior ablative margin in images obtained by the fusion of real-time ultrasonography (US) and 3-dimensional (3D) US or magnetic resonance (MR) images of an experimental tumor model for radiofrequency ablation. Chickpeas (n=12) and bovine rump meat (n=12) were used as an experimental tumor model. Grayscale 3D US and T1-weighted MR images were pre-acquired for use as reference datasets. US and MR/3D US fusion was performed for one group (n=4), and US and 3D US fusion only (n=8) was performed for the other group. Half of the models in each group were completely ablated, while the other half were incompletely ablated. Hyperechoic ablation areas were extracted using an active contour model from real-time US images, and the posterior margin of the ablation zone was estimated from the anterior margin. After the experiments, the ablated pieces of bovine rump meat were cut along the electrode path and the cut planes were photographed. The US images with the estimated posterior margin were compared with the photographs and post-ablation MR images. The extracted contours of the ablation zones from 12 US fusion videos and post-ablation MR images were also matched. In the four models fused under real-time US with MR/3D US, compression from the transducer and the insertion of an electrode resulted in misregistration between the real-time US and MR images, making the estimation of the ablation zones less accurate than was achieved through fusion between real-time US and 3D US. Eight of the 12 post-ablation 3D US images were graded as good when compared with the sectioned specimens, and 10 of the 12 were graded as good in a comparison with nicotinamide adenine dinucleotide staining and histopathologic results. Estimating the posterior ablative margin using an active contour model is a feasible way of predicting the ablation area, and US/3D US fusion was more accurate than US/MR fusion.

Spalled, aerodynamically modified moldavite from Slavice, Moravia, Czechoslovakia

USGS Publications Warehouse

Chao, E.C.T.

1964-01-01

A Czechoslovakian tektite or moldavite shows clear, indirect evidence of aerodynamic ablation. This large tektite has the shape of a teardrop, with a strongly convex, deeply corroded, but clearly identifiable front and a planoconvex, relatively smooth, posterior surface. In spite of much erosion and corrosion, demarcation of the posterior and the anterior part of the specimen (the keel) is clearly preserved locally. This specimen provides the first tangible evidence that moldavites entered the atmosphere cold, probably at a velocity exceeding 5 kilometers per second; the result was selective heating of the anterior face and perhaps ablation during the second melting. This provides evidence of the extraterrestial origin of moldavites.

Some Simple Formulas for Posterior Convergence Rates

PubMed Central

2014-01-01

We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a “penalized divergence” of the prior, which measures the ability of the prior distribution to propose a nonnegligible set of working models to approximate the true model and a “norm complexity” of the prior, which measures the complexity of the prior support, weighted by the prior probability masses. These formulas are explicit and involve no essential assumptions and are easy to apply. We apply this approach to the case with model averaging and derive some useful oracle inequalities that can optimize the performance adaptively without knowing the true model. PMID:27379278

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

A Multidimensional Item Response Model: Constrained Latent Class Analysis Using the Gibbs Sampler and Posterior Predictive Checks.

ERIC Educational Resources Information Center

Hoijtink, Herbert; Molenaar, Ivo W.

1997-01-01

This paper shows that a certain class of constrained latent class models may be interpreted as a special case of nonparametric multidimensional item response models. Parameters of this latent class model are estimated using an application of the Gibbs sampler, and model fit is investigated using posterior predictive checks. (SLD)

Value of Weather Information in Cranberry Marketing Decisions.

NASA Astrophysics Data System (ADS)

Morzuch, Bernard J.; Willis, Cleve E.

1982-04-01

Econometric techniques are used to establish a functional relationship between cranberry yields and important precipitation, temperature, and sunshine variables. Crop forecasts are derived from the model and are used to establish posterior probabilities to be used in a Bayesian decision context pertaining to leasing space for the storage of the berries.

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…

Lateralization of temporal lobe epilepsy by multimodal multinomial hippocampal response-driven models.

PubMed

Nazem-Zadeh, Mohammad-Reza; Elisevich, Kost V; Schwalb, Jason M; Bagher-Ebadian, Hassan; Mahmoudi, Fariborz; Soltanian-Zadeh, Hamid

2014-12-15

Multiple modalities are used in determining laterality in mesial temporal lobe epilepsy (mTLE). It is unclear how much different imaging modalities should be weighted in decision-making. The purpose of this study is to develop response-driven multimodal multinomial models for lateralization of epileptogenicity in mTLE patients based upon imaging features in order to maximize the accuracy of noninvasive studies. The volumes, means and standard deviations of FLAIR intensity and means of normalized ictal-interictal SPECT intensity of the left and right hippocampi were extracted from preoperative images of a retrospective cohort of 45 mTLE patients with Engel class I surgical outcomes, as well as images of a cohort of 20 control, nonepileptic subjects. Using multinomial logistic function regression, the parameters of various univariate and multivariate models were estimated. Based on the Bayesian model averaging (BMA) theorem, response models were developed as compositions of independent univariate models. A BMA model composed of posterior probabilities of univariate response models of hippocampal volumes, means and standard deviations of FLAIR intensity, and means of SPECT intensity with the estimated weighting coefficients of 0.28, 0.32, 0.09, and 0.31, respectively, as well as a multivariate response model incorporating all mentioned attributes, demonstrated complete reliability by achieving a probability of detection of one with no false alarms to establish proper laterality in all mTLE patients. The proposed multinomial multivariate response-driven model provides a reliable lateralization of mesial temporal epileptogenicity including those patients who require phase II assessment. Copyright © 2014 Elsevier B.V. All rights reserved.

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.

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 explorations of fault slip evolution over the earthquake cycle

NASA Astrophysics Data System (ADS)

Duputel, Z.; Jolivet, R.; Benoit, A.; Gombert, B.

2017-12-01

The ever-increasing amount of geophysical data continuously opens new perspectives on fundamental aspects of the seismogenic behavior of active faults. In this context, the recent fleet of SAR satellites including Sentinel-1 and COSMO-SkyMED permits the use of InSAR for time-dependent slip modeling with unprecedented resolution in time and space. However, existing time-dependent slip models rely on spatial smoothing regularization schemes, which can produce unrealistically smooth slip distributions. In addition, these models usually do not include uncertainty estimates thereby reducing the utility of such estimates. Here, we develop an entirely new approach to derive probabilistic time-dependent slip models. This Markov-Chain Monte Carlo method involves a series of transitional steps to predict and update posterior Probability Density Functions (PDFs) of slip as a function of time. We assess the viability of our approach using various slow-slip event scenarios. Using a dense set of SAR images, we also use this method to quantify the spatial distribution and temporal evolution of slip along a creeping segment of the North Anatolian Fault. This allows us to track a shallow aseismic slip transient lasting for about a month with a maximum slip of about 2 cm.

D-score: a search engine independent MD-score.

PubMed

Vaudel, Marc; Breiter, Daniela; Beck, Florian; Rahnenführer, Jörg; Martens, Lennart; Zahedi, René P

2013-03-01

While peptides carrying PTMs are routinely identified in gel-free MS, the localization of the PTMs onto the peptide sequences remains challenging. Search engine scores of secondary peptide matches have been used in different approaches in order to infer the quality of site inference, by penalizing the localization whenever the search engine similarly scored two candidate peptides with different site assignments. In the present work, we show how the estimation of posterior error probabilities for peptide candidates allows the estimation of a PTM score called the D-score, for multiple search engine studies. We demonstrate the applicability of this score to three popular search engines: Mascot, OMSSA, and X!Tandem, and evaluate its performance using an already published high resolution data set of synthetic phosphopeptides. For those peptides with phosphorylation site inference uncertainty, the number of spectrum matches with correctly localized phosphorylation increased by up to 25.7% when compared to using Mascot alone, although the actual increase depended on the fragmentation method used. Since this method relies only on search engine scores, it can be readily applied to the scoring of the localization of virtually any modification at no additional experimental or in silico cost. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A random-censoring Poisson model for underreported data.

PubMed

de Oliveira, Guilherme Lopes; Loschi, Rosangela Helena; Assunção, Renato Martins

2017-12-30

A major challenge when monitoring risks in socially deprived areas of under developed countries is that economic, epidemiological, and social data are typically underreported. Thus, statistical models that do not take the data quality into account will produce biased estimates. To deal with this problem, counts in suspected regions are usually approached as censored information. The censored Poisson model can be considered, but all censored regions must be precisely known a priori, which is not a reasonable assumption in most practical situations. We introduce the random-censoring Poisson model (RCPM) which accounts for the uncertainty about both the count and the data reporting processes. Consequently, for each region, we will be able to estimate the relative risk for the event of interest as well as the censoring probability. To facilitate the posterior sampling process, we propose a Markov chain Monte Carlo scheme based on the data augmentation technique. We run a simulation study comparing the proposed RCPM with 2 competitive models. Different scenarios are considered. RCPM and censored Poisson model are applied to account for potential underreporting of early neonatal mortality counts in regions of Minas Gerais State, Brazil, where data quality is known to be poor. Copyright © 2017 John Wiley & Sons, Ltd.

A family-based probabilistic method for capturing de novo mutations from high-throughput short-read sequencing data.

PubMed

Cartwright, Reed A; Hussin, Julie; Keebler, Jonathan E M; Stone, Eric A; Awadalla, Philip

2012-01-06

Recent advances in high-throughput DNA sequencing technologies and associated statistical analyses have enabled in-depth analysis of whole-genome sequences. As this technology is applied to a growing number of individual human genomes, entire families are now being sequenced. Information contained within the pedigree of a sequenced family can be leveraged when inferring the donors' genotypes. The presence of a de novo mutation within the pedigree is indicated by a violation of Mendelian inheritance laws. Here, we present a method for probabilistically inferring genotypes across a pedigree using high-throughput sequencing data and producing the posterior probability of de novo mutation at each genomic site examined. This framework can be used to disentangle the effects of germline and somatic mutational processes and to simultaneously estimate the effect of sequencing error and the initial genetic variation in the population from which the founders of the pedigree arise. This approach is examined in detail through simulations and areas for method improvement are noted. By applying this method to data from members of a well-defined nuclear family with accurate pedigree information, the stage is set to make the most direct estimates of the human mutation rate to date.

Effect of depth on shear-wave elastography estimated in the internal and external cervical os during pregnancy

PubMed Central

Hernandez-Andrade, Edgar; Aurioles-Garibay, Alma; Garcia, Maynor; Korzeniewski, Steven J.; Schwartz, Alyse G.; Ahn, Hyunyoung; Martinez-Varea, Alicia; Yeo, Lami; Chaiworapongsa, Tinnakorn; Hassan, Sonia S.; Romero, Roberto

2014-01-01

Aim To investigate the effect of depth on cervical shear-wave elastography. Methods Shear-wave elastography was applied to estimate the velocity of propagation of the acoustic force impulse (shear-wave) in the cervix of 154 pregnant women at 11-36 weeks of gestation. Shear-wave speed (SWS) was evaluated in cross-sectional views of the internal and external cervical os in five regions of interest: anterior, posterior, lateral right, lateral left, and endocervix. Distance from the center of the US transducer to the center of the each region of interest was registered. Results In all regions, SWS decreased significantly with gestational age (p=0.006). In the internal os SWS was similar among the anterior, posterior and lateral regions, and lower in the endocervix. In the external os, the endocervix and anterior regions showed similar SWS values, lower than those from the posterior and lateral regions. In the endocervix, these differences remained significant after adjustment for depth, gestational age and cervical length. SWS estimations in all regions of the internal os were higher than those of the external os, suggesting denser tissue. Conclusion Depth from the ultrasound probe to different regions in the cervix did not significantly affect the SWS estimations. PMID:25029081

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.

