Using Alien Coins to Test Whether Simple Inference Is Bayesian

ERIC Educational Resources Information Center

Cassey, Peter; Hawkins, Guy E.; Donkin, Chris; Brown, Scott D.

2016-01-01

Reasoning and inference are well-studied aspects of basic cognition that have been explained as statistically optimal Bayesian inference. Using a simplified experimental design, we conducted quantitative comparisons between Bayesian inference and human inference at the level of individuals. In 3 experiments, with more than 13,000 participants, we…

RISK ASSESSMENT FOR CRYPTOSPORIDIUM: A HIERARCHICAL BAYESIAN ANALYSIS OF HUMAN DOSE-RESPONSE DATA. (R828035)

EPA Science Inventory

Three dose_¯response studies were conducted with healthy volunteers using different Cryptosporidium parvum isolates (IOWA, TAMU, and UCP). The study data were previously analyzed for median infectious dose (ID₅₀) using a simple cumulative perce...

RISK ASSESSMENT FOR CRYPTOSPORIDIUM: A HIERARCHICAL BAYESIAN ANALYSIS OF HUMAN DOSE-RESPONSE DATA. (R829180)

EPA Science Inventory

Three dose–response studies were conducted with healthy volunteers using different Cryptosporidium parvum isolates (IOWA, TAMU, and UCP). The study data were previously analyzed for median infectious dose (ID₅₀) using a simple cumulative percent endpoi...

Bayesian data analysis tools for atomic physics

NASA Astrophysics Data System (ADS)

Trassinelli, Martino

2017-10-01

We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes' theorem and its applications. In particular we discuss about how to calculate simple and joint probability distributions and the Bayesian evidence, a model dependent quantity that allows to assign probabilities to different hypotheses from the analysis of a same data set. To give some practical examples, these methods are applied to two concrete cases. In the first example, the presence or not of a satellite line in an atomic spectrum is investigated. In the second example, we determine the most probable model among a set of possible profiles from the analysis of a statistically poor spectrum. We show also how to calculate the probability distribution of the main spectral component without having to determine uniquely the spectrum modeling. For these two studies, we implement the program Nested_fit to calculate the different probability distributions and other related quantities. Nested_fit is a Fortran90/Python code developed during the last years for analysis of atomic spectra. As indicated by the name, it is based on the nested algorithm, which is presented in details together with the program itself.

Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis

PubMed Central

Turner, Rebecca M; Jackson, Dan; Wei, Yinghui; Thompson, Simon G; Higgins, Julian P T

2015-01-01

Numerous meta-analyses in healthcare research combine results from only a small number of studies, for which the variance representing between-study heterogeneity is estimated imprecisely. A Bayesian approach to estimation allows external evidence on the expected magnitude of heterogeneity to be incorporated. The aim of this paper is to provide tools that improve the accessibility of Bayesian meta-analysis. We present two methods for implementing Bayesian meta-analysis, using numerical integration and importance sampling techniques. Based on 14 886 binary outcome meta-analyses in the Cochrane Database of Systematic Reviews, we derive a novel set of predictive distributions for the degree of heterogeneity expected in 80 settings depending on the outcomes assessed and comparisons made. These can be used as prior distributions for heterogeneity in future meta-analyses. The two methods are implemented in R, for which code is provided. Both methods produce equivalent results to standard but more complex Markov chain Monte Carlo approaches. The priors are derived as log-normal distributions for the between-study variance, applicable to meta-analyses of binary outcomes on the log odds-ratio scale. The methods are applied to two example meta-analyses, incorporating the relevant predictive distributions as prior distributions for between-study heterogeneity. We have provided resources to facilitate Bayesian meta-analysis, in a form accessible to applied researchers, which allow relevant prior information on the degree of heterogeneity to be incorporated. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd. PMID:25475839

A Monte Carlo–Based Bayesian Approach for Measuring Agreement in a Qualitative Scale

PubMed Central

Pérez Sánchez, Carlos Javier

2014-01-01

Agreement analysis has been an active research area whose techniques have been widely applied in psychology and other fields. However, statistical agreement among raters has been mainly considered from a classical statistics point of view. Bayesian methodology is a viable alternative that allows the inclusion of subjective initial information coming from expert opinions, personal judgments, or historical data. A Bayesian approach is proposed by providing a unified Monte Carlo–based framework to estimate all types of measures of agreement in a qualitative scale of response. The approach is conceptually simple and it has a low computational cost. Both informative and non-informative scenarios are considered. In case no initial information is available, the results are in line with the classical methodology, but providing more information on the measures of agreement. For the informative case, some guidelines are presented to elicitate the prior distribution. The approach has been applied to two applications related to schizophrenia diagnosis and sensory analysis. PMID:29881002

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.

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

PubMed

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

2008-04-01

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

Beginning Bayes

ERIC Educational Resources Information Center

Erickson, Tim

2017-01-01

Understanding a Bayesian perspective demands comfort with conditional probability and with probabilities that appear to change as we acquire additional information. This paper suggests a simple context in conditional probability that helps develop the understanding students would need for a successful introduction to Bayesian reasoning.

A Bayesian Model of the Memory Colour Effect.

PubMed

Witzel, Christoph; Olkkonen, Maria; Gegenfurtner, Karl R

2018-01-01

According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects.

A Bayesian Model of the Memory Colour Effect

PubMed Central

Olkkonen, Maria; Gegenfurtner, Karl R.

2018-01-01

According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects. PMID:29760874

Integrating health economics modeling in the product development cycle of medical devices: a Bayesian approach.

PubMed

Vallejo-Torres, Laura; Steuten, Lotte M G; Buxton, Martin J; Girling, Alan J; Lilford, Richard J; Young, Terry

2008-01-01

Medical device companies are under growing pressure to provide health-economic evaluations of their products. Cost-effectiveness analyses are commonly undertaken as a one-off exercise at the late stage of development of new technologies; however, the benefits of an iterative use of economic evaluation during the development process of new products have been acknowledged in the literature. Furthermore, the use of Bayesian methods within health technology assessment has been shown to be of particular value in the dynamic framework of technology appraisal when new information becomes available in the life cycle of technologies. In this study, we set out a methodology to adapt these methods for their application to directly support investment decisions in a commercial setting from early stages of the development of new medical devices. Starting with relatively simple analysis from the very early development phase and proceeding to greater depth of analysis at later stages, a Bayesian approach facilitates the incorporation of all available evidence and would help companies to make better informed choices at each decision point.

Search Parameter Optimization for Discrete, Bayesian, and Continuous Search Algorithms

DTIC Science & Technology

2017-09-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS SEARCH PARAMETER OPTIMIZATION FOR DISCRETE , BAYESIAN, AND CONTINUOUS SEARCH ALGORITHMS by...to 09-22-2017 4. TITLE AND SUBTITLE SEARCH PARAMETER OPTIMIZATION FOR DISCRETE , BAYESIAN, AND CON- TINUOUS SEARCH ALGORITHMS 5. FUNDING NUMBERS 6...simple search and rescue acts to prosecuting aerial/surface/submersible targets on mission. This research looks at varying the known discrete and

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.

Information-Decay Pursuit of Dynamic Parameters in Student Models

DTIC Science & Technology

1994-04-01

simple worked-through example). Commercially available computer programs for structuring and using Bayesian inference include ERGO ( Noetic Systems...Tukey, J.W. (1977). Data analysis and Regression: A second course in statistics. Reading, MA: Addison-Wesley. Noetic Systems, Inc. (1991). ERGO...Naval Academy Division of Educational Studies Annapolis MD 21402-5002 Elmory Univerity Dr Janice Gifford 210 Fiabburne Bldg University of

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

PubMed

Spertus, Jacob V; Normand, Sharon-Lise T

2018-04-23

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

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

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin; Feeney, Stephen

2018-07-01

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

Planetary micro-rover operations on Mars using a Bayesian framework for inference and control

NASA Astrophysics Data System (ADS)

Post, Mark A.; Li, Junquan; Quine, Brendan M.

2016-03-01

With the recent progress toward the application of commercially-available hardware to small-scale space missions, it is now becoming feasible for groups of small, efficient robots based on low-power embedded hardware to perform simple tasks on other planets in the place of large-scale, heavy and expensive robots. In this paper, we describe design and programming of the Beaver micro-rover developed for Northern Light, a Canadian initiative to send a small lander and rover to Mars to study the Martian surface and subsurface. For a small, hardware-limited rover to handle an uncertain and mostly unknown environment without constant management by human operators, we use a Bayesian network of discrete random variables as an abstraction of expert knowledge about the rover and its environment, and inference operations for control. A framework for efficient construction and inference into a Bayesian network using only the C language and fixed-point mathematics on embedded hardware has been developed for the Beaver to make intelligent decisions with minimal sensor data. We study the performance of the Beaver as it probabilistically maps a simple outdoor environment with sensor models that include uncertainty. Results indicate that the Beaver and other small and simple robotic platforms can make use of a Bayesian network to make intelligent decisions in uncertain planetary environments.

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

PubMed Central

2010-01-01

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

Of bugs and birds: Markov Chain Monte Carlo for hierarchical modeling in wildlife research

USGS Publications Warehouse

Link, W.A.; Cam, E.; Nichols, J.D.; Cooch, E.G.