Attentional Demands Predict Short-Term Memory Load Response in Posterior Parietal Cortex

ERIC Educational Resources Information Center

Magen, Hagit; Emmanouil, Tatiana-Aloi; McMains, Stephanie A.; Kastner, Sabine; Treisman, Anne

2009-01-01

Limits to the capacity of visual short-term memory (VSTM) indicate a maximum storage of only 3 or 4 items. Recently, it has been suggested that activity in a specific part of the brain, the posterior parietal cortex (PPC), is correlated with behavioral estimates of VSTM capacity and might reflect a capacity-limited store. In three experiments that…

Probability Theory Plus Noise: Descriptive Estimation and Inferential Judgment.

PubMed

Costello, Fintan; Watts, Paul

2018-01-01

We describe a computational model of two central aspects of people's probabilistic reasoning: descriptive probability estimation and inferential probability judgment. This model assumes that people's reasoning follows standard frequentist probability theory, but it is subject to random noise. This random noise has a regressive effect in descriptive probability estimation, moving probability estimates away from normative probabilities and toward the center of the probability scale. This random noise has an anti-regressive effect in inferential judgement, however. These regressive and anti-regressive effects explain various reliable and systematic biases seen in people's descriptive probability estimation and inferential probability judgment. This model predicts that these contrary effects will tend to cancel out in tasks that involve both descriptive estimation and inferential judgement, leading to unbiased responses in those tasks. We test this model by applying it to one such task, described by Gallistel et al. ). Participants' median responses in this task were unbiased, agreeing with normative probability theory over the full range of responses. Our model captures the pattern of unbiased responses in this task, while simultaneously explaining systematic biases away from normatively correct probabilities seen in other tasks. Copyright © 2018 Cognitive Science Society, Inc.

A lower and more constrained estimate of climate sensitivity using updated observations and detailed radiative forcing time series

NASA Astrophysics Data System (ADS)

Skeie, R. B.; Berntsen, T.; Aldrin, M.; Holden, M.; Myhre, G.

2012-04-01

A key question in climate science is to quantify the sensitivity of the climate system to perturbation in the radiative forcing (RF). This sensitivity is often represented by the equilibrium climate sensitivity, but this quantity is poorly constrained with significant probabilities for high values. In this work the equilibrium climate sensitivity (ECS) is estimated based on observed near-surface temperature change from the instrumental record, changes in ocean heat content and detailed RF time series. RF time series from pre-industrial times to 2010 for all main anthropogenic and natural forcing mechanisms are estimated and the cloud lifetime effect and the semi-direct effect, which are not RF mechanisms in a strict sense, are included in the analysis. The RF time series are linked to the observations of ocean heat content and temperature change through an energy balance model and a stochastic model, using a Bayesian approach to estimate the ECS from the data. The posterior mean of the ECS is 1.9˚C with 90% credible interval (C.I.) ranging from 1.2 to 2.9˚C, which is tighter than previously published estimates. Observational data up to and including year 2010 are used in this study. This is at least ten additional years compared to the majority of previously published studies that have used the instrumental record in attempts to constrain the ECS. We show that the additional 10 years of data, and especially 10 years of additional ocean heat content data, have significantly narrowed the probability density function of the ECS. If only data up to and including year 2000 are used in the analysis, the 90% C.I. is 1.4 to 10.6˚C with a pronounced heavy tail in line with previous estimates of ECS constrained by observations in the 20th century. Also the transient climate response (TCR) is estimated in this study. Using observational data up to and including year 2010 gives a 90% C.I. of 1.0 to 2.1˚C, while the 90% C.I. is significantly broader ranging from 1.1 to 3.4 ˚C if only data up to and including year 2000 is used.

International comparative evaluation of knee replacement with fixed or mobile-bearing posterior-stabilized prostheses.

PubMed

Graves, Stephen; Sedrakyan, Art; Baste, Valborg; Gioe, Terence J; Namba, Robert; Martínez Cruz, Olga; Stea, Susanna; Paxton, Elizabeth; Banerjee, Samprit; Isaacs, Abby J; Robertsson, Otto

2014-12-17

Posterior-stabilized total knee prostheses were introduced to address instability secondary to loss of posterior cruciate ligament function, and they have either fixed or mobile bearings. Mobile bearings were developed to improve the function and longevity of total knee prostheses. In this study, the International Consortium of Orthopaedic Registries used a distributed health data network to study a large cohort of posterior-stabilized prostheses to determine if the outcome of a posterior-stabilized total knee prosthesis differs depending on whether it has a fixed or mobile-bearing design. Aggregated registry data were collected with a distributed health data network that was developed by the International Consortium of Orthopaedic Registries to reduce barriers to participation (e.g., security, proprietary, legal, and privacy issues) that have the potential to occur with the alternate centralized data warehouse approach. A distributed health data network is a decentralized model that allows secure storage and analysis of data from different registries. Each registry provided data on mobile and fixed-bearing posterior-stabilized prostheses implanted between 2001 and 2010. Only prostheses associated with primary total knee arthroplasties performed for the treatment of osteoarthritis were included. Prostheses with all types of fixation were included except for those with the rarely used reverse hybrid (cementless tibial and cemented femoral components) fixation. The use of patellar resurfacing was reported. The outcome of interest was time to first revision (for any reason). Multivariate meta-analysis was performed with linear mixed models with survival probability as the unit of analysis. This study includes 137,616 posterior-stabilized knee prostheses; 62% were in female patients, and 17.6% had a mobile bearing. The results of the fixed-effects model indicate that in the first year the mobile-bearing posterior-stabilized prostheses had a significantly higher hazard ratio (1.86) than did the fixed-bearing posterior-stabilized prostheses (95% confidence interval, 1.28 to 2.7; p = 0.001). For all other time intervals, the mobile-bearing posterior-stabilized prostheses had higher hazard ratios; however, these differences were not significant. Mobile-bearing posterior-stabilized prostheses had an increased rate of revision compared with fixed-bearing posterior-stabilized prostheses. This difference was evident in the first year. Copyright © 2014 by The Journal of Bone and Joint Surgery, Incorporated.

Defecatory dysfunction and fecal incontinence in women with or without posterior vaginal wall prolapse as measured by pelvic organ prolapse quantification (POP-Q).

PubMed

Augusto, Kathiane Lustosa; Bezerra, Leonardo Robson Pinheiro Sobreira; Murad-Regadas, Sthela Maria; Vasconcelos Neto, José Ananias; Vasconcelos, Camila Teixeira Moreira; Karbage, Sara Arcanjo Lino; Bilhar, Andreisa Paiva Monteiro; Regadas, Francisco Sérgio Pinheiro

2017-07-01

Pelvic Floor Dysfunction is a complex condition that may be asymptomatic or may involve a loto f symptoms. This study evaluates defecatory dysfunction, fecal incontinence, and quality of life in relation to presence of posterior vaginal prolapse. 265 patients were divided into two groups according to posterior POP-Q stage: posterior POP-Q stage ≥2 and posterior POP-Q stage <2. The two groups were compared regarding demographic and clinical data; overall POP-Q stage, percentage of patients with defecatory dysfunction, percentage of patients with fecal incontinence, pelvic floor muscle strength, and quality of life scores. The correlation between severity of the prolapse and severity of constipation was calculated using ρ de Spearman (rho). Women with Bp stage ≥2 were significantly older and had significantly higher BMI, numbers of pregnancies and births, and overall POP-Q stage than women with stage <2. No significant differences between the groups were observed regarding proportion of patients with defecatory dysfunction or incontinence, pelvic floor muscle strength, quality of life (ICIQ-SF), or sexual impact (PISQ-12). POP-Q stage did not correlate with severity of constipation and incontinence. General quality of life perception on the SF-36 was significantly worse in patients with POP-Q stage ≥2 than in those with POP-Q stage <2. The lack of a clinically important association between the presence of posterior vaginal prolapse and symptoms of constipation or anal incontinence leads us to agree with the conclusion that posterior vaginal prolapse probably is not an independent cause defecatory dysfunction or fecal incontinence. Copyright © 2017 Elsevier B.V. All rights reserved.

New KF-PP-SVM classification method for EEG in brain-computer interfaces.

PubMed

Yang, Banghua; Han, Zhijun; Zan, Peng; Wang, Qian

2014-01-01

Classification methods are a crucial direction in the current study of brain-computer interfaces (BCIs). To improve the classification accuracy for electroencephalogram (EEG) signals, a novel KF-PP-SVM (kernel fisher, posterior probability, and support vector machine) classification method is developed. Its detailed process entails the use of common spatial patterns to obtain features, based on which the within-class scatter is calculated. Then the scatter is added into the kernel function of a radial basis function to construct a new kernel function. This new kernel is integrated into the SVM to obtain a new classification model. Finally, the output of SVM is calculated based on posterior probability and the final recognition result is obtained. To evaluate the effectiveness of the proposed KF-PP-SVM method, EEG data collected from laboratory are processed with four different classification schemes (KF-PP-SVM, KF-SVM, PP-SVM, and SVM). The results showed that the overall average improvements arising from the use of the KF-PP-SVM scheme as opposed to KF-SVM, PP-SVM and SVM schemes are 2.49%, 5.83 % and 6.49 % respectively.

Laser Raman detection for oral cancer based on an adaptive Gaussian process classification method with posterior probabilities

NASA Astrophysics Data System (ADS)

Du, Zhanwei; Yang, Yongjian; Bai, Yuan; Wang, Lijun; Su, Le; Chen, Yong; Li, Xianchang; Zhou, Xiaodong; Jia, Jun; Shen, Aiguo; Hu, Jiming

2013-03-01

The existing methods for early and differential diagnosis of oral cancer are limited due to the unapparent early symptoms and the imperfect imaging examination methods. In this paper, the classification models of oral adenocarcinoma, carcinoma tissues and a control group with just four features are established by utilizing the hybrid Gaussian process (HGP) classification algorithm, with the introduction of the mechanisms of noise reduction and posterior probability. HGP shows much better performance in the experimental results. During the experimental process, oral tissues were divided into three groups, adenocarcinoma (n = 87), carcinoma (n = 100) and the control group (n = 134). The spectral data for these groups were collected. The prospective application of the proposed HGP classification method improved the diagnostic sensitivity to 56.35% and the specificity to about 70.00%, and resulted in a Matthews correlation coefficient (MCC) of 0.36. It is proved that the utilization of HGP in LRS detection analysis for the diagnosis of oral cancer gives accurate results. The prospect of application is also satisfactory.