2002-01-01

Markov chain Monte Carlo (MCMC) is a statistical innovation that allows researchers to fit far more complex models to data than is feasible using conventional methods. Despite its widespread use in a variety of scientific fields, MCMC appears to be underutilized in wildlife applications. This may be due to a misconception that MCMC requires the adoption of a subjective Bayesian analysis, or perhaps simply to its lack of familiarity among wildlife researchers. We introduce the basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling), stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathematical sophistication. We illustrate the use of MCMC with an analysis of the association between latent factors governing individual heterogeneity in breeding and survival rates of kittiwakes (Rissa tridactyla). We conclude with a discussion of the importance of individual heterogeneity for understanding population dynamics and designing management plans.

Bayesian Inference for Source Term Estimation: Application to the International Monitoring System Radionuclide Network

DTIC Science & Technology

2014-10-01

de l’exactitude et de la précision), comparativement au modèle de mesure plus simple qui n’utilise pas de multiplicateurs. Importance pour la défense...3) Bayesian experimental design for receptor placement in order to maximize the expected information in the measured concen- tration data for...applications of the Bayesian inferential methodology for source recon- struction have used high-quality concentration data from well- designed atmospheric

On the Bayesian Nonparametric Generalization of IRT-Type Models

ERIC Educational Resources Information Center

San Martin, Ernesto; Jara, Alejandro; Rolin, Jean-Marie; Mouchart, Michel

2011-01-01

We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general…

Back to BaySICS: a user-friendly program for Bayesian Statistical Inference from Coalescent Simulations.

PubMed

Sandoval-Castellanos, Edson; Palkopoulou, Eleftheria; Dalén, Love

2014-01-01

Inference of population demographic history has vastly improved in recent years due to a number of technological and theoretical advances including the use of ancient DNA. Approximate Bayesian computation (ABC) stands among the most promising methods due to its simple theoretical fundament and exceptional flexibility. However, limited availability of user-friendly programs that perform ABC analysis renders it difficult to implement, and hence programming skills are frequently required. In addition, there is limited availability of programs able to deal with heterochronous data. Here we present the software BaySICS: Bayesian Statistical Inference of Coalescent Simulations. BaySICS provides an integrated and user-friendly platform that performs ABC analyses by means of coalescent simulations from DNA sequence data. It estimates historical demographic population parameters and performs hypothesis testing by means of Bayes factors obtained from model comparisons. Although providing specific features that improve inference from datasets with heterochronous data, BaySICS also has several capabilities making it a suitable tool for analysing contemporary genetic datasets. Those capabilities include joint analysis of independent tables, a graphical interface and the implementation of Markov-chain Monte Carlo without likelihoods.

A Simple Approach to Inference in Covariance Structure Modeling with Missing Data: Bayesian Analysis. Project 2.4, Quantitative Models To Monitor the Status and Progress of Learning and Performance and Their Antecedents.

ERIC Educational Resources Information Center

Muthen, Bengt

This paper investigates methods that avoid using multiple groups to represent the missing data patterns in covariance structure modeling, attempting instead to do a single-group analysis where the only action the analyst has to take is to indicate that data is missing. A new covariance structure approach developed by B. Muthen and G. Arminger is…

The influence of baseline marijuana use on treatment of cocaine dependence: application of an informative-priors bayesian approach.

PubMed

Green, Charles; Schmitz, Joy; Lindsay, Jan; Pedroza, Claudia; Lane, Scott; Agnelli, Rob; Kjome, Kimberley; Moeller, F Gerard

2012-01-01

Marijuana use is prevalent among patients with cocaine dependence and often non-exclusionary in clinical trials of potential cocaine medications. The dual-focus of this study was to (1) examine the moderating effect of baseline marijuana use on response to treatment with levodopa/carbidopa for cocaine dependence; and (2) apply an informative-priors, Bayesian approach for estimating the probability of a subgroup-by-treatment interaction effect. A secondary data analysis of two previously published, double-blind, randomized controlled trials provided complete data for the historical (Study 1: N = 64 placebo), and current (Study 2: N = 113) data sets. Negative binomial regression evaluated Treatment Effectiveness Scores (TES) as a function of medication condition (levodopa/carbidopa, placebo), baseline marijuana use (days in past 30), and their interaction. Bayesian analysis indicated that there was a 96% chance that baseline marijuana use predicts differential response to treatment with levodopa/carbidopa. Simple effects indicated that among participants receiving levodopa/carbidopa the probability that baseline marijuana confers harm in terms of reducing TES was 0.981; whereas the probability that marijuana confers harm within the placebo condition was 0.163. For every additional day of marijuana use reported at baseline, participants in the levodopa/carbidopa condition demonstrated a 5.4% decrease in TES; while participants in the placebo condition demonstrated a 4.9% increase in TES. The potential moderating effect of marijuana on cocaine treatment response should be considered in future trial designs. Applying Bayesian subgroup analysis proved informative in characterizing this patient-treatment interaction effect.

The Influence of Baseline Marijuana Use on Treatment of Cocaine Dependence: Application of an Informative-Priors Bayesian Approach

PubMed Central

Green, Charles; Schmitz, Joy; Lindsay, Jan; Pedroza, Claudia; Lane, Scott; Agnelli, Rob; Kjome, Kimberley; Moeller, F. Gerard

2012-01-01

Background: Marijuana use is prevalent among patients with cocaine dependence and often non-exclusionary in clinical trials of potential cocaine medications. The dual-focus of this study was to (1) examine the moderating effect of baseline marijuana use on response to treatment with levodopa/carbidopa for cocaine dependence; and (2) apply an informative-priors, Bayesian approach for estimating the probability of a subgroup-by-treatment interaction effect. Method: A secondary data analysis of two previously published, double-blind, randomized controlled trials provided complete data for the historical (Study 1: N = 64 placebo), and current (Study 2: N = 113) data sets. Negative binomial regression evaluated Treatment Effectiveness Scores (TES) as a function of medication condition (levodopa/carbidopa, placebo), baseline marijuana use (days in past 30), and their interaction. Results: Bayesian analysis indicated that there was a 96% chance that baseline marijuana use predicts differential response to treatment with levodopa/carbidopa. Simple effects indicated that among participants receiving levodopa/carbidopa the probability that baseline marijuana confers harm in terms of reducing TES was 0.981; whereas the probability that marijuana confers harm within the placebo condition was 0.163. For every additional day of marijuana use reported at baseline, participants in the levodopa/carbidopa condition demonstrated a 5.4% decrease in TES; while participants in the placebo condition demonstrated a 4.9% increase in TES. Conclusion: The potential moderating effect of marijuana on cocaine treatment response should be considered in future trial designs. Applying Bayesian subgroup analysis proved informative in characterizing this patient-treatment interaction effect. PMID:23115553

A Bayesian Beta-Mixture Model for Nonparametric IRT (BBM-IRT)

ERIC Educational Resources Information Center

Arenson, Ethan A.; Karabatsos, George

2017-01-01

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model…

How Recent History Affects Perception: The Normative Approach and Its Heuristic Approximation

PubMed Central

Raviv, Ofri; Ahissar, Merav; Loewenstein, Yonatan

2012-01-01

There is accumulating evidence that prior knowledge about expectations plays an important role in perception. The Bayesian framework is the standard computational approach to explain how prior knowledge about the distribution of expected stimuli is incorporated with noisy observations in order to improve performance. However, it is unclear what information about the prior distribution is acquired by the perceptual system over short periods of time and how this information is utilized in the process of perceptual decision making. Here we address this question using a simple two-tone discrimination task. We find that the “contraction bias”, in which small magnitudes are overestimated and large magnitudes are underestimated, dominates the pattern of responses of human participants. This contraction bias is consistent with the Bayesian hypothesis in which the true prior information is available to the decision-maker. However, a trial-by-trial analysis of the pattern of responses reveals that the contribution of most recent trials to performance is overweighted compared with the predictions of a standard Bayesian model. Moreover, we study participants' performance in a-typical distributions of stimuli and demonstrate substantial deviations from the ideal Bayesian detector, suggesting that the brain utilizes a heuristic approximation of the Bayesian inference. We propose a biologically plausible model, in which decision in the two-tone discrimination task is based on a comparison between the second tone and an exponentially-decaying average of the first tone and past tones. We show that this model accounts for both the contraction bias and the deviations from the ideal Bayesian detector hypothesis. These findings demonstrate the power of Bayesian-like heuristics in the brain, as well as their limitations in their failure to fully adapt to novel environments. PMID:23133343

Radiation dose reduction in computed tomography perfusion using spatial-temporal Bayesian methods

NASA Astrophysics Data System (ADS)

Fang, Ruogu; Raj, Ashish; Chen, Tsuhan; Sanelli, Pina C.