Bayesian inference for the genetic control of water deficit tolerance in spring wheat by stochastic search variable selection.

PubMed

Safari, Parviz; Danyali, Syyedeh Fatemeh; Rahimi, Mehdi

2018-06-02

Drought is the main abiotic stress seriously influencing wheat production. Information about the inheritance of drought tolerance is necessary to determine the most appropriate strategy to develop tolerant cultivars and populations. In this study, generation means analysis to identify the genetic effects controlling grain yield inheritance in water deficit and normal conditions was considered as a model selection problem in a Bayesian framework. Stochastic search variable selection (SSVS) was applied to identify the most important genetic effects and the best fitted models using different generations obtained from two crosses applying two water regimes in two growing seasons. The SSVS is used to evaluate the effect of each variable on the dependent variable via posterior variable inclusion probabilities. The model with the highest posterior probability is selected as the best model. In this study, the grain yield was controlled by the main effects (additive and non-additive effects) and epistatic. The results demonstrate that breeding methods such as recurrent selection and subsequent pedigree method and hybrid production can be useful to improve grain yield.

Estimating the concordance probability in a survival analysis with a discrete number of risk groups.

PubMed

Heller, Glenn; Mo, Qianxing

2016-04-01

A clinical risk classification system is an important component of a treatment decision algorithm. A measure used to assess the strength of a risk classification system is discrimination, and when the outcome is survival time, the most commonly applied global measure of discrimination is the concordance probability. The concordance probability represents the pairwise probability of lower patient risk given longer survival time. The c-index and the concordance probability estimate have been used to estimate the concordance probability when patient-specific risk scores are continuous. In the current paper, the concordance probability estimate and an inverse probability censoring weighted c-index are modified to account for discrete risk scores. Simulations are generated to assess the finite sample properties of the concordance probability estimate and the weighted c-index. An application of these measures of discriminatory power to a metastatic prostate cancer risk classification system is examined.

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.

Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

NASA Astrophysics Data System (ADS)

Rizki, S. W.; Mara, M. N.; Sulistianingsih, E.

2017-06-01

This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior {\\hat{λ }}BL by using Linex approximation. After getting {\\hat{λ }}BL, the estimators of hazard function {\\hat{h}}BL and survival function {\\hat{S}}BL can be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.

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.

Real-time localization of mobile device by filtering method for sensor fusion

NASA Astrophysics Data System (ADS)

Fuse, Takashi; Nagara, Keita

2017-06-01

Most of the applications with mobile devices require self-localization of the devices. GPS cannot be used in indoor environment, the positions of mobile devices are estimated autonomously by using IMU. Since the self-localization is based on IMU of low accuracy, and then the self-localization in indoor environment is still challenging. The selflocalization method using images have been developed, and the accuracy of the method is increasing. This paper develops the self-localization method without GPS in indoor environment by integrating sensors, such as IMU and cameras, on mobile devices simultaneously. The proposed method consists of observations, forecasting and filtering. The position and velocity of the mobile device are defined as a state vector. In the self-localization, observations correspond to observation data from IMU and camera (observation vector), forecasting to mobile device moving model (system model) and filtering to tracking method by inertial surveying and coplanarity condition and inverse depth model (observation model). Positions of a mobile device being tracked are estimated by system model (forecasting step), which are assumed as linearly moving model. Then estimated positions are optimized referring to the new observation data based on likelihood (filtering step). The optimization at filtering step corresponds to estimation of the maximum a posterior probability. Particle filter are utilized for the calculation through forecasting and filtering steps. The proposed method is applied to data acquired by mobile devices in indoor environment. Through the experiments, the high performance of the method is confirmed.

A robust method to forecast volcanic ash clouds

USGS Publications Warehouse

Denlinger, Roger P.; Pavolonis, Mike; Sieglaff, Justin

2012-01-01

Ash clouds emanating from volcanic eruption columns often form trails of ash extending thousands of kilometers through the Earth's atmosphere, disrupting air traffic and posing a significant hazard to air travel. To mitigate such hazards, the community charged with reducing flight risk must accurately assess risk of ash ingestion for any flight path and provide robust forecasts of volcanic ash dispersal. In response to this need, a number of different transport models have been developed for this purpose and applied to recent eruptions, providing a means to assess uncertainty in forecasts. Here we provide a framework for optimal forecasts and their uncertainties given any model and any observational data. This involves random sampling of the probability distributions of input (source) parameters to a transport model and iteratively running the model with different inputs, each time assessing the predictions that the model makes about ash dispersal by direct comparison with satellite data. The results of these comparisons are embodied in a likelihood function whose maximum corresponds to the minimum misfit between model output and observations. Bayes theorem is then used to determine a normalized posterior probability distribution and from that a forecast of future uncertainty in ash dispersal. The nature of ash clouds in heterogeneous wind fields creates a strong maximum likelihood estimate in which most of the probability is localized to narrow ranges of model source parameters. This property is used here to accelerate probability assessment, producing a method to rapidly generate a prediction of future ash concentrations and their distribution based upon assimilation of satellite data as well as model and data uncertainties. Applying this method to the recent eruption of Eyjafjallajökull in Iceland, we show that the 3 and 6 h forecasts of ash cloud location probability encompassed the location of observed satellite-determined ash cloud loads, providing an efficient means to assess all of the hazards associated with these ash clouds.

An Integrative Framework for Bayesian Variable Selection with Informative Priors for Identifying Genes and Pathways

PubMed Central

Ander, Bradley P.; Zhang, Xiaoshuai; Xue, Fuzhong; Sharp, Frank R.; Yang, Xiaowei

2013-01-01

The discovery of genetic or genomic markers plays a central role in the development of personalized medicine. A notable challenge exists when dealing with the high dimensionality of the data sets, as thousands of genes or millions of genetic variants are collected on a relatively small number of subjects. Traditional gene-wise selection methods using univariate analyses face difficulty to incorporate correlational, structural, or functional structures amongst the molecular measures. For microarray gene expression data, we first summarize solutions in dealing with ‘large p, small n’ problems, and then propose an integrative Bayesian variable selection (iBVS) framework for simultaneously identifying causal or marker genes and regulatory pathways. A novel partial least squares (PLS) g-prior for iBVS is developed to allow the incorporation of prior knowledge on gene-gene interactions or functional relationships. From the point view of systems biology, iBVS enables user to directly target the joint effects of multiple genes and pathways in a hierarchical modeling diagram to predict disease status or phenotype. The estimated posterior selection probabilities offer probabilitic and biological interpretations. Both simulated data and a set of microarray data in predicting stroke status are used in validating the performance of iBVS in a Probit model with binary outcomes. iBVS offers a general framework for effective discovery of various molecular biomarkers by combining data-based statistics and knowledge-based priors. Guidelines on making posterior inferences, determining Bayesian significance levels, and improving computational efficiencies are also discussed. PMID:23844055

An integrative framework for Bayesian variable selection with informative priors for identifying genes and pathways.

PubMed

Peng, Bin; Zhu, Dianwen; Ander, Bradley P; Zhang, Xiaoshuai; Xue, Fuzhong; Sharp, Frank R; Yang, Xiaowei

2013-01-01

The discovery of genetic or genomic markers plays a central role in the development of personalized medicine. A notable challenge exists when dealing with the high dimensionality of the data sets, as thousands of genes or millions of genetic variants are collected on a relatively small number of subjects. Traditional gene-wise selection methods using univariate analyses face difficulty to incorporate correlational, structural, or functional structures amongst the molecular measures. For microarray gene expression data, we first summarize solutions in dealing with 'large p, small n' problems, and then propose an integrative Bayesian variable selection (iBVS) framework for simultaneously identifying causal or marker genes and regulatory pathways. A novel partial least squares (PLS) g-prior for iBVS is developed to allow the incorporation of prior knowledge on gene-gene interactions or functional relationships. From the point view of systems biology, iBVS enables user to directly target the joint effects of multiple genes and pathways in a hierarchical modeling diagram to predict disease status or phenotype. The estimated posterior selection probabilities offer probabilitic and biological interpretations. Both simulated data and a set of microarray data in predicting stroke status are used in validating the performance of iBVS in a Probit model with binary outcomes. iBVS offers a general framework for effective discovery of various molecular biomarkers by combining data-based statistics and knowledge-based priors. Guidelines on making posterior inferences, determining Bayesian significance levels, and improving computational efficiencies are also discussed.

Topographical relations between the posterior cricothyroid ligament and the inferior laryngeal nerve.

PubMed

Reidenbach, M M

1995-01-01

The posterior cricothyroid ligament and its topographic relation to the inferior laryngeal nerve were studied in 54 human adult male and female larynges. Fourteen specimens were impregnated with curable polymers and cut into 600-800 microns sections along different planes. Forty formalin-fixed hemi-larynges were dissected and various measurements were made. The posterior cricothyroid ligament provides a dorsal strengthening for the joint capsule of the cricothyroid joint. Its fibers spread in a fan-like manner from a small area of origin at the cricoid cartilage to a more extended area of attachment at the inferior thyroid cornu. The ligament consists of one (7.5%) to four (12.5%), in most cases of three (45.0%) or two (35.0%), individual parts oriented from mediocranial to latero-caudal. The inferior laryngeal nerve courses immediately dorsal to the ligament. In 60% it is covered by fibers of the posterior cricoarytenoid muscle, in the remaining 40% it is not. In this latter topographic situation there is almost no soft tissue interposed between the nerve and the hypopharynx. Therefore, the nerve may be exposed to pressure forces exerted from dorsally. It may be pushed against the unyielding posterior cricothyroid ligament and suffer functional or structural impairment. Probably, this mechanism may explain some of the laryngeal nerve lesions described in the literature after insertion of gastric tubes.

Pott disease in the thoracolumbar spine with marked kyphosis and progressive paraplegia necessitating posterior vertebral column resection and anterior reconstruction with a cage.

PubMed

Pappou, Ioannis P; Papadopoulos, Elias C; Swanson, Andrew N; Mermer, Matthew J; Fantini, Gary A; Urban, Michael K; Russell, Linda; Cammisa, Frank P; Girardi, Federico P

2006-02-15

Case report. To report on a patient with Pott disease, progressive neurologic deficit, and severe kyphotic deformity, who had medical treatment fail and required posterior/anterior decompression with instrumented fusion. Treatment options will be discussed. Tuberculous spondylitis is an increasingly common disease worldwide, with an estimated prevalence of 800,000 cases. Surgical treatment consisting of extensive posterior decompression/instrumented fusion and 3-level posterior vertebral column resection, followed by anterior debridement/fusion with cage reconstruction. Neurologic improvement at 6-month follow-up (Frankel B to Frankel D), with evidence of radiographic fusion. A 70-year-old patient with progressive Pott paraplegia and severe kyphotic deformity, for whom medical treatment failed is presented. A posterior vertebral column resection, multiple level posterior decompression, and instrumented fusion, followed by an anterior interbody fusion with cage was used to decompress the spinal cord, restore sagittal alignment, and debride the infection. At 6-month follow-up, the patient obtained excellent pain relief, correction of deformity, elimination of the tuberculous foci, and significant recovery of neurologic function.