2012-03-01

In current computed tomography (CT) examinations, the associated X-ray radiation dose is of significant concern to patients and operators, especially CT perfusion (CTP) imaging that has higher radiation dose due to its cine scanning technique. A simple and cost-effective means to perform the examinations is to lower the milliampere-seconds (mAs) parameter as low as reasonably achievable in data acquisition. However, lowering the mAs parameter will unavoidably increase data noise and degrade CT perfusion maps greatly if no adequate noise control is applied during image reconstruction. To capture the essential dynamics of CT perfusion, a simple spatial-temporal Bayesian method that uses a piecewise parametric model of the residual function is used, and then the model parameters are estimated from a Bayesian formulation of prior smoothness constraints on perfusion parameters. From the fitted residual function, reliable CTP parameter maps are obtained from low dose CT data. The merit of this scheme exists in the combination of analytical piecewise residual function with Bayesian framework using a simpler prior spatial constrain for CT perfusion application. On a dataset of 22 patients, this dynamic spatial-temporal Bayesian model yielded an increase in signal-tonoise-ratio (SNR) of 78% and a decrease in mean-square-error (MSE) of 40% at low dose radiation of 43mA.

BOP2: Bayesian optimal design for phase II clinical trials with simple and complex endpoints.

PubMed

Zhou, Heng; Lee, J Jack; Yuan, Ying

2017-09-20

We propose a flexible Bayesian optimal phase II (BOP2) design that is capable of handling simple (e.g., binary) and complicated (e.g., ordinal, nested, and co-primary) endpoints under a unified framework. We use a Dirichlet-multinomial model to accommodate different types of endpoints. At each interim, the go/no-go decision is made by evaluating a set of posterior probabilities of the events of interest, which is optimized to maximize power or minimize the number of patients under the null hypothesis. Unlike other existing Bayesian designs, the BOP2 design explicitly controls the type I error rate, thereby bridging the gap between Bayesian designs and frequentist designs. In addition, the stopping boundary of the BOP2 design can be enumerated prior to the onset of the trial. These features make the BOP2 design accessible to a wide range of users and regulatory agencies and particularly easy to implement in practice. Simulation studies show that the BOP2 design has favorable operating characteristics with higher power and lower risk of incorrectly terminating the trial than some existing Bayesian phase II designs. The software to implement the BOP2 design is freely available at www.trialdesign.org. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Bias in logistic regression due to imperfect diagnostic test results and practical correction approaches.

PubMed

Valle, Denis; Lima, Joanna M Tucker; Millar, Justin; Amratia, Punam; Haque, Ubydul

2015-11-04

Logistic regression is a statistical model widely used in cross-sectional and cohort studies to identify and quantify the effects of potential disease risk factors. However, the impact of imperfect tests on adjusted odds ratios (and thus on the identification of risk factors) is under-appreciated. The purpose of this article is to draw attention to the problem associated with modelling imperfect diagnostic tests, and propose simple Bayesian models to adequately address this issue. A systematic literature review was conducted to determine the proportion of malaria studies that appropriately accounted for false-negatives/false-positives in a logistic regression setting. Inference from the standard logistic regression was also compared with that from three proposed Bayesian models using simulations and malaria data from the western Brazilian Amazon. A systematic literature review suggests that malaria epidemiologists are largely unaware of the problem of using logistic regression to model imperfect diagnostic test results. Simulation results reveal that statistical inference can be substantially improved when using the proposed Bayesian models versus the standard logistic regression. Finally, analysis of original malaria data with one of the proposed Bayesian models reveals that microscopy sensitivity is strongly influenced by how long people have lived in the study region, and an important risk factor (i.e., participation in forest extractivism) is identified that would have been missed by standard logistic regression. Given the numerous diagnostic methods employed by malaria researchers and the ubiquitous use of logistic regression to model the results of these diagnostic tests, this paper provides critical guidelines to improve data analysis practice in the presence of misclassification error. Easy-to-use code that can be readily adapted to WinBUGS is provided, enabling straightforward implementation of the proposed Bayesian models.

QUEST - A Bayesian adaptive psychometric method

NASA Technical Reports Server (NTRS)

Watson, A. B.; Pelli, D. G.

1983-01-01

An adaptive psychometric procedure that places each trial at the current most probable Bayesian estimate of threshold is described. The procedure takes advantage of the common finding that the human psychometric function is invariant in form when expressed as a function of log intensity. The procedure is simple, fast, and efficient, and may be easily implemented on any computer.

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

NASA Astrophysics Data System (ADS)

Mélèse, Victor; Blanchet, Juliette; Molinié, Gilles

2018-03-01

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

Bayesian outcome-based strategy classification.

PubMed

Lee, Michael D

2016-03-01

Hilbig and Moshagen (Psychonomic Bulletin & Review, 21, 1431-1443, 2014) recently developed a method for making inferences about the decision processes people use in multi-attribute forced choice tasks. Their paper makes a number of worthwhile theoretical and methodological contributions. Theoretically, they provide an insightful psychological motivation for a probabilistic extension of the widely-used "weighted additive" (WADD) model, and show how this model, as well as other important models like "take-the-best" (TTB), can and should be expressed in terms of meaningful priors. Methodologically, they develop an inference approach based on the Minimum Description Length (MDL) principles that balances both the goodness-of-fit and complexity of the decision models they consider. This paper aims to preserve these useful contributions, but provide a complementary Bayesian approach with some theoretical and methodological advantages. We develop a simple graphical model, implemented in JAGS, that allows for fully Bayesian inferences about which models people use to make decisions. To demonstrate the Bayesian approach, we apply it to the models and data considered by Hilbig and Moshagen (Psychonomic Bulletin & Review, 21, 1431-1443, 2014), showing how a prior predictive analysis of the models, and posterior inferences about which models people use and the parameter settings at which they use them, can contribute to our understanding of human decision making.

Heuristic Bayesian segmentation for discovery of coexpressed genes within genomic regions.

PubMed

Pehkonen, Petri; Wong, Garry; Törönen, Petri

2010-01-01

Segmentation aims to separate homogeneous areas from the sequential data, and plays a central role in data mining. It has applications ranging from finance to molecular biology, where bioinformatics tasks such as genome data analysis are active application fields. In this paper, we present a novel application of segmentation in locating genomic regions with coexpressed genes. We aim at automated discovery of such regions without requirement for user-given parameters. In order to perform the segmentation within a reasonable time, we use heuristics. Most of the heuristic segmentation algorithms require some decision on the number of segments. This is usually accomplished by using asymptotic model selection methods like the Bayesian information criterion. Such methods are based on some simplification, which can limit their usage. In this paper, we propose a Bayesian model selection to choose the most proper result from heuristic segmentation. Our Bayesian model presents a simple prior for the segmentation solutions with various segment numbers and a modified Dirichlet prior for modeling multinomial data. We show with various artificial data sets in our benchmark system that our model selection criterion has the best overall performance. The application of our method in yeast cell-cycle gene expression data reveals potential active and passive regions of the genome.

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

PubMed

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

2013-12-01

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

Bayesian truthing and experimental validation in homeland security and defense

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Forrester, Thomas; Wang, Wenjian; Kostrzewski, Andrew; Pradhan, Ranjit

2014-05-01

In this paper we discuss relations between Bayesian Truthing (experimental validation), Bayesian statistics, and Binary Sensing in the context of selected Homeland Security and Intelligence, Surveillance, Reconnaissance (ISR) optical and nonoptical application scenarios. The basic Figure of Merit (FoM) is Positive Predictive Value (PPV), as well as false positives and false negatives. By using these simple binary statistics, we can analyze, classify, and evaluate a broad variety of events including: ISR; natural disasters; QC; and terrorism-related, GIS-related, law enforcement-related, and other C3I events.

Heuristics as Bayesian inference under extreme priors.

PubMed

Parpart, Paula; Jones, Matt; Love, Bradley C

2018-05-01

Simple heuristics are often regarded as tractable decision strategies because they ignore a great deal of information in the input data. One puzzle is why heuristics can outperform full-information models, such as linear regression, which make full use of the available information. These "less-is-more" effects, in which a relatively simpler model outperforms a more complex model, are prevalent throughout cognitive science, and are frequently argued to demonstrate an inherent advantage of simplifying computation or ignoring information. In contrast, we show at the computational level (where algorithmic restrictions are set aside) that it is never optimal to discard information. Through a formal Bayesian analysis, we prove that popular heuristics, such as tallying and take-the-best, are formally equivalent to Bayesian inference under the limit of infinitely strong priors. Varying the strength of the prior yields a continuum of Bayesian models with the heuristics at one end and ordinary regression at the other. Critically, intermediate models perform better across all our simulations, suggesting that down-weighting information with the appropriate prior is preferable to entirely ignoring it. Rather than because of their simplicity, our analyses suggest heuristics perform well because they implement strong priors that approximate the actual structure of the environment. We end by considering how new heuristics could be derived by infinitely strengthening the priors of other Bayesian models. These formal results have implications for work in psychology, machine learning and economics. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

A simple Bayesian approach to quantifying confidence level of adverse event incidence proportion in small samples.

PubMed

Liu, Fang

2016-01-01

In both clinical development and post-marketing of a new therapy or a new treatment, incidence of an adverse event (AE) is always a concern. When sample sizes are small, large sample-based inferential approaches on an AE incidence proportion in a certain time period no longer apply. In this brief discussion, we introduce a simple Bayesian framework to quantify, in small sample studies and the rare AE case, (1) the confidence level that the incidence proportion of a particular AE p is over or below a threshold, (2) the lower or upper bounds on p with a certain level of confidence, and (3) the minimum required number of patients with an AE before we can be certain that p surpasses a specific threshold, or the maximum allowable number of patients with an AE after which we can no longer be certain that p is below a certain threshold, given a certain confidence level. The method is easy to understand and implement; the interpretation of the results is intuitive. This article also demonstrates the usefulness of simple Bayesian concepts when it comes to answering practical questions.

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.

Data analysis using scale-space filtering and Bayesian probabilistic reasoning

NASA Technical Reports Server (NTRS)

Kulkarni, Deepak; Kutulakos, Kiriakos; Robinson, Peter

1991-01-01

This paper describes a program for analysis of output curves from Differential Thermal Analyzer (DTA). The program first extracts probabilistic qualitative features from a DTA curve of a soil sample, and then uses Bayesian probabilistic reasoning to infer the mineral in the soil. The qualifier module employs a simple and efficient extension of scale-space filtering suitable for handling DTA data. We have observed that points can vanish from contours in the scale-space image when filtering operations are not highly accurate. To handle the problem of vanishing points, perceptual organizations heuristics are used to group the points into lines. Next, these lines are grouped into contours by using additional heuristics. Probabilities are associated with these contours using domain-specific correlations. A Bayes tree classifier processes probabilistic features to infer the presence of different minerals in the soil. Experiments show that the algorithm that uses domain-specific correlation to infer qualitative features outperforms a domain-independent algorithm that does not.

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

PubMed

Chung, Yujin; Hey, Jody

2017-06-01

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

Comparison between the basic least squares and the Bayesian approach for elastic constants identification

NASA Astrophysics Data System (ADS)

Gogu, C.; Haftka, R.; LeRiche, R.; Molimard, J.; Vautrin, A.; Sankar, B.

2008-11-01

The basic formulation of the least squares method, based on the L2 norm of the misfit, is still widely used today for identifying elastic material properties from experimental data. An alternative statistical approach is the Bayesian method. We seek here situations with significant difference between the material properties found by the two methods. For a simple three bar truss example we illustrate three such situations in which the Bayesian approach leads to more accurate results: different magnitude of the measurements, different uncertainty in the measurements and correlation among measurements. When all three effects add up, the Bayesian approach can have a large advantage. We then compared the two methods for identification of elastic constants from plate vibration natural frequencies.

Multinomial Bayesian learning for modeling classical and nonclassical receptive field properties.

PubMed

Hosoya, Haruo

2012-08-01

We study the interplay of Bayesian inference and natural image learning in a hierarchical vision system, in relation to the response properties of early visual cortex. We particularly focus on a Bayesian network with multinomial variables that can represent discrete feature spaces similar to hypercolumns combining minicolumns, enforce sparsity of activation to learn efficient representations, and explain divisive normalization. We demonstrate that maximal-likelihood learning using sampling-based Bayesian inference gives rise to classical receptive field properties similar to V1 simple cells and V2 cells, while inference performed on the trained network yields nonclassical context-dependent response properties such as cross-orientation suppression and filling in. Comparison with known physiological properties reveals some qualitative and quantitative similarities.

Generative models for discovering sparse distributed representations.

PubMed Central

Hinton, G E; Ghahramani, Z

1997-01-01

We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottom-up, top-down and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demonstrate that the network learns to extract sparse, distributed, hierarchical representations. PMID:9304685

Analysis of femtosecond pump-probe photoelectron-photoion coincidence measurements applying Bayesian probability theory

NASA Astrophysics Data System (ADS)

Rumetshofer, M.; Heim, P.; Thaler, B.; Ernst, W. E.; Koch, M.; von der Linden, W.

2018-06-01

Ultrafast dynamical processes in photoexcited molecules can be observed with pump-probe measurements, in which information about the dynamics is obtained from the transient signal associated with the excited state. Background signals provoked by pump and/or probe pulses alone often obscure these excited-state signals. Simple subtraction of pump-only and/or probe-only measurements from the pump-probe measurement, as commonly applied, results in a degradation of the signal-to-noise ratio and, in the case of coincidence detection, the danger of overrated background subtraction. Coincidence measurements additionally suffer from false coincidences, requiring long data-acquisition times to keep erroneous signals at an acceptable level. Here we present a probabilistic approach based on Bayesian probability theory that overcomes these problems. For a pump-probe experiment with photoelectron-photoion coincidence detection, we reconstruct the interesting excited-state spectrum from pump-probe and pump-only measurements. This approach allows us to treat background and false coincidences consistently and on the same footing. We demonstrate that the Bayesian formalism has the following advantages over simple signal subtraction: (i) the signal-to-noise ratio is significantly increased, (ii) the pump-only contribution is not overestimated, (iii) false coincidences are excluded, (iv) prior knowledge, such as positivity, is consistently incorporated, (v) confidence intervals are provided for the reconstructed spectrum, and (vi) it is applicable to any experimental situation and noise statistics. Most importantly, by accounting for false coincidences, the Bayesian approach allows us to run experiments at higher ionization rates, resulting in a significant reduction of data acquisition times. The probabilistic approach is thoroughly scrutinized by challenging mock data. The application to pump-probe coincidence measurements on acetone molecules enables quantitative interpretations about the molecular decay dynamics and fragmentation behavior. All results underline the superiority of a consistent probabilistic approach over ad hoc estimations.

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

ERIC Educational Resources Information Center

van de Schoot, Rens; Kaplan, David; Denissen, Jaap; Asendorpf, Jens B.; Neyer, Franz J.; van Aken, Marcel A. G.

2014-01-01

Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are…

Multi-objective calibration and uncertainty analysis of hydrologic models; A comparative study between formal and informal methods

NASA Astrophysics Data System (ADS)

Shafii, M.; Tolson, B.; Matott, L. S.

2012-04-01

Hydrologic modeling has benefited from significant developments over the past two decades. This has resulted in building of higher levels of complexity into hydrologic models, which eventually makes the model evaluation process (parameter estimation via calibration and uncertainty analysis) more challenging. In order to avoid unreasonable parameter estimates, many researchers have suggested implementation of multi-criteria calibration schemes. Furthermore, for predictive hydrologic models to be useful, proper consideration of uncertainty is essential. Consequently, recent research has emphasized comprehensive model assessment procedures in which multi-criteria parameter estimation is combined with statistically-based uncertainty analysis routines such as Bayesian inference using Markov Chain Monte Carlo (MCMC) sampling. Such a procedure relies on the use of formal likelihood functions based on statistical assumptions, and moreover, the Bayesian inference structured on MCMC samplers requires a considerably large number of simulations. Due to these issues, especially in complex non-linear hydrological models, a variety of alternative informal approaches have been proposed for uncertainty analysis in the multi-criteria context. This study aims at exploring a number of such informal uncertainty analysis techniques in multi-criteria calibration of hydrological models. The informal methods addressed in this study are (i) Pareto optimality which quantifies the parameter uncertainty using the Pareto solutions, (ii) DDS-AU which uses the weighted sum of objective functions to derive the prediction limits, and (iii) GLUE which describes the total uncertainty through identification of behavioral solutions. The main objective is to compare such methods with MCMC-based Bayesian inference with respect to factors such as computational burden, and predictive capacity, which are evaluated based on multiple comparative measures. The measures for comparison are calculated both for calibration and evaluation periods. The uncertainty analysis methodologies are applied to a simple 5-parameter rainfall-runoff model, called HYMOD.

Bayesian data analysis in population ecology: motivations, methods, and benefits

USGS Publications Warehouse

Dorazio, Robert

2016-01-01

During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.

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.

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from hypothesis testing to estimation has been dubbed "the New Statistics" (Cumming 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to hypothesis testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Raymond, C.; Smrekar, S.; Millbury, C.

2004-01-01

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

Natural frequencies improve Bayesian reasoning in simple and complex inference tasks

PubMed Central

Hoffrage, Ulrich; Krauss, Stefan; Martignon, Laura; Gigerenzer, Gerd

2015-01-01

Representing statistical information in terms of natural frequencies rather than probabilities improves performance in Bayesian inference tasks. This beneficial effect of natural frequencies has been demonstrated in a variety of applied domains such as medicine, law, and education. Yet all the research and applications so far have been limited to situations where one dichotomous cue is used to infer which of two hypotheses is true. Real-life applications, however, often involve situations where cues (e.g., medical tests) have more than one value, where more than two hypotheses (e.g., diseases) are considered, or where more than one cue is available. In Study 1, we show that natural frequencies, compared to information stated in terms of probabilities, consistently increase the proportion of Bayesian inferences made by medical students in four conditions—three cue values, three hypotheses, two cues, or three cues—by an average of 37 percentage points. In Study 2, we show that teaching natural frequencies for simple tasks with one dichotomous cue and two hypotheses leads to a transfer of learning to complex tasks with three cue values and two cues, with a proportion of 40 and 81% correct inferences, respectively. Thus, natural frequencies facilitate Bayesian reasoning in a much broader class of situations than previously thought. PMID:26528197

Adversarial risk analysis with incomplete information: a level-k approach.