Semiparametric Bayesian analysis of gene-environment interactions with error in measurement of environmental covariates and missing genetic data.

PubMed

Lobach, Iryna; Mallick, Bani; Carroll, Raymond J

2011-01-01

Case-control studies are widely used to detect gene-environment interactions in the etiology of complex diseases. Many variables that are of interest to biomedical researchers are difficult to measure on an individual level, e.g. nutrient intake, cigarette smoking exposure, long-term toxic exposure. Measurement error causes bias in parameter estimates, thus masking key features of data and leading to loss of power and spurious/masked associations. We develop a Bayesian methodology for analysis of case-control studies for the case when measurement error is present in an environmental covariate and the genetic variable has missing data. This approach offers several advantages. It allows prior information to enter the model to make estimation and inference more precise. The environmental covariates measured exactly are modeled completely nonparametrically. Further, information about the probability of disease can be incorporated in the estimation procedure to improve quality of parameter estimates, what cannot be done in conventional case-control studies. A unique feature of the procedure under investigation is that the analysis is based on a pseudo-likelihood function therefore conventional Bayesian techniques may not be technically correct. We propose an approach using Markov Chain Monte Carlo sampling as well as a computationally simple method based on an asymptotic posterior distribution. Simulation experiments demonstrated that our method produced parameter estimates that are nearly unbiased even for small sample sizes. An application of our method is illustrated using a population-based case-control study of the association between calcium intake with the risk of colorectal adenoma development.

Estimating cross-validatory predictive p-values with integrated importance sampling for disease mapping models.

PubMed

Li, Longhai; Feng, Cindy X; Qiu, Shi

2017-06-30

An important statistical task in disease mapping problems is to identify divergent regions with unusually high or low risk of disease. Leave-one-out cross-validatory (LOOCV) model assessment is the gold standard for estimating predictive p-values that can flag such divergent regions. However, actual LOOCV is time-consuming because one needs to rerun a Markov chain Monte Carlo analysis for each posterior distribution in which an observation is held out as a test case. This paper introduces a new method, called integrated importance sampling (iIS), for estimating LOOCV predictive p-values with only Markov chain samples drawn from the posterior based on a full data set. The key step in iIS is that we integrate away the latent variables associated the test observation with respect to their conditional distribution without reference to the actual observation. By following the general theory for importance sampling, the formula used by iIS can be proved to be equivalent to the LOOCV predictive p-value. We compare iIS and other three existing methods in the literature with two disease mapping datasets. Our empirical results show that the predictive p-values estimated with iIS are almost identical to the predictive p-values estimated with actual LOOCV and outperform those given by the existing three methods, namely, the posterior predictive checking, the ordinary importance sampling, and the ghosting method by Marshall and Spiegelhalter (2003). Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Estimating parameters for probabilistic linkage of privacy-preserved datasets.

PubMed

Brown, Adrian P; Randall, Sean M; Ferrante, Anna M; Semmens, James B; Boyd, James H

2017-07-10

Probabilistic record linkage is a process used to bring together person-based records from within the same dataset (de-duplication) or from disparate datasets using pairwise comparisons and matching probabilities. The linkage strategy and associated match probabilities are often estimated through investigations into data quality and manual inspection. However, as privacy-preserved datasets comprise encrypted data, such methods are not possible. In this paper, we present a method for estimating the probabilities and threshold values for probabilistic privacy-preserved record linkage using Bloom filters. Our method was tested through a simulation study using synthetic data, followed by an application using real-world administrative data. Synthetic datasets were generated with error rates from zero to 20% error. Our method was used to estimate parameters (probabilities and thresholds) for de-duplication linkages. Linkage quality was determined by F-measure. Each dataset was privacy-preserved using separate Bloom filters for each field. Match probabilities were estimated using the expectation-maximisation (EM) algorithm on the privacy-preserved data. Threshold cut-off values were determined by an extension to the EM algorithm allowing linkage quality to be estimated for each possible threshold. De-duplication linkages of each privacy-preserved dataset were performed using both estimated and calculated probabilities. Linkage quality using the F-measure at the estimated threshold values was also compared to the highest F-measure. Three large administrative datasets were used to demonstrate the applicability of the probability and threshold estimation technique on real-world data. Linkage of the synthetic datasets using the estimated probabilities produced an F-measure that was comparable to the F-measure using calculated probabilities, even with up to 20% error. Linkage of the administrative datasets using estimated probabilities produced an F-measure that was higher than the F-measure using calculated probabilities. Further, the threshold estimation yielded results for F-measure that were only slightly below the highest possible for those probabilities. The method appears highly accurate across a spectrum of datasets with varying degrees of error. As there are few alternatives for parameter estimation, the approach is a major step towards providing a complete operational approach for probabilistic linkage of privacy-preserved datasets.

Posterior open occlusion management by registration of overlay removable partial denture: A clinical report

PubMed Central

Nosouhian, Saeid; Davoudi, Amin; Derhami, Mohammad

2015-01-01

This clinical report describes prosthetic rehabilitation of posterior open bite relationship in a patient with several missing teeth and skeletal Class III malocclusion. Primary diagnostic esthetic evaluations were performed by mounting casts in centric relation and estimating lost vertical dimension of occlusion. Exclusive treatments were designated by applying overlay removable partial denture with external attachment systems for higher retentions. PMID:26929544

Posterior open occlusion management by registration of overlay removable partial denture: A clinical report.

PubMed

Nosouhian, Saeid; Davoudi, Amin; Derhami, Mohammad

2015-01-01

This clinical report describes prosthetic rehabilitation of posterior open bite relationship in a patient with several missing teeth and skeletal Class III malocclusion. Primary diagnostic esthetic evaluations were performed by mounting casts in centric relation and estimating lost vertical dimension of occlusion. Exclusive treatments were designated by applying overlay removable partial denture with external attachment systems for higher retentions.

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.

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.

Bayesian estimation of multicomponent relaxation parameters in magnetic resonance fingerprinting.

PubMed

McGivney, Debra; Deshmane, Anagha; Jiang, Yun; Ma, Dan; Badve, Chaitra; Sloan, Andrew; Gulani, Vikas; Griswold, Mark

2018-07-01

To estimate multiple components within a single voxel in magnetic resonance fingerprinting when the number and types of tissues comprising the voxel are not known a priori. Multiple tissue components within a single voxel are potentially separable with magnetic resonance fingerprinting as a result of differences in signal evolutions of each component. The Bayesian framework for inverse problems provides a natural and flexible setting for solving this problem when the tissue composition per voxel is unknown. Assuming that only a few entries from the dictionary contribute to a mixed signal, sparsity-promoting priors can be placed upon the solution. An iterative algorithm is applied to compute the maximum a posteriori estimator of the posterior probability density to determine the magnetic resonance fingerprinting dictionary entries that contribute most significantly to mixed or pure voxels. Simulation results show that the algorithm is robust in finding the component tissues of mixed voxels. Preliminary in vivo data confirm this result, and show good agreement in voxels containing pure tissue. The Bayesian framework and algorithm shown provide accurate solutions for the partial-volume problem in magnetic resonance fingerprinting. The flexibility of the method will allow further study into different priors and hyperpriors that can be applied in the model. Magn Reson Med 80:159-170, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates

PubMed Central

An, Qian; Kang, Jian; Song, Ruiguang; Hall, H. Irene

2016-01-01

Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS-free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS-free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS-free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA. PMID:26567891

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.

Live Imaging-Based Model Selection Reveals Periodic Regulation of the Stochastic G1/S Phase Transition in Vertebrate Axial Development

PubMed Central

Kurokawa, Hiroshi; Sakaue-Sawano, Asako; Imamura, Takeshi; Miyawaki, Atsushi; Iimura, Tadahiro

2014-01-01

In multicellular organism development, a stochastic cellular response is observed, even when a population of cells is exposed to the same environmental conditions. Retrieving the spatiotemporal regulatory mode hidden in the heterogeneous cellular behavior is a challenging task. The G1/S transition observed in cell cycle progression is a highly stochastic process. By taking advantage of a fluorescence cell cycle indicator, Fucci technology, we aimed to unveil a hidden regulatory mode of cell cycle progression in developing zebrafish. Fluorescence live imaging of Cecyil, a zebrafish line genetically expressing Fucci, demonstrated that newly formed notochordal cells from the posterior tip of the embryonic mesoderm exhibited the red (G1) fluorescence signal in the developing notochord. Prior to their initial vacuolation, these cells showed a fluorescence color switch from red to green, indicating G1/S transitions. This G1/S transition did not occur in a synchronous manner, but rather exhibited a stochastic process, since a mixed population of red and green cells was always inserted between newly formed red (G1) notochordal cells and vacuolating green cells. We termed this mixed population of notochordal cells, the G1/S transition window. We first performed quantitative analyses of live imaging data and a numerical estimation of the probability of the G1/S transition, which demonstrated the existence of a posteriorly traveling regulatory wave of the G1/S transition window. To obtain a better understanding of this regulatory mode, we constructed a mathematical model and performed a model selection by comparing the results obtained from the models with those from the experimental data. Our analyses demonstrated that the stochastic G1/S transition window in the notochord travels posteriorly in a periodic fashion, with doubled the periodicity of the neighboring paraxial mesoderm segmentation. This approach may have implications for the characterization of the pathophysiological tissue growth mode. PMID:25474567

Probability density of spatially distributed soil moisture inferred from crosshole georadar traveltime measurements

NASA Astrophysics Data System (ADS)

Linde, N.; Vrugt, J. A.

2009-04-01

Geophysical models are increasingly used in hydrological simulations and inversions, where they are typically treated as an artificial data source with known uncorrelated "data errors". The model appraisal problem in classical deterministic linear and non-linear inversion approaches based on linearization is often addressed by calculating model resolution and model covariance matrices. These measures offer only a limited potential to assign a more appropriate "data covariance matrix" for future hydrological applications, simply because the regularization operators used to construct a stable inverse solution bear a strong imprint on such estimates and because the non-linearity of the geophysical inverse problem is not explored. We present a parallelized Markov Chain Monte Carlo (MCMC) scheme to efficiently derive the posterior spatially distributed radar slowness and water content between boreholes given first-arrival traveltimes. This method is called DiffeRential Evolution Adaptive Metropolis (DREAM_ZS) with snooker updater and sampling from past states. Our inverse scheme does not impose any smoothness on the final solution, and uses uniform prior ranges of the parameters. The posterior distribution of radar slowness is converted into spatially distributed soil moisture values using a petrophysical relationship. To benchmark the performance of DREAM_ZS, we first apply our inverse method to a synthetic two-dimensional infiltration experiment using 9421 traveltimes contaminated with Gaussian errors and 80 different model parameters, corresponding to a model discretization of 0.3 m × 0.3 m. After this, the method is applied to field data acquired in the vadose zone during snowmelt. This work demonstrates that fully non-linear stochastic inversion can be applied with few limiting assumptions to a range of common two-dimensional tomographic geophysical problems. The main advantage of DREAM_ZS is that it provides a full view of the posterior distribution of spatially distributed soil moisture, which is key to appropriately treat geophysical parameter uncertainty and infer hydrologic models.