PubMed

Rothschild, Casey; McLay, Laura; Guikema, Seth

2012-07-01

This article proposes, develops, and illustrates the application of level-k game theory to adversarial risk analysis. Level-k reasoning, which assumes that players play strategically but have bounded rationality, is useful for operationalizing a Bayesian approach to adversarial risk analysis. It can be applied in a broad class of settings, including settings with asynchronous play and partial but incomplete revelation of early moves. Its computational and elicitation requirements are modest. We illustrate the approach with an application to a simple defend-attack model in which the defender's countermeasures are revealed with a probability less than one to the attacker before he decides on how or whether to attack. © 2011 Society for Risk Analysis.

Bayesian function-on-function regression for multilevel functional data.

PubMed

Meyer, Mark J; Coull, Brent A; Versace, Francesco; Cinciripini, Paul; Morris, Jeffrey S

2015-09-01

Medical and public health research increasingly involves the collection of complex and high dimensional data. In particular, functional data-where the unit of observation is a curve or set of curves that are finely sampled over a grid-is frequently obtained. Moreover, researchers often sample multiple curves per person resulting in repeated functional measures. A common question is how to analyze the relationship between two functional variables. We propose a general function-on-function regression model for repeatedly sampled functional data on a fine grid, presenting a simple model as well as a more extensive mixed model framework, and introducing various functional Bayesian inferential procedures that account for multiple testing. We examine these models via simulation and a data analysis with data from a study that used event-related potentials to examine how the brain processes various types of images. © 2015, The International Biometric Society.

Bayesian Estimation of the Spatially Varying Completeness Magnitude of Earthquake Catalogs

NASA Astrophysics Data System (ADS)

Mignan, A.; Werner, M.; Wiemer, S.; Chen, C.; Wu, Y.

2010-12-01

Assessing the completeness magnitude Mc of earthquake catalogs is an essential prerequisite for any seismicity analysis. We employ a simple model to compute Mc in space, based on the proximity to seismic stations in a network. We show that a relationship of the form Mcpred(d) = ad^b+c, with d the distance to the 5th nearest seismic station, fits the observations well. We then propose a new Mc mapping approach, the Bayesian Magnitude of Completeness (BMC) method, based on a 2-step procedure: (1) a spatial resolution optimization to minimize spatial heterogeneities and uncertainties in Mc estimates and (2) a Bayesian approach that merges prior information about Mc based on the proximity to seismic stations with locally observed values weighted by their respective uncertainties. This new methodology eliminates most weaknesses associated with current Mc mapping procedures: the radius that defines which earthquakes to include in the local magnitude distribution is chosen according to an objective criterion and there are no gaps in the spatial estimation of Mc. The method solely requires the coordinates of seismic stations. Here, we investigate the Taiwan Central Weather Bureau (CWB) earthquake catalog by computing a Mc map for the period 1994-2010.

Is probabilistic bias analysis approximately Bayesian?

PubMed Central

MacLehose, Richard F.; Gustafson, Paul

2011-01-01

Case-control studies are particularly susceptible to differential exposure misclassification when exposure status is determined following incident case status. Probabilistic bias analysis methods have been developed as ways to adjust standard effect estimates based on the sensitivity and specificity of exposure misclassification. The iterative sampling method advocated in probabilistic bias analysis bears a distinct resemblance to a Bayesian adjustment; however, it is not identical. Furthermore, without a formal theoretical framework (Bayesian or frequentist), the results of a probabilistic bias analysis remain somewhat difficult to interpret. We describe, both theoretically and empirically, the extent to which probabilistic bias analysis can be viewed as approximately Bayesian. While the differences between probabilistic bias analysis and Bayesian approaches to misclassification can be substantial, these situations often involve unrealistic prior specifications and are relatively easy to detect. Outside of these special cases, probabilistic bias analysis and Bayesian approaches to exposure misclassification in case-control studies appear to perform equally well. PMID:22157311

Bayesian Mediation Analysis

ERIC Educational Resources Information Center

Yuan, Ying; MacKinnon, David P.

2009-01-01

In this article, we propose Bayesian analysis of mediation effects. Compared with conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian…

Prior approval: the growth of Bayesian methods in psychology.

PubMed

Andrews, Mark; Baguley, Thom

2013-02-01

Within the last few years, Bayesian methods of data analysis in psychology have proliferated. In this paper, we briefly review the history or the Bayesian approach to statistics, and consider the implications that Bayesian methods have for the theory and practice of data analysis in psychology.

Application of Inter-Simple Sequence Repeat Markers in the Analysis of Populations of the Chagas Disease Vector Triatoma infestans (Hemiptera, Reduviidae)

PubMed Central

Pérez de Rosas, Alicia R.; Restelli, María F.; Fernández, Cintia J.; Blariza, María J.; García, Beatriz A.

2017-01-01

Here we apply inter-simple sequence repeat (ISSR) markers to explore the fine-scale genetic structure and dispersal in populations of Triatoma infestans. Five selected primers from 30 primers were used to amplify ISSRs by polymerase chain reaction. A total of 90 polymorphic bands were detected across 134 individuals captured from 11 peridomestic sites from the locality of San Martín (Capayán Department, Catamarca Province, Argentina). Significant levels of genetic differentiation suggest limited gene flow among sampling sites. Spatial autocorrelation analysis confirms that dispersal occurs on the scale of ∼469 m, suggesting that insecticide spraying should be extended at least within a radius of ∼500 m around the infested area. Moreover, Bayesian clustering algorithms indicated genetic exchange among different sites analyzed, supporting the hypothesis of an important role of peridomestic structures in the process of reinfestation. PMID:28115670

Bayesian Model Averaging for Propensity Score Analysis

ERIC Educational Resources Information Center

Kaplan, David; Chen, Jianshen

2013-01-01

The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…

Bayesian statistics as a new tool for spectral analysis - I. Application for the determination of basic parameters of massive stars

NASA Astrophysics Data System (ADS)

Mugnes, J.-M.; Robert, C.

2015-11-01

Spectral analysis is a powerful tool to investigate stellar properties and it has been widely used for decades now. However, the methods considered to perform this kind of analysis are mostly based on iteration among a few diagnostic lines to determine the stellar parameters. While these methods are often simple and fast, they can lead to errors and large uncertainties due to the required assumptions. Here, we present a method based on Bayesian statistics to find simultaneously the best combination of effective temperature, surface gravity, projected rotational velocity, and microturbulence velocity, using all the available spectral lines. Different tests are discussed to demonstrate the strength of our method, which we apply to 54 mid-resolution spectra of field and cluster B stars obtained at the Observatoire du Mont-Mégantic. We compare our results with those found in the literature. Differences are seen which are well explained by the different methods used. We conclude that the B-star microturbulence velocities are often underestimated. We also confirm the trend that B stars in clusters are on average faster rotators than field B stars.

Bayesian analyses of time-interval data for environmental radiation monitoring.

PubMed

Luo, Peng; Sharp, Julia L; DeVol, Timothy A

2013-01-01

Time-interval (time difference between two consecutive pulses) analysis based on the principles of Bayesian inference was investigated for online radiation monitoring. Using experimental and simulated data, Bayesian analysis of time-interval data [Bayesian (ti)] was compared with Bayesian and a conventional frequentist analysis of counts in a fixed count time [Bayesian (cnt) and single interval test (SIT), respectively]. The performances of the three methods were compared in terms of average run length (ARL) and detection probability for several simulated detection scenarios. Experimental data were acquired with a DGF-4C system in list mode. Simulated data were obtained using Monte Carlo techniques to obtain a random sampling of the Poisson distribution. All statistical algorithms were developed using the R Project for statistical computing. Bayesian analysis of time-interval information provided a similar detection probability as Bayesian analysis of count information, but the authors were able to make a decision with fewer pulses at relatively higher radiation levels. In addition, for the cases with very short presence of the source (< count time), time-interval information is more sensitive to detect a change than count information since the source data is averaged by the background data over the entire count time. The relationships of the source time, change points, and modifications to the Bayesian approach for increasing detection probability are presented.

Robust Bayesian linear regression with application to an analysis of the CODATA values for the Planck constant

NASA Astrophysics Data System (ADS)

Wübbeler, Gerd; Bodnar, Olha; Elster, Clemens

2018-02-01

Weighted least-squares estimation is commonly applied in metrology to fit models to measurements that are accompanied with quoted uncertainties. The weights are chosen in dependence on the quoted uncertainties. However, when data and model are inconsistent in view of the quoted uncertainties, this procedure does not yield adequate results. When it can be assumed that all uncertainties ought to be rescaled by a common factor, weighted least-squares estimation may still be used, provided that a simple correction of the uncertainty obtained for the estimated model is applied. We show that these uncertainties and credible intervals are robust, as they do not rely on the assumption of a Gaussian distribution of the data. Hence, common software for weighted least-squares estimation may still safely be employed in such a case, followed by a simple modification of the uncertainties obtained by that software. We also provide means of checking the assumptions of such an approach. The Bayesian regression procedure is applied to analyze the CODATA values for the Planck constant published over the past decades in terms of three different models: a constant model, a straight line model and a spline model. Our results indicate that the CODATA values may not have yet stabilized.

Comparison of different strategies for using fossil calibrations to generate the time prior in Bayesian molecular clock dating.

PubMed

Barba-Montoya, Jose; Dos Reis, Mario; Yang, Ziheng

2017-09-01

Fossil calibrations are the utmost source of information for resolving the distances between molecular sequences into estimates of absolute times and absolute rates in molecular clock dating analysis. The quality of calibrations is thus expected to have a major impact on divergence time estimates even if a huge amount of molecular data is available. In Bayesian molecular clock dating, fossil calibration information is incorporated in the analysis through the prior on divergence times (the time prior). Here, we evaluate three strategies for converting fossil calibrations (in the form of minimum- and maximum-age bounds) into the prior on times, which differ according to whether they borrow information from the maximum age of ancestral nodes and minimum age of descendent nodes to form constraints for any given node on the phylogeny. We study a simple example that is analytically tractable, and analyze two real datasets (one of 10 primate species and another of 48 seed plant species) using three Bayesian dating programs: MCMCTree, MrBayes and BEAST2. We examine how different calibration strategies, the birth-death process, and automatic truncation (to enforce the constraint that ancestral nodes are older than descendent nodes) interact to determine the time prior. In general, truncation has a great impact on calibrations so that the effective priors on the calibration node ages after the truncation can be very different from the user-specified calibration densities. The different strategies for generating the effective prior also had considerable impact, leading to very different marginal effective priors. Arbitrary parameters used to implement minimum-bound calibrations were found to have a strong impact upon the prior and posterior of the divergence times. Our results highlight the importance of inspecting the joint time prior used by the dating program before any Bayesian dating analysis. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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.

A SAS Interface for Bayesian Analysis with WinBUGS

ERIC Educational Resources Information Center

Zhang, Zhiyong; McArdle, John J.; Wang, Lijuan; Hamagami, Fumiaki

2008-01-01

Bayesian methods are becoming very popular despite some practical difficulties in implementation. To assist in the practical application of Bayesian methods, we show how to implement Bayesian analysis with WinBUGS as part of a standard set of SAS routines. This implementation procedure is first illustrated by fitting a multiple regression model…

A Cross-Correlational Analysis between Electroencephalographic and End-Tidal Carbon Dioxide Signals: Methodological Issues in the Presence of Missing Data and Real Data Results

PubMed Central

Morelli, Maria Sole; Giannoni, Alberto; Passino, Claudio; Landini, Luigi; Emdin, Michele; Vanello, Nicola

2016-01-01

Electroencephalographic (EEG) irreducible artifacts are common and the removal of corrupted segments from the analysis may be required. The present study aims at exploring the effects of different EEG Missing Data Segment (MDS) distributions on cross-correlation analysis, involving EEG and physiological signals. The reliability of cross-correlation analysis both at single subject and at group level as a function of missing data statistics was evaluated using dedicated simulations. Moreover, a Bayesian-based approach for combining the single subject results at group level by considering each subject’s reliability was introduced. Starting from the above considerations, the cross-correlation function between EEG Global Field Power (GFP) in delta band and end-tidal CO2 (PETCO2) during rest and voluntary breath-hold was evaluated in six healthy subjects. The analysis of simulated data results at single subject level revealed a worsening of precision and accuracy in the cross-correlation analysis in the presence of MDS. At the group level, a large improvement in the results’ reliability with respect to single subject analysis was observed. The proposed Bayesian approach showed a slight improvement with respect to simple average results. Real data results were discussed in light of the simulated data tests and of the current physiological findings. PMID:27809243

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

PubMed Central

van de Schoot, Rens; Kaplan, David; Denissen, Jaap; Asendorpf, Jens B; Neyer, Franz J; van Aken, Marcel AG

2014-01-01

Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are introduced using a simplified example. Thereafter, the advantages and pitfalls of the specification of prior knowledge are discussed. To illustrate Bayesian methods explained in this study, in a second example a series of studies that examine the theoretical framework of dynamic interactionism are considered. In the Discussion the advantages and disadvantages of using Bayesian statistics are reviewed, and guidelines on how to report on Bayesian statistics are provided. PMID:24116396

APPLICATION OF BAYESIAN MONTE CARLO ANALYSIS TO A LAGRANGIAN PHOTOCHEMICAL AIR QUALITY MODEL. (R824792)

EPA Science Inventory

Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...

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

NASA Astrophysics Data System (ADS)

Kasibhatla, P.

2004-12-01

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

Structural mapping in statistical word problems: A relational reasoning approach to Bayesian inference.

PubMed

Johnson, Eric D; Tubau, Elisabet

2017-06-01

Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nevertheless, many people, including highly educated and skilled reasoners, still fail to provide Bayesian responses to these computationally simple problems. We show that the complexity of relational reasoning (e.g., the structural mapping between the presented and requested relations) can help explain the remaining difficulties. With a non-Bayesian inference that required identical arithmetic but afforded a more direct structural mapping, performance was universally high. Furthermore, reducing the relational demands of the task through questions that directed reasoners to use the presented statistics, as compared with questions that prompted the representation of a second, similar sample, also significantly improved reasoning. Distinct error patterns were also observed between these presented- and similar-sample scenarios, which suggested differences in relational-reasoning strategies. On the other hand, while higher numeracy was associated with better Bayesian reasoning, higher-numerate reasoners were not immune to the relational complexity of the task. Together, these findings validate the relational-reasoning view of Bayesian problem solving and highlight the importance of considering not only the presented task structure, but also the complexity of the structural alignment between the presented and requested relations.

Bayesian survival analysis in clinical trials: What methods are used in practice?

PubMed

Brard, Caroline; Le Teuff, Gwénaël; Le Deley, Marie-Cécile; Hampson, Lisa V

2017-02-01

Background Bayesian statistics are an appealing alternative to the traditional frequentist approach to designing, analysing, and reporting of clinical trials, especially in rare diseases. Time-to-event endpoints are widely used in many medical fields. There are additional complexities to designing Bayesian survival trials which arise from the need to specify a model for the survival distribution. The objective of this article was to critically review the use and reporting of Bayesian methods in survival trials. Methods A systematic review of clinical trials using Bayesian survival analyses was performed through PubMed and Web of Science databases. This was complemented by a full text search of the online repositories of pre-selected journals. Cost-effectiveness, dose-finding studies, meta-analyses, and methodological papers using clinical trials were excluded. Results In total, 28 articles met the inclusion criteria, 25 were original reports of clinical trials and 3 were re-analyses of a clinical trial. Most trials were in oncology (n = 25), were randomised controlled (n = 21) phase III trials (n = 13), and half considered a rare disease (n = 13). Bayesian approaches were used for monitoring in 14 trials and for the final analysis only in 14 trials. In the latter case, Bayesian survival analyses were used for the primary analysis in four cases, for the secondary analysis in seven cases, and for the trial re-analysis in three cases. Overall, 12 articles reported fitting Bayesian regression models (semi-parametric, n = 3; parametric, n = 9). Prior distributions were often incompletely reported: 20 articles did not define the prior distribution used for the parameter of interest. Over half of the trials used only non-informative priors for monitoring and the final analysis (n = 12) when it was specified. Indeed, no articles fitting Bayesian regression models placed informative priors on the parameter of interest. The prior for the treatment effect was based on historical data in only four trials. Decision rules were pre-defined in eight cases when trials used Bayesian monitoring, and in only one case when trials adopted a Bayesian approach to the final analysis. Conclusion Few trials implemented a Bayesian survival analysis and few incorporated external data into priors. There is scope to improve the quality of reporting of Bayesian methods in survival trials. Extension of the Consolidated Standards of Reporting Trials statement for reporting Bayesian clinical trials is recommended.

The Application of Bayesian Analysis to Issues in Developmental Research

ERIC Educational Resources Information Center

Walker, Lawrence J.; Gustafson, Paul; Frimer, Jeremy A.

2007-01-01

This article reviews the concepts and methods of Bayesian statistical analysis, which can offer innovative and powerful solutions to some challenging analytical problems that characterize developmental research. In this article, we demonstrate the utility of Bayesian analysis, explain its unique adeptness in some circumstances, address some…

A default Bayesian hypothesis test for mediation.

PubMed

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

2015-03-01

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

Bayesian Estimation and Inference Using Stochastic Electronics

PubMed Central

Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M.; Hamilton, Tara J.; Tapson, Jonathan; van Schaik, André

2016-01-01

In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream. PMID:27047326

Bayesian Estimation and Inference Using Stochastic Electronics.

PubMed

Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André

2016-01-01

In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

A Tutorial in Bayesian Potential Outcomes Mediation Analysis.

PubMed

Miočević, Milica; Gonzalez, Oscar; Valente, Matthew J; MacKinnon, David P

2018-01-01

Statistical mediation analysis is used to investigate intermediate variables in the relation between independent and dependent variables. Causal interpretation of mediation analyses is challenging because randomization of subjects to levels of the independent variable does not rule out the possibility of unmeasured confounders of the mediator to outcome relation. Furthermore, commonly used frequentist methods for mediation analysis compute the probability of the data given the null hypothesis, which is not the probability of a hypothesis given the data as in Bayesian analysis. Under certain assumptions, applying the potential outcomes framework to mediation analysis allows for the computation of causal effects, and statistical mediation in the Bayesian framework gives indirect effects probabilistic interpretations. This tutorial combines causal inference and Bayesian methods for mediation analysis so the indirect and direct effects have both causal and probabilistic interpretations. Steps in Bayesian causal mediation analysis are shown in the application to an empirical example.