Comparison of Anterior, Posterior, and Total Corneal Astigmatism Measured Using a Single Scheimpflug Camera in Healthy and Keratoconus Eyes.

PubMed

Choi, Young; Eom, Youngsub; Song, Jong Suk; Kim, Hyo Myung

2018-05-15

To compare the effect of posterior corneal astigmatism on the estimation of total corneal astigmatism using anterior corneal measurements (simulated keratometry [K]) between eyes with keratoconus and healthy eyes. Thirty-three eyes of 33 patients with keratoconus of grade I or II and 33 eyes of 33 age- and sex-matched healthy control subjects were enrolled. Anterior, posterior, and total corneal cylinder powers and flat meridians measured by a single Scheimpflug camera were analyzed. The difference in corneal astigmatism between the simulated K and total cornea was evaluated. The mean anterior, posterior, and total corneal cylinder powers of the keratoconus group (4.37 ± 1.73, 0.95 ± 0.39, and 4.36 ± 1.74 CD, respectively) were significantly greater than those of the control group (1.10 ± 0.68, 0.39 ± 0.18, and 0.97 ± 0.63 CD, respectively). The cylinder power difference between the simulated K and total cornea was positively correlated with the posterior corneal cylinder power and negatively correlated with the absolute flat meridian difference between the simulated K and total cornea in both groups. The mean magnitude of the vector difference between the astigmatism of the simulated K and total cornea of the keratoconus group (0.67 ± 0.67 CD) was significantly larger than that of the control group (0.28 ± 0.12 CD). Eyes with keratoconus had greater estimation errors of total corneal astigmatism based on anterior corneal measurement than did healthy eyes. Posterior corneal surface measurement should be more emphasized to determine the total corneal astigmatism in eyes with keratoconus. © 2018 The Korean Ophthalmological Society.

Comparison of Anterior, Posterior, and Total Corneal Astigmatism Measured Using a Single Scheimpflug Camera in Healthy and Keratoconus Eyes

PubMed Central

Choi, Young; Song, Jong Suk; Kim, Hyo Myung

2018-01-01

Purpose To compare the effect of posterior corneal astigmatism on the estimation of total corneal astigmatism using anterior corneal measurements (simulated keratometry [K]) between eyes with keratoconus and healthy eyes. Methods Thirty-three eyes of 33 patients with keratoconus of grade I or II and 33 eyes of 33 age- and sex-matched healthy control subjects were enrolled. Anterior, posterior, and total corneal cylinder powers and flat meridians measured by a single Scheimpflug camera were analyzed. The difference in corneal astigmatism between the simulated K and total cornea was evaluated. Results The mean anterior, posterior, and total corneal cylinder powers of the keratoconus group (4.37 ± 1.73, 0.95 ± 0.39, and 4.36 ± 1.74 cylinder diopters [CD], respectively) were significantly greater than those of the control group (1.10 ± 0.68, 0.39 ± 0.18, and 0.97 ± 0.63 CD, respectively). The cylinder power difference between the simulated K and total cornea was positively correlated with the posterior corneal cylinder power and negatively correlated with the absolute flat meridian difference between the simulated K and total cornea in both groups. The mean magnitude of the vector difference between the astigmatism of the simulated K and total cornea of the keratoconus group (0.67 ± 0.67 CD) was significantly larger than that of the control group (0.28 ± 0.12 CD). Conclusions Eyes with keratoconus had greater estimation errors of total corneal astigmatism based on anterior corneal measurement than did healthy eyes. Posterior corneal surface measurement should be more emphasized to determine the total corneal astigmatism in eyes with keratoconus. PMID:29770640

The neural correlates of subjective utility of monetary outcome and probability weight in economic and in motor decision under risk

PubMed Central

Wu, Shih-Wei; Delgado, Mauricio R.; Maloney, Laurence T.

2011-01-01

In decision under risk, people choose between lotteries that contain a list of potential outcomes paired with their probabilities of occurrence. We previously developed a method for translating such lotteries to mathematically equivalent motor lotteries. The probability of each outcome in a motor lottery is determined by the subject’s noise in executing a movement. In this study, we used functional magnetic resonance imaging in humans to compare the neural correlates of monetary outcome and probability in classical lottery tasks where information about probability was explicitly communicated to the subjects and in mathematically equivalent motor lottery tasks where probability was implicit in the subjects’ own motor noise. We found that activity in the medial prefrontal cortex (mPFC) and the posterior cingulate cortex (PCC) quantitatively represent the subjective utility of monetary outcome in both tasks. For probability, we found that the mPFC significantly tracked the distortion of such information in both tasks. Specifically, activity in mPFC represents probability information but not the physical properties of the stimuli correlated with this information. Together, the results demonstrate that mPFC represents probability from two distinct forms of decision under risk. PMID:21677166

The neural correlates of subjective utility of monetary outcome and probability weight in economic and in motor decision under risk.

PubMed

Wu, Shih-Wei; Delgado, Mauricio R; Maloney, Laurence T

2011-06-15

In decision under risk, people choose between lotteries that contain a list of potential outcomes paired with their probabilities of occurrence. We previously developed a method for translating such lotteries to mathematically equivalent "motor lotteries." The probability of each outcome in a motor lottery is determined by the subject's noise in executing a movement. In this study, we used functional magnetic resonance imaging in humans to compare the neural correlates of monetary outcome and probability in classical lottery tasks in which information about probability was explicitly communicated to the subjects and in mathematically equivalent motor lottery tasks in which probability was implicit in the subjects' own motor noise. We found that activity in the medial prefrontal cortex (mPFC) and the posterior cingulate cortex quantitatively represent the subjective utility of monetary outcome in both tasks. For probability, we found that the mPFC significantly tracked the distortion of such information in both tasks. Specifically, activity in mPFC represents probability information but not the physical properties of the stimuli correlated with this information. Together, the results demonstrate that mPFC represents probability from two distinct forms of decision under risk.

The contribution of threat probability estimates to reexperiencing symptoms: a prospective analog study.

PubMed

Regambal, Marci J; Alden, Lynn E

2012-09-01

Individuals with posttraumatic stress disorder (PTSD) are hypothesized to have a "sense of current threat." Perceived threat from the environment (i.e., external threat), can lead to overestimating the probability of the traumatic event reoccurring (Ehlers & Clark, 2000). However, it is unclear if external threat judgments are a pre-existing vulnerability for PTSD or a consequence of trauma exposure. We used trauma analog methodology to prospectively measure probability estimates of a traumatic event, and investigate how these estimates were related to cognitive processes implicated in PTSD development. 151 participants estimated the probability of being in car-accident related situations, watched a movie of a car accident victim, and then completed a measure of data-driven processing during the movie. One week later, participants re-estimated the probabilities, and completed measures of reexperiencing symptoms and symptom appraisals/reactions. Path analysis revealed that higher pre-existing probability estimates predicted greater data-driven processing which was associated with negative appraisals and responses to intrusions. Furthermore, lower pre-existing probability estimates and negative responses to intrusions were both associated with a greater change in probability estimates. Reexperiencing symptoms were predicted by negative responses to intrusions and, to a lesser degree, by greater changes in probability estimates. The undergraduate student sample may not be representative of the general public. The reexperiencing symptoms are less severe than what would be found in a trauma sample. Threat estimates present both a vulnerability and a consequence of exposure to a distressing event. Furthermore, changes in these estimates are associated with cognitive processes implicated in PTSD. Copyright © 2012 Elsevier Ltd. All rights reserved.

Pretest expectations strongly influence interpretation of abnormal laboratory results and further management

PubMed Central

2010-01-01

Background Abnormal results of diagnostic laboratory tests can be difficult to interpret when disease probability is very low. Although most physicians generally do not use Bayesian calculations to interpret abnormal results, their estimates of pretest disease probability and reasons for ordering diagnostic tests may - in a more implicit manner - influence test interpretation and further management. A better understanding of this influence may help to improve test interpretation and management. Therefore, the objective of this study was to examine the influence of physicians' pretest disease probability estimates, and their reasons for ordering diagnostic tests, on test result interpretation, posttest probability estimates and further management. Methods Prospective study among 87 primary care physicians in the Netherlands who each ordered laboratory tests for 25 patients. They recorded their reasons for ordering the tests (to exclude or confirm disease or to reassure patients) and their pretest disease probability estimates. Upon receiving the results they recorded how they interpreted the tests, their posttest probability estimates and further management. Logistic regression was used to analyse whether the pretest probability and the reasons for ordering tests influenced the interpretation, the posttest probability estimates and the decisions on further management. Results The physicians ordered tests for diagnostic purposes for 1253 patients; 742 patients had an abnormal result (64%). Physicians' pretest probability estimates and their reasons for ordering diagnostic tests influenced test interpretation, posttest probability estimates and further management. Abnormal results of tests ordered for reasons of reassurance were significantly more likely to be interpreted as normal (65.8%) compared to tests ordered to confirm a diagnosis or exclude a disease (27.7% and 50.9%, respectively). The odds for abnormal results to be interpreted as normal were much lower when the physician estimated a high pretest disease probability, compared to a low pretest probability estimate (OR = 0.18, 95% CI = 0.07-0.52, p < 0.001). Conclusions Interpretation and management of abnormal test results were strongly influenced by physicians' estimation of pretest disease probability and by the reason for ordering the test. By relating abnormal laboratory results to their pretest expectations, physicians may seek a balance between over- and under-reacting to laboratory test results. PMID:20158908

Pretest expectations strongly influence interpretation of abnormal laboratory results and further management.

PubMed

Houben, Paul H H; van der Weijden, Trudy; Winkens, Bjorn; Winkens, Ron A G; Grol, Richard P T M

2010-02-16

Abnormal results of diagnostic laboratory tests can be difficult to interpret when disease probability is very low. Although most physicians generally do not use Bayesian calculations to interpret abnormal results, their estimates of pretest disease probability and reasons for ordering diagnostic tests may--in a more implicit manner--influence test interpretation and further management. A better understanding of this influence may help to improve test interpretation and management. Therefore, the objective of this study was to examine the influence of physicians' pretest disease probability estimates, and their reasons for ordering diagnostic tests, on test result interpretation, posttest probability estimates and further management. Prospective study among 87 primary care physicians in the Netherlands who each ordered laboratory tests for 25 patients. They recorded their reasons for ordering the tests (to exclude or confirm disease or to reassure patients) and their pretest disease probability estimates. Upon receiving the results they recorded how they interpreted the tests, their posttest probability estimates and further management. Logistic regression was used to analyse whether the pretest probability and the reasons for ordering tests influenced the interpretation, the posttest probability estimates and the decisions on further management. The physicians ordered tests for diagnostic purposes for 1253 patients; 742 patients had an abnormal result (64%). Physicians' pretest probability estimates and their reasons for ordering diagnostic tests influenced test interpretation, posttest probability estimates and further management. Abnormal results of tests ordered for reasons of reassurance were significantly more likely to be interpreted as normal (65.8%) compared to tests ordered to confirm a diagnosis or exclude a disease (27.7% and 50.9%, respectively). The odds for abnormal results to be interpreted as normal were much lower when the physician estimated a high pretest disease probability, compared to a low pretest probability estimate (OR = 0.18, 95% CI = 0.07-0.52, p < 0.001). Interpretation and management of abnormal test results were strongly influenced by physicians' estimation of pretest disease probability and by the reason for ordering the test. By relating abnormal laboratory results to their pretest expectations, physicians may seek a balance between over- and under-reacting to laboratory test results.

Diagnostic causal reasoning with verbal information.

PubMed

Meder, Björn; Mayrhofer, Ralf

2017-08-01

In diagnostic causal reasoning, the goal is to infer the probability of causes from one or multiple observed effects. Typically, studies investigating such tasks provide subjects with precise quantitative information regarding the strength of the relations between causes and effects or sample data from which the relevant quantities can be learned. By contrast, we sought to examine people's inferences when causal information is communicated through qualitative, rather vague verbal expressions (e.g., "X occasionally causes A"). We conducted three experiments using a sequential diagnostic inference task, where multiple pieces of evidence were obtained one after the other. Quantitative predictions of different probabilistic models were derived using the numerical equivalents of the verbal terms, taken from an unrelated study with different subjects. We present a novel Bayesian model that allows for incorporating the temporal weighting of information in sequential diagnostic reasoning, which can be used to model both primacy and recency effects. On the basis of 19,848 judgments from 292 subjects, we found a remarkably close correspondence between the diagnostic inferences made by subjects who received only verbal information and those of a matched control group to whom information was presented numerically. Whether information was conveyed through verbal terms or numerical estimates, diagnostic judgments closely resembled the posterior probabilities entailed by the causes' prior probabilities and the effects' likelihoods. We observed interindividual differences regarding the temporal weighting of evidence in sequential diagnostic reasoning. Our work provides pathways for investigating judgment and decision making with verbal information within a computational modeling framework. Copyright © 2017 Elsevier Inc. All rights reserved.

On the Origins of Suboptimality in Human Probabilistic Inference

PubMed Central

Acerbi, Luigi; Vijayakumar, Sethu; Wolpert, Daniel M.

2014-01-01

Humans have been shown to combine noisy sensory information with previous experience (priors), in qualitative and sometimes quantitative agreement with the statistically-optimal predictions of Bayesian integration. However, when the prior distribution becomes more complex than a simple Gaussian, such as skewed or bimodal, training takes much longer and performance appears suboptimal. It is unclear whether such suboptimality arises from an imprecise internal representation of the complex prior, or from additional constraints in performing probabilistic computations on complex distributions, even when accurately represented. Here we probe the sources of suboptimality in probabilistic inference using a novel estimation task in which subjects are exposed to an explicitly provided distribution, thereby removing the need to remember the prior. Subjects had to estimate the location of a target given a noisy cue and a visual representation of the prior probability density over locations, which changed on each trial. Different classes of priors were examined (Gaussian, unimodal, bimodal). Subjects' performance was in qualitative agreement with the predictions of Bayesian Decision Theory although generally suboptimal. The degree of suboptimality was modulated by statistical features of the priors but was largely independent of the class of the prior and level of noise in the cue, suggesting that suboptimality in dealing with complex statistical features, such as bimodality, may be due to a problem of acquiring the priors rather than computing with them. We performed a factorial model comparison across a large set of Bayesian observer models to identify additional sources of noise and suboptimality. Our analysis rejects several models of stochastic behavior, including probability matching and sample-averaging strategies. Instead we show that subjects' response variability was mainly driven by a combination of a noisy estimation of the parameters of the priors, and by variability in the decision process, which we represent as a noisy or stochastic posterior. PMID:24945142

iProphet: Multi-level Integrative Analysis of Shotgun Proteomic Data Improves Peptide and Protein Identification Rates and Error Estimates*

PubMed Central

Shteynberg, David; Deutsch, Eric W.; Lam, Henry; Eng, Jimmy K.; Sun, Zhi; Tasman, Natalie; Mendoza, Luis; Moritz, Robert L.; Aebersold, Ruedi; Nesvizhskii, Alexey I.

2011-01-01

The combination of tandem mass spectrometry and sequence database searching is the method of choice for the identification of peptides and the mapping of proteomes. Over the last several years, the volume of data generated in proteomic studies has increased dramatically, which challenges the computational approaches previously developed for these data. Furthermore, a multitude of search engines have been developed that identify different, overlapping subsets of the sample peptides from a particular set of tandem mass spectrometry spectra. We present iProphet, the new addition to the widely used open-source suite of proteomic data analysis tools Trans-Proteomics Pipeline. Applied in tandem with PeptideProphet, it provides more accurate representation of the multilevel nature of shotgun proteomic data. iProphet combines the evidence from multiple identifications of the same peptide sequences across different spectra, experiments, precursor ion charge states, and modified states. It also allows accurate and effective integration of the results from multiple database search engines applied to the same data. The use of iProphet in the Trans-Proteomics Pipeline increases the number of correctly identified peptides at a constant false discovery rate as compared with both PeptideProphet and another state-of-the-art tool Percolator. As the main outcome, iProphet permits the calculation of accurate posterior probabilities and false discovery rate estimates at the level of sequence identical peptide identifications, which in turn leads to more accurate probability estimates at the protein level. Fully integrated with the Trans-Proteomics Pipeline, it supports all commonly used MS instruments, search engines, and computer platforms. The performance of iProphet is demonstrated on two publicly available data sets: data from a human whole cell lysate proteome profiling experiment representative of typical proteomic data sets, and from a set of Streptococcus pyogenes experiments more representative of organism-specific composite data sets. PMID:21876204

WE-H-207A-06: Hypoxia Quantification in Static PET Images: The Signal in the Noise

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

Keller, H; Yeung, I; Milosevic, M

2016-06-15

Purpose: Quantification of hypoxia from PET images is of considerable clinical interest. In the absence of dynamic PET imaging the hypoxic fraction (HF) of a tumor has to be estimated from voxel values of activity concentration of a radioactive hypoxia tracer. This work is part of an effort to standardize quantification of tumor hypoxic fraction from PET images. Methods: A simple hypoxia imaging model in the tumor was developed. The distribution of the tracer activity was described as the sum of two different probability distributions, one for the normoxic (and necrotic), the other for the hypoxic voxels. The widths ofmore » the distributions arise due to variability of the transport, tumor tissue inhomogeneity, tracer binding kinetics, and due to PET image noise. Quantification of HF was performed for various levels of variability using two different methodologies: a) classification thresholds between normoxic and hypoxic voxels based on a non-hypoxic surrogate (muscle), and b) estimation of the (posterior) probability distributions based on maximizing likelihood optimization that does not require a surrogate. Data from the hypoxia imaging model and from 27 cervical cancer patients enrolled in a FAZA PET study were analyzed. Results: In the model, where the true value of HF is known, thresholds usually underestimate the value for large variability. For the patients, a significant uncertainty of the HF values (an average intra-patient range of 17%) was caused by spatial non-uniformity of image noise which is a hallmark of all PET images. Maximum likelihood estimation (MLE) is able to directly optimize for the weights of both distributions, however, may suffer from poor optimization convergence. For some patients, MLE-based HF values showed significant differences to threshold-based HF-values. Conclusion: HF-values depend critically on the magnitude of the different sources of tracer uptake variability. A measure of confidence should also be reported.« less

Gaussian functional regression for output prediction: Model assimilation and experimental design

NASA Astrophysics Data System (ADS)

Nguyen, N. C.; Peraire, J.

2016-03-01

In this paper, we introduce a Gaussian functional regression (GFR) technique that integrates multi-fidelity models with model reduction to efficiently predict the input-output relationship of a high-fidelity model. The GFR method combines the high-fidelity model with a low-fidelity model to provide an estimate of the output of the high-fidelity model in the form of a posterior distribution that can characterize uncertainty in the prediction. A reduced basis approximation is constructed upon the low-fidelity model and incorporated into the GFR method to yield an inexpensive posterior distribution of the output estimate. As this posterior distribution depends crucially on a set of training inputs at which the high-fidelity models are simulated, we develop a greedy sampling algorithm to select the training inputs. Our approach results in an output prediction model that inherits the fidelity of the high-fidelity model and has the computational complexity of the reduced basis approximation. Numerical results are presented to demonstrate the proposed approach.

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

[The therapeutic drug monitoring network server of tacrolimus for Chinese renal transplant patients].

PubMed

Deng, Chen-Hui; Zhang, Guan-Min; Bi, Shan-Shan; Zhou, Tian-Yan; Lu, Wei

2011-07-01

This study is to develop a therapeutic drug monitoring (TDM) network server of tacrolimus for Chinese renal transplant patients, which can facilitate doctor to manage patients' information and provide three levels of predictions. Database management system MySQL was employed to build and manage the database of patients and doctors' information, and hypertext mark-up language (HTML) and Java server pages (JSP) technology were employed to construct network server for database management. Based on the population pharmacokinetic model of tacrolimus for Chinese renal transplant patients, above program languages were used to construct the population prediction and subpopulation prediction modules. Based on Bayesian principle and maximization of the posterior probability function, an objective function was established, and minimized by an optimization algorithm to estimate patient's individual pharmacokinetic parameters. It is proved that the network server has the basic functions for database management and three levels of prediction to aid doctor to optimize the regimen of tacrolimus for Chinese renal transplant patients.

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.

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…

Frequency and determinants for hemorrhagic transformation of posterior cerebral stroke : Posterior ischemic stroke and hemorrhagic transformation.

PubMed

Valentino, Francesca; Gentile, Luana; Terruso, Valeria; Mastrilli, Sergio; Aridon, Paolo; Ragonese, Paolo; Sarno, Caterina; Savettieri, Giovanni; D'Amelio, Marco

2017-11-13

hemorrhagic transformation is a threatening ischemic stroke complication. Frequency of hemorrhagic transformation differs greatly among studies, and its risk factors have been usually studied in patients with anterior ischemic stroke who received thrombolytic therapy. We evaluated, in a hospital-based series of patients with posterior ischemic stroke not treated with thrombolysis, frequency and risk factors of hemorrhagic transformation. Patients with posterior circulation stroke were seen in our Department during the period January 2004 to December 2009. Demographic and clinical information were collected. We estimated risk for spontaneous hemorrhagic transformation by means of uni- and multivariate logistic regression analyses. 119 consecutive patients were included (73 males, 61.3%). Hemorrhagic transformation was observed in 7 patients (5.9%). Only clinical worsening was significantly associated with hemorrhagic transformation (OR 6.8, 95% CI 1.3-34.5). Our findings indicate that patients with posterior have a low risk of spontaneous hemorrhagic transformation, suggesting that these patients might have greater advantage from intravenous thrombolysis.