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

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

Brown, Justin; Hund, Lauren

2017-02-01

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

A Bayesian blind survey for cold molecular gas in the Universe

NASA Astrophysics Data System (ADS)

Lentati, L.; Carilli, C.; Alexander, P.; Walter, F.; Decarli, R.

2014-10-01

A new Bayesian method for performing an image domain search for line-emitting galaxies is presented. The method uses both spatial and spectral information to robustly determine the source properties, employing either simple Gaussian, or other physically motivated models whilst using the evidence to determine the probability that the source is real. In this paper, we describe the method, and its application to both a simulated data set, and a blind survey for cold molecular gas using observations of the Hubble Deep Field-North taken with the Plateau de Bure Interferometer. We make a total of six robust detections in the survey, five of which have counterparts in other observing bands. We identify the most secure detections found in a previous investigation, while finding one new probable line source with an optical ID not seen in the previous analysis. This study acts as a pilot application of Bayesian statistics to future searches to be carried out both for low-J CO transitions of high-redshift galaxies using the Jansky Very Large Array (JVLA), and at millimetre wavelengths with Atacama Large Millimeter/submillimeter Array (ALMA), enabling the inference of robust scientific conclusions about the history of the molecular gas properties of star-forming galaxies in the Universe through cosmic time.

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.

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

PubMed Central

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

2015-01-01

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

When Absence of Evidence Is Evidence of Absence: Rational Inferences From Absent Data.

PubMed

Hsu, Anne S; Horng, Andy; Griffiths, Thomas L; Chater, Nick

2017-05-01

Identifying patterns in the world requires noticing not only unusual occurrences, but also unusual absences. We examined how people learn from absences, manipulating the extent to which an absence is expected. People can make two types of inferences from the absence of an event: either the event is possible but has not yet occurred, or the event never occurs. A rational analysis using Bayesian inference predicts that inferences from absent data should depend on how much the absence is expected to occur, with less probable absences being more salient. We tested this prediction in two experiments in which we elicited people's judgments about patterns in the data as a function of absence salience. We found that people were able to decide that absences either were mere coincidences or were indicative of a significant pattern in the data in a manner that was consistent with predictions of a simple Bayesian model. Copyright © 2016 Cognitive Science Society, Inc.

Testing averaged cosmology with type Ia supernovae and BAO data

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

Santos, B.; Alcaniz, J.S.; Coley, A.A.

An important problem in precision cosmology is the determination of the effects of averaging and backreaction on observational predictions, particularly in view of the wealth of new observational data and improved statistical techniques. In this paper, we discuss the observational viability of a class of averaged cosmologies which consist of a simple parametrized phenomenological two-scale backreaction model with decoupled spatial curvature parameters. We perform a Bayesian model selection analysis and find that this class of averaged phenomenological cosmological models is favored with respect to the standard ΛCDM cosmological scenario when a joint analysis of current SNe Ia and BAO datamore » is performed. In particular, the analysis provides observational evidence for non-trivial spatial curvature.« less

Using auxiliary information to improve wildlife disease surveillance when infected animals are not detected: a Bayesian approach

USGS Publications Warehouse

Heisey, Dennis M.; Jennelle, Christopher S.; Russell, Robin E.; Walsh, Daniel P.

2014-01-01

There are numerous situations in which it is important to determine whether a particular disease of interest is present in a free-ranging wildlife population. However adequate disease surveillance can be labor-intensive and expensive and thus there is substantial motivation to conduct it as efficiently as possible. Surveillance is often based on the assumption of a simple random sample, but this can almost always be improved upon if there is auxiliary information available about disease risk factors. We present a Bayesian approach to disease surveillance when auxiliary risk information is available which will usually allow for substantial improvements over simple random sampling. Others have employed risk weights in surveillance, but this can result in overly optimistic statements regarding freedom from disease due to not accounting for the uncertainty in the auxiliary information; our approach remedies this. We compare our Bayesian approach to a published example of risk weights applied to chronic wasting disease in deer in Colorado, and we also present calculations to examine when uncertainty in the auxiliary information has a serious impact on the risk weights approach. Our approach allows “apples-to-apples” comparisons of surveillance efficiencies between units where heterogeneous samples were collected

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus

2015-08-01

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

Incorporating uncertainty into medical decision making: an approach to unexpected test results.

PubMed

Bianchi, Matt T; Alexander, Brian M; Cash, Sydney S

2009-01-01

The utility of diagnostic tests derives from the ability to translate the population concepts of sensitivity and specificity into information that will be useful for the individual patient: the predictive value of the result. As the array of available diagnostic testing broadens, there is a temptation to de-emphasize history and physical findings and defer to the objective rigor of technology. However, diagnostic test interpretation is not always straightforward. One significant barrier to routine use of probability-based test interpretation is the uncertainty inherent in pretest probability estimation, the critical first step of Bayesian reasoning. The context in which this uncertainty presents the greatest challenge is when test results oppose clinical judgment. It is this situation when decision support would be most helpful. The authors propose a simple graphical approach that incorporates uncertainty in pretest probability and has specific application to the interpretation of unexpected results. This method quantitatively demonstrates how uncertainty in disease probability may be amplified when test results are unexpected (opposing clinical judgment), even for tests with high sensitivity and specificity. The authors provide a simple nomogram for determining whether an unexpected test result suggests that one should "switch diagnostic sides.'' This graphical framework overcomes the limitation of pretest probability uncertainty in Bayesian analysis and guides decision making when it is most challenging: interpretation of unexpected test results.

Probabilistic hindcasts and projections of the coupled climate, carbon cycle and Atlantic meridional overturning circulation system: a Bayesian fusion of century-scale observations with a simple model

NASA Astrophysics Data System (ADS)

Urban, Nathan M.; Keller, Klaus

2010-10-01

How has the Atlantic Meridional Overturning Circulation (AMOC) varied over the past centuries and what is the risk of an anthropogenic AMOC collapse? We report probabilistic projections of the future climate which improve on previous AMOC projection studies by (i) greatly expanding the considered observational constraints and (ii) carefully sampling the tail areas of the parameter probability distribution function (pdf). We use a Bayesian inversion to constrain a simple model of the coupled climate, carbon cycle and AMOC systems using observations to derive multicentury hindcasts and projections. Our hindcasts show considerable skill in representing the observational constraints. We show that robust AMOC risk estimates can require carefully sampling the parameter pdfs. We find a low probability of experiencing an AMOC collapse within the 21st century for a business-as-usual emissions scenario. The probability of experiencing an AMOC collapse within two centuries is 1/10. The probability of crossing a forcing threshold and triggering a future AMOC collapse (by 2300) is approximately 1/30 in the 21st century and over 1/3 in the 22nd. Given the simplicity of the model structure and uncertainty in the forcing assumptions, our analysis should be considered a proof of concept and the quantitative conclusions subject to severe caveats.

Bayesian Statistics for Biological Data: Pedigree Analysis

ERIC Educational Resources Information Center

Stanfield, William D.; Carlton, Matthew A.

2004-01-01

The use of Bayes' formula is applied to the biological problem of pedigree analysis to show that the Bayes' formula and non-Bayesian or "classical" methods of probability calculation give different answers. First year college students of biology can be introduced to the Bayesian statistics.

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.

Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy

NASA Astrophysics Data System (ADS)

Sharma, Sanjib

2017-08-01

Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in the number of papers that employ Monte Carlo based Bayesian analysis. New, efficient Monte Carlo based methods are continuously being developed and explored. In this review, we first explain the basics of Bayesian theory and discuss how to set up data analysis problems within this framework. Next, we provide an overview of various Monte Carlo based methods for performing Bayesian data analysis. Finally, we discuss advanced ideas that enable us to tackle complex problems and thus hold great promise for the future. We also distribute downloadable computer software (available at https://github.com/sanjibs/bmcmc/ ) that implements some of the algorithms and examples discussed here.

Power in Bayesian Mediation Analysis for Small Sample Research

PubMed Central

Miočević, Milica; MacKinnon, David P.; Levy, Roy

2018-01-01

It was suggested that Bayesian methods have potential for increasing power in mediation analysis (Koopman, Howe, Hollenbeck, & Sin, 2015; Yuan & MacKinnon, 2009). This paper compares the power of Bayesian credibility intervals for the mediated effect to the power of normal theory, distribution of the product, percentile, and bias-corrected bootstrap confidence intervals at N≤ 200. Bayesian methods with diffuse priors have power comparable to the distribution of the product and bootstrap methods, and Bayesian methods with informative priors had the most power. Varying degrees of precision of prior distributions were also examined. Increased precision led to greater power only when N≥ 100 and the effects were small, N < 60 and the effects were large, and N < 200 and the effects were medium. An empirical example from psychology illustrated a Bayesian analysis of the single mediator model from prior selection to interpreting results. PMID:29662296

Power in Bayesian Mediation Analysis for Small Sample Research.

PubMed

Miočević, Milica; MacKinnon, David P; Levy, Roy

2017-01-01

It was suggested that Bayesian methods have potential for increasing power in mediation analysis (Koopman, Howe, Hollenbeck, & Sin, 2015; Yuan & MacKinnon, 2009). This paper compares the power of Bayesian credibility intervals for the mediated effect to the power of normal theory, distribution of the product, percentile, and bias-corrected bootstrap confidence intervals at N≤ 200. Bayesian methods with diffuse priors have power comparable to the distribution of the product and bootstrap methods, and Bayesian methods with informative priors had the most power. Varying degrees of precision of prior distributions were also examined. Increased precision led to greater power only when N≥ 100 and the effects were small, N < 60 and the effects were large, and N < 200 and the effects were medium. An empirical example from psychology illustrated a Bayesian analysis of the single mediator model from prior selection to interpreting results.

Bayesian methods including nonrandomized study data increased the efficiency of postlaunch RCTs.

PubMed

Schmidt, Amand F; Klugkist, Irene; Klungel, Olaf H; Nielen, Mirjam; de Boer, Anthonius; Hoes, Arno W; Groenwold, Rolf H H

2015-04-01

Findings from nonrandomized studies on safety or efficacy of treatment in patient subgroups may trigger postlaunch randomized clinical trials (RCTs). In the analysis of such RCTs, results from nonrandomized studies are typically ignored. This study explores the trade-off between bias and power of Bayesian RCT analysis incorporating information from nonrandomized studies. A simulation study was conducted to compare frequentist with Bayesian analyses using noninformative and informative priors in their ability to detect interaction effects. In simulated subgroups, the effect of a hypothetical treatment differed between subgroups (odds ratio 1.00 vs. 2.33). Simulations varied in sample size, proportions of the subgroups, and specification of the priors. As expected, the results for the informative Bayesian analyses were more biased than those from the noninformative Bayesian analysis or frequentist analysis. However, because of a reduction in posterior variance, informative Bayesian analyses were generally more powerful to detect an effect. In scenarios where the informative priors were in the opposite direction of the RCT data, type 1 error rates could be 100% and power 0%. Bayesian methods incorporating data from nonrandomized studies can meaningfully increase power of interaction tests in postlaunch RCTs. Copyright © 2015 Elsevier Inc. All rights reserved.

Confidence of compliance: a Bayesian approach for percentile standards.

PubMed

McBride, G B; Ellis, J C

2001-04-01

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

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

PubMed

Gajewski, Byron J; Mayo, Matthew S

2006-08-15

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

An inquiry into computer understanding

NASA Technical Reports Server (NTRS)

Cheeseman, Peter

1988-01-01

The paper examines issues connected with the choice of the best method for representing and reasoning about common sense. McDermott (1978) has shown that a direct translation of common sense reasoning into logical form leads to insurmountable difficulties. It is shown, in the present work, that if Bayesian probability is used instead of logic as the language of such reasoning, none of the technical difficulties found in using logic arise. Bayesian inference is applied to a simple example of linguistic information to illustrate the potential of this type of inference for artificial intelligence.

Bayesian design of decision rules for failure detection

NASA Technical Reports Server (NTRS)

Chow, E. Y.; Willsky, A. S.

1984-01-01

The formulation of the decision making process of a failure detection algorithm as a Bayes sequential decision problem provides a simple conceptualization of the decision rule design problem. As the optimal Bayes rule is not computable, a methodology that is based on the Bayesian approach and aimed at a reduced computational requirement is developed for designing suboptimal rules. A numerical algorithm is constructed to facilitate the design and performance evaluation of these suboptimal rules. The result of applying this design methodology to an example shows that this approach is potentially a useful one.

Maximum a posteriori Bayesian estimation of mycophenolic Acid area under the concentration-time curve: is this clinically useful for dosage prediction yet?

PubMed

Staatz, Christine E; Tett, Susan E

2011-12-01

This review seeks to summarize the available data about Bayesian estimation of area under the plasma concentration-time curve (AUC) and dosage prediction for mycophenolic acid (MPA) and evaluate whether sufficient evidence is available for routine use of Bayesian dosage prediction in clinical practice. A literature search identified 14 studies that assessed the predictive performance of maximum a posteriori Bayesian estimation of MPA AUC and one report that retrospectively evaluated how closely dosage recommendations based on Bayesian forecasting achieved targeted MPA exposure. Studies to date have mostly been undertaken in renal transplant recipients, with limited investigation in patients treated with MPA for autoimmune disease or haematopoietic stem cell transplantation. All of these studies have involved use of the mycophenolate mofetil (MMF) formulation of MPA, rather than the enteric-coated mycophenolate sodium (EC-MPS) formulation. Bias associated with estimation of MPA AUC using Bayesian forecasting was generally less than 10%. However some difficulties with imprecision was evident, with values ranging from 4% to 34% (based on estimation involving two or more concentration measurements). Evaluation of whether MPA dosing decisions based on Bayesian forecasting (by the free website service https://pharmaco.chu-limoges.fr) achieved target drug exposure has only been undertaken once. When MMF dosage recommendations were applied by clinicians, a higher proportion (72-80%) of subsequent estimated MPA AUC values were within the 30-60 mg · h/L target range, compared with when dosage recommendations were not followed (only 39-57% within target range). Such findings provide evidence that Bayesian dosage prediction is clinically useful for achieving target MPA AUC. This study, however, was retrospective and focussed only on adult renal transplant recipients. Furthermore, in this study, Bayesian-generated AUC estimations and dosage predictions were not compared with a later full measured AUC but rather with a further AUC estimate based on a second Bayesian analysis. This study also provided some evidence that a useful monitoring schedule for MPA AUC following adult renal transplant would be every 2 weeks during the first month post-transplant, every 1-3 months between months 1 and 12, and each year thereafter. It will be interesting to see further validations in different patient groups using the free website service. In summary, the predictive performance of Bayesian estimation of MPA, comparing estimated with measured AUC values, has been reported in several studies. However, the next step of predicting dosages based on these Bayesian-estimated AUCs, and prospectively determining how closely these predicted dosages give drug exposure matching targeted AUCs, remains largely unaddressed. Further prospective studies are required, particularly in non-renal transplant patients and with the EC-MPS formulation. Other important questions remain to be answered, such as: do Bayesian forecasting methods devised to date use the best population pharmacokinetic models or most accurate algorithms; are the methods simple to use for routine clinical practice; do the algorithms actually improve dosage estimations beyond empirical recommendations in all groups that receive MPA therapy; and, importantly, do the dosage predictions, when followed, improve patient health outcomes?

Hierarchy Bayesian model based services awareness of high-speed optical access networks

NASA Astrophysics Data System (ADS)

Bai, Hui-feng

2018-03-01

As the speed of optical access networks soars with ever increasing multiple services, the service-supporting ability of optical access networks suffers greatly from the shortage of service awareness. Aiming to solve this problem, a hierarchy Bayesian model based services awareness mechanism is proposed for high-speed optical access networks. This approach builds a so-called hierarchy Bayesian model, according to the structure of typical optical access networks. Moreover, the proposed scheme is able to conduct simple services awareness operation in each optical network unit (ONU) and to perform complex services awareness from the whole view of system in optical line terminal (OLT). Simulation results show that the proposed scheme is able to achieve better quality of services (QoS), in terms of packet loss rate and time delay.

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Moving beyond qualitative evaluations of Bayesian models of cognition.

PubMed

Hemmer, Pernille; Tauber, Sean; Steyvers, Mark

2015-06-01

Bayesian models of cognition provide a powerful way to understand the behavior and goals of individuals from a computational point of view. Much of the focus in the Bayesian cognitive modeling approach has been on qualitative model evaluations, where predictions from the models are compared to data that is often averaged over individuals. In many cognitive tasks, however, there are pervasive individual differences. We introduce an approach to directly infer individual differences related to subjective mental representations within the framework of Bayesian models of cognition. In this approach, Bayesian data analysis methods are used to estimate cognitive parameters and motivate the inference process within a Bayesian cognitive model. We illustrate this integrative Bayesian approach on a model of memory. We apply the model to behavioral data from a memory experiment involving the recall of heights of people. A cross-validation analysis shows that the Bayesian memory model with inferred subjective priors predicts withheld data better than a Bayesian model where the priors are based on environmental statistics. In addition, the model with inferred priors at the individual subject level led to the best overall generalization performance, suggesting that individual differences are important to consider in Bayesian models of cognition.

A Preliminary Bayesian Analysis of Incomplete Longitudinal Data from a Small Sample: Methodological Advances in an International Comparative Study of Educational Inequality

ERIC Educational Resources Information Center

Hsieh, Chueh-An; Maier, Kimberly S.

2009-01-01

The capacity of Bayesian methods in estimating complex statistical models is undeniable. Bayesian data analysis is seen as having a range of advantages, such as an intuitive probabilistic interpretation of the parameters of interest, the efficient incorporation of prior information to empirical data analysis, model averaging and model selection.…

Informative Bayesian Type A uncertainty evaluation, especially applicable to a small number of observations

NASA Astrophysics Data System (ADS)

Cox, M.; Shirono, K.

2017-10-01

A criticism levelled at the Guide to the Expression of Uncertainty in Measurement (GUM) is that it is based on a mixture of frequentist and Bayesian thinking. In particular, the GUM’s Type A (statistical) uncertainty evaluations are frequentist, whereas the Type B evaluations, using state-of-knowledge distributions, are Bayesian. In contrast, making the GUM fully Bayesian implies, among other things, that a conventional objective Bayesian approach