Regression without truth with Markov chain Monte-Carlo

NASA Astrophysics Data System (ADS)

Madan, Hennadii; Pernuš, Franjo; Likar, Boštjan; Å piclin, Žiga

2017-03-01

Regression without truth (RWT) is a statistical technique for estimating error model parameters of each method in a group of methods used for measurement of a certain quantity. A very attractive aspect of RWT is that it does not rely on a reference method or "gold standard" data, which is otherwise difficult RWT was used for a reference-free performance comparison of several methods for measuring left ventricular ejection fraction (EF), i.e. a percentage of blood leaving the ventricle each time the heart contracts, and has since been applied for various other quantitative imaging biomarkerss (QIBs). Herein, we show how Markov chain Monte-Carlo (MCMC), a computational technique for drawing samples from a statistical distribution with probability density function known only up to a normalizing coefficient, can be used to augment RWT to gain a number of important benefits compared to the original approach based on iterative optimization. For instance, the proposed MCMC-based RWT enables the estimation of joint posterior distribution of the parameters of the error model, straightforward quantification of uncertainty of the estimates, estimation of true value of the measurand and corresponding credible intervals (CIs), does not require a finite support for prior distribution of the measureand generally has a much improved robustness against convergence to non-global maxima. The proposed approach is validated using synthetic data that emulate the EF data for 45 patients measured with 8 different methods. The obtained results show that 90% CI of the corresponding parameter estimates contain the true values of all error model parameters and the measurand. A potential real-world application is to take measurements of a certain QIB several different methods and then use the proposed framework to compute the estimates of the true values and their uncertainty, a vital information for diagnosis based on QIB.

Bone-breaking bite force of Basilosaurus isis (Mammalia, Cetacea) from the late Eocene of Egypt estimated by finite element analysis.

PubMed

Snively, Eric; Fahlke, Julia M; Welsh, Robert C

2015-01-01

Bite marks suggest that the late Eocence archaeocete whale Basilosaurus isis (Birket Qarun Formation, Egypt) fed upon juveniles of the contemporary basilosaurid Dorudon atrox. Finite element analysis (FEA) of a nearly complete adult cranium of B. isis enables estimates of its bite force and tests the animal's capabilities for crushing bone. Two loadcases reflect different biting scenarios: 1) an intitial closing phase, with all adductors active and a full condylar reaction force; and 2) a shearing phase, with the posterior temporalis active and minimized condylar force. The latter is considered probable when the jaws were nearly closed because the preserved jaws do not articulate as the molariform teeth come into occulusion. Reaction forces with all muscles active indicate that B. isis maintained relatively greater bite force anteriorly than seen in large crocodilians, and exerted a maximum bite force of at least 16,400 N at its upper P3. Under the shearing scenario with minimized condylar forces, tooth reaction forces could exceed 20,000 N despite lower magnitudes of muscle force. These bite forces at the teeth are consistent with bone indentations on Dorudon crania, reatract-and-shear hypotheses of Basilosaurus bite function, and seizure of prey by anterior teeth as proposed for other archaeocetes. The whale's bite forces match those estimated for pliosaurus when skull lengths are equalized, suggesting similar tradeoffs of bite function and hydrodynamics. Reaction forces in B. isis were lower than maxima estimated for large crocodylians and carnivorous dinosaurs. However, comparison of force estimates from FEA and regression data indicate that B. isis exerted the largest bite forces yet estimated for any mammal, and greater force than expected from its skull width. Cephalic feeding biomechanics of Basilosaurus isis are thus consistent with habitual predation.

The Role of Wildfire, Prescribed Fire, and Mountain Pine Beetle Infestations on the Population Dynamics of Black-Backed Woodpeckers in the Black Hills, South Dakota

PubMed Central

Rota, Christopher T.; Millspaugh, Joshua J.; Rumble, Mark A.; Lehman, Chad P.; Kesler, Dylan C.

2014-01-01

Wildfire and mountain pine beetle infestations are naturally occurring disturbances in western North American forests. Black-backed woodpeckers (Picoides arcticus) are emblematic of the role these disturbances play in creating wildlife habitat, since they are strongly associated with recently-killed forests. However, management practices aimed at reducing the economic impact of natural disturbances can result in habitat loss for this species. Although black-backed woodpeckers occupy habitats created by wildfire, prescribed fire, and mountain pine beetle infestations, the relative value of these habitats remains unknown. We studied habitat-specific adult and juvenile survival probabilities and reproductive rates between April 2008 and August 2012 in the Black Hills, South Dakota. We estimated habitat-specific adult and juvenile survival probability with Bayesian multi-state models and habitat-specific reproductive success with Bayesian nest survival models. We calculated asymptotic population growth rates from estimated demographic rates with matrix projection models. Adult and juvenile survival and nest success were highest in habitat created by summer wildfire, intermediate in MPB infestations, and lowest in habitat created by fall prescribed fire. Mean posterior distributions of population growth rates indicated growing populations in habitat created by summer wildfire and declining populations in fall prescribed fire and mountain pine beetle infestations. Our finding that population growth rates were positive only in habitat created by summer wildfire underscores the need to maintain early post-wildfire habitat across the landscape. The lower growth rates in fall prescribed fire and MPB infestations may be attributed to differences in predator communities and food resources relative to summer wildfire. PMID:24736502

Clinical evaluation incorporating a personal genome

PubMed Central

Ashley, Euan A.; Butte, Atul J.; Wheeler, Matthew T.; Chen, Rong; Klein, Teri E.; Dewey, Frederick E.; Dudley, Joel T.; Ormond, Kelly E.; Pavlovic, Aleksandra; Hudgins, Louanne; Gong, Li; Hodges, Laura M.; Berlin, Dorit S.; Thorn, Caroline F.; Sangkuhl, Katrin; Hebert, Joan M.; Woon, Mark; Sagreiya, Hersh; Whaley, Ryan; Morgan, Alexander A.; Pushkarev, Dmitry; Neff, Norma F; Knowles, Joshua W.; Chou, Mike; Thakuria, Joseph; Rosenbaum, Abraham; Zaranek, Alexander Wait; Church, George; Greely, Henry T.; Quake, Stephen R.; Altman, Russ B.

2010-01-01

Background The cost of genomic information has fallen steeply but the path to clinical translation of risk estimates for common variants found in genome wide association studies remains unclear. Since the speed and cost of sequencing complete genomes is rapidly declining, more comprehensive means of analyzing these data in concert with rare variants for genetic risk assessment and individualisation of therapy are required. Here, we present the first integrated analysis of a complete human genome in a clinical context. Methods An individual with a family history of vascular disease and early sudden death was evaluated. Clinical assessment included risk prediction for coronary artery disease, screening for causes of sudden cardiac death, and genetic counselling. Genetic analysis included the development of novel methods for the integration of whole genome sequence data including 2.6 million single nucleotide polymorphisms and 752 copy number variations. The algorithm focused on predicting genetic risk of genes associated with known Mendelian disease, recognised drug responses, and pathogenicity for novel variants. In addition, since integration of risk ratios derived from case control studies is challenging, we estimated posterior probabilities from age and sex appropriate prior probability and likelihood ratios derived for each genotype. In addition, we developed a visualisation approach to account for gene-environment interactions and conditionally dependent risks. Findings We found increased genetic risk for myocardial infarction, type II diabetes and certain cancers. Rare variants in LPA are consistent with the family history of coronary artery disease. Pharmacogenomic analysis suggested a positive response to lipid lowering therapy, likely clopidogrel resistance, and a low initial dosing requirement for warfarin. Many variants of uncertain significance were reported. Interpretation Although challenges remain, our results suggest that whole genome sequencing can yield useful and clinically relevant information for individual patients, especially for those with a strong family history of significant disease. PMID:20435227

StarHorse: a Bayesian tool for determining stellar masses, ages, distances, and extinctions for field stars

NASA Astrophysics Data System (ADS)

Queiroz, A. B. A.; Anders, F.; Santiago, B. X.; Chiappini, C.; Steinmetz, M.; Dal Ponte, M.; Stassun, K. G.; da Costa, L. N.; Maia, M. A. G.; Crestani, J.; Beers, T. C.; Fernández-Trincado, J. G.; García-Hernández, D. A.; Roman-Lopes, A.; Zamora, O.

2018-05-01

Understanding the formation and evolution of our Galaxy requires accurate distances, ages, and chemistry for large populations of field stars. Here, we present several updates to our spectrophotometric distance code, which can now also be used to estimate ages, masses, and extinctions for individual stars. Given a set of measured spectrophotometric parameters, we calculate the posterior probability distribution over a given grid of stellar evolutionary models, using flexible Galactic stellar-population priors. The code (called StarHorse) can accommodate different observational data sets, prior options, partially missing data, and the inclusion of parallax information into the estimated probabilities. We validate the code using a variety of simulated stars as well as real stars with parameters determined from asteroseismology, eclipsing binaries, and isochrone fits to star clusters. Our main goal in this validation process is to test the applicability of the code to field stars with known Gaia-like parallaxes. The typical internal precisions (obtained from realistic simulations of an APOGEE+Gaia-like sample) are {˜eq } 8 {per cent} in distance, {˜eq } 20 {per cent} in age, {˜eq } 6 {per cent} in mass, and ≃ 0.04 mag in AV. The median external precision (derived from comparisons with earlier work for real stars) varies with the sample used, but lies in the range of {˜eq } [0,2] {per cent} for distances, {˜eq } [12,31] {per cent} for ages, {˜eq } [4,12] {per cent} for masses, and ≃ 0.07 mag for AV. We provide StarHorse distances and extinctions for the APOGEE DR14, RAVE DR5, GES DR3, and GALAH DR1 catalogues.

The role of wildfire, prescribed fire, and mountain pine beetle infestations on the population dynamics of black-backed woodpeckers in the black hills, South Dakota.

PubMed

Rota, Christopher T; Millspaugh, Joshua J; Rumble, Mark A; Lehman, Chad P; Kesler, Dylan C

2014-01-01

Wildfire and mountain pine beetle infestations are naturally occurring disturbances in western North American forests. Black-backed woodpeckers (Picoides arcticus) are emblematic of the role these disturbances play in creating wildlife habitat, since they are strongly associated with recently-killed forests. However, management practices aimed at reducing the economic impact of natural disturbances can result in habitat loss for this species. Although black-backed woodpeckers occupy habitats created by wildfire, prescribed fire, and mountain pine beetle infestations, the relative value of these habitats remains unknown. We studied habitat-specific adult and juvenile survival probabilities and reproductive rates between April 2008 and August 2012 in the Black Hills, South Dakota. We estimated habitat-specific adult and juvenile survival probability with Bayesian multi-state models and habitat-specific reproductive success with Bayesian nest survival models. We calculated asymptotic population growth rates from estimated demographic rates with matrix projection models. Adult and juvenile survival and nest success were highest in habitat created by summer wildfire, intermediate in MPB infestations, and lowest in habitat created by fall prescribed fire. Mean posterior distributions of population growth rates indicated growing populations in habitat created by summer wildfire and declining populations in fall prescribed fire and mountain pine beetle infestations. Our finding that population growth rates were positive only in habitat created by summer wildfire underscores the need to maintain early post-wildfire habitat across the landscape. The lower growth rates in fall prescribed fire and MPB infestations may be attributed to differences in predator communities and food resources relative to summer wildfire.

Paleogeodesy of the Southern Santa Cruz Mountains Frontal Thrusts, Silicon Valley, CA

NASA Astrophysics Data System (ADS)

Aron, F.; Johnstone, S. A.; Mavrommatis, A. P.; Sare, R.; Hilley, G. E.

2015-12-01

We present a method to infer long-term fault slip rate distributions using topography by coupling a three-dimensional elastic boundary element model with a geomorphic incision rule. In particular, we used a 10-m-resolution digital elevation model (DEM) to calculate channel steepness (ksn) throughout the actively deforming southern Santa Cruz Mountains in Central California. We then used these values with a power-law incision rule and the Poly3D code to estimate slip rates over seismogenic, kilometer-scale thrust faults accommodating differential uplift of the relief throughout geologic time. Implicit in such an analysis is the assumption that the topographic surface remains unchanged over time as rock is uplifted by slip on the underlying structures. The fault geometries within the area are defined based on surface mapping, as well as active and passive geophysical imaging. Fault elements are assumed to be traction-free in shear (i.e., frictionless), while opening along them is prohibited. The free parameters in the inversion include the components of the remote strain-rate tensor (ɛij) and the bedrock resistance to channel incision (K), which is allowed to vary according to the mapped distribution of geologic units exposed at the surface. The nonlinear components of the geomorphic model required the use of a Markov chain Monte Carlo method, which simulated the posterior density of the components of the remote strain-rate tensor and values of K for the different mapped geologic units. Interestingly, posterior probability distributions of ɛij and K fall well within the broad range of reported values, suggesting that the joint use of elastic boundary element and geomorphic models may have utility in estimating long-term fault slip-rate distributions. Given an adequate DEM, geologic mapping, and fault models, the proposed paleogeodetic method could be applied to other crustal faults with geological and morphological expressions of long-term uplift.

Spatiotemporal Variation in Distance Dependent Animal Movement Contacts: One Size Doesn’t Fit All

PubMed Central

Brommesson, Peter; Wennergren, Uno; Lindström, Tom

2016-01-01

The structure of contacts that mediate transmission has a pronounced effect on the outbreak dynamics of infectious disease and simulation models are powerful tools to inform policy decisions. Most simulation models of livestock disease spread rely to some degree on predictions of animal movement between holdings. Typically, movements are more common between nearby farms than between those located far away from each other. Here, we assessed spatiotemporal variation in such distance dependence of animal movement contacts from an epidemiological perspective. We evaluated and compared nine statistical models, applied to Swedish movement data from 2008. The models differed in at what level (if at all), they accounted for regional and/or seasonal heterogeneities in the distance dependence of the contacts. Using a kernel approach to describe how probability of contacts between farms changes with distance, we developed a hierarchical Bayesian framework and estimated parameters by using Markov Chain Monte Carlo techniques. We evaluated models by three different approaches of model selection. First, we used Deviance Information Criterion to evaluate their performance relative to each other. Secondly, we estimated the log predictive posterior distribution, this was also used to evaluate their relative performance. Thirdly, we performed posterior predictive checks by simulating movements with each of the parameterized models and evaluated their ability to recapture relevant summary statistics. Independent of selection criteria, we found that accounting for regional heterogeneity improved model accuracy. We also found that accounting for seasonal heterogeneity was beneficial, in terms of model accuracy, according to two of three methods used for model selection. Our results have important implications for livestock disease spread models where movement is an important risk factor for between farm transmission. We argue that modelers should refrain from using methods to simulate animal movements that assume the same pattern across all regions and seasons without explicitly testing for spatiotemporal variation. PMID:27760155

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.

Pseudo Bayes Estimates for Test Score Distributions and Chained Equipercentile Equating. Research Report. ETS RR-09-47

ERIC Educational Resources Information Center

Moses, Tim; Oh, Hyeonjoo J.

2009-01-01

Pseudo Bayes probability estimates are weighted averages of raw and modeled probabilities; these estimates have been studied primarily in nonpsychometric contexts. The purpose of this study was to evaluate pseudo Bayes probability estimates as applied to the estimation of psychometric test score distributions and chained equipercentile equating…

Incorporating detection probability into northern Great Plains pronghorn population estimates

USGS Publications Warehouse

Jacques, Christopher N.; Jenks, Jonathan A.; Grovenburg, Troy W.; Klaver, Robert W.; DePerno, Christopher S.

2014-01-01

Pronghorn (Antilocapra americana) abundances commonly are estimated using fixed-wing surveys, but these estimates are likely to be negatively biased because of violations of key assumptions underpinning line-transect methodology. Reducing bias and improving precision of abundance estimates through use of detection probability and mark-resight models may allow for more responsive pronghorn management actions. Given their potential application in population estimation, we evaluated detection probability and mark-resight models for use in estimating pronghorn population abundance. We used logistic regression to quantify probabilities that detecting pronghorn might be influenced by group size, animal activity, percent vegetation, cover type, and topography. We estimated pronghorn population size by study area and year using mixed logit-normal mark-resight (MLNM) models. Pronghorn detection probability increased with group size, animal activity, and percent vegetation; overall detection probability was 0.639 (95% CI = 0.612–0.667) with 396 of 620 pronghorn groups detected. Despite model selection uncertainty, the best detection probability models were 44% (range = 8–79%) and 180% (range = 139–217%) greater than traditional pronghorn population estimates. Similarly, the best MLNM models were 28% (range = 3–58%) and 147% (range = 124–180%) greater than traditional population estimates. Detection probability of pronghorn was not constant but depended on both intrinsic and extrinsic factors. When pronghorn detection probability is a function of animal group size, animal activity, landscape complexity, and percent vegetation, traditional aerial survey techniques will result in biased pronghorn abundance estimates. Standardizing survey conditions, increasing resighting occasions, or accounting for variation in individual heterogeneity in mark-resight models will increase the accuracy and precision of pronghorn population estimates.

Depression of the Thoracolumbar Posterior Vertebral Body on the Estimation of Cement Leakage in Vertebroplasty and Kyphoplasty Operations

PubMed Central

Chen, Hao; Jia, Pu; Bao, Li; Feng, Fei; Yang, He; Li, Jin-Jun; Tang, Hai

2015-01-01

Background: The cross-section of thoracolumbar vertebral body is kidney-shaped with depressed posterior boundary. The anterior wall of the vertebral canal is separated from the posterior wall of the vertebral body on the lateral X-ray image. This study was designed to determine the sagittal distance between the anterior border of the vertebral canal and the posterior border of the vertebral body (DBCV) and to analyze the potential role of DBCV in the estimation of cement leakage during percutaneous vertebroplasty (PVP) or percutaneous kyphoplasty (PKP). Methods: We retrospectively recruited 233 patients who had osteoporotic vertebral compression fractures and were treated with PVP or PKP. Computed tomography images of T11–L2 normal vertebrae were measured to obtain DBCV. The distance from cement to the posterior wall of the vertebral body (DCPW) of thoracolumbar vertebrae was measured from C-arm images. The selected vertebrae were divided into two groups according to DCPW, with the fracture levels, fracture grades and leakage rates of the two groups compared. A relative operating characteristic (ROC) curve was applied to determine whether the DCPW difference can be used to estimate the degree of cement leakage. The data were processed by statistical software SPSS version 21.0 using independent sample t-test and Chi-square tests. Results: The maximum DBCV was 6.40 mm and the average DBCV was 3.74 ± 0.95 mm. DBCV appeared to be longer in males than in females, but the difference was not statistically significant. The average DCPW of type-B leakage vertebrae (2.59 ± 1.20 mm) was shorter than that of other vertebrae (7.83 ± 2.38 mm, P < 0.001). The leakage rate of group DCPW ≤6.40 mm was lower than that of group DCPW >6.40 mm for type-C and type-S, but much higher for type-B. ROC curve revealed that DCPW only has a predictive value for type-B leakage (area under the curve: 0.98, 95% confidence interval: 0.95–0.99, P < 0.001), and when the cut-off value was 4.05 mm, the diagnostic sensitivity and the specificity were 94.87% and 93.02%, respectively. Conclusions: Depression of the thoracolumbar posterior vertebral body may be informative for the estimation of cement location on C-arm images. To reduce type-B leakage, DCPW should be made longer than DBCV on C-arm images for safety during PVP or PKP. PMID:26612289

Depression of the Thoracolumbar Posterior Vertebral Body on the Estimation of Cement Leakage in Vertebroplasty and Kyphoplasty Operations.

PubMed

Chen, Hao; Jia, Pu; Bao, Li; Feng, Fei; Yang, He; Li, Jin-Jun; Tang, Hai

2015-12-05

The cross-section of thoracolumbar vertebral body is kidney-shaped with depressed posterior boundary. The anterior wall of the vertebral canal is separated from the posterior wall of the vertebral body on the lateral X-ray image. This study was designed to determine the sagittal distance between the anterior border of the vertebral canal and the posterior border of the vertebral body (DBCV) and to analyze the potential role of DBCV in the estimation of cement leakage during percutaneous vertebroplasty (PVP) or percutaneous kyphoplasty (PKP). We retrospectively recruited 233 patients who had osteoporotic vertebral compression fractures and were treated with PVP or PKP. Computed tomography images of T11-L2 normal vertebrae were measured to obtain DBCV. The distance from cement to the posterior wall of the vertebral body (DCPW) of thoracolumbar vertebrae was measured from C-arm images. The selected vertebrae were divided into two groups according to DCPW, with the fracture levels, fracture grades and leakage rates of the two groups compared. A relative operating characteristic (ROC) curve was applied to determine whether the DCPW difference can be used to estimate the degree of cement leakage. The data were processed by statistical software SPSS version 21.0 using independent sample t-test and Chi-square tests. The maximum DBCV was 6.40 mm and the average DBCV was 3.74 ± 0.95 mm. DBCV appeared to be longer in males than in females, but the difference was not statistically significant. The average DCPW of type-B leakage vertebrae (2.59 ± 1.20 mm) was shorter than that of other vertebrae (7.83 ± 2.38 mm, P < 0.001). The leakage rate of group DCPW ≤6.40 mm was lower than that of group DCPW >6.40 mm for type-C and type-S, but much higher for type-B. ROC curve revealed that DCPW only has a predictive value for type-B leakage (area under the curve: 0.98, 95% confidence interval: 0.95-0.99, P < 0.001), and when the cut-off value was 4.05 mm, the diagnostic sensitivity and the specificity were 94.87% and 93.02%, respectively. Depression of the thoracolumbar posterior vertebral body may be informative for the estimation of cement location on C-arm images. To reduce type-B leakage, DCPW should be made longer than DBCV on C-arm images for safety during PVP or PKP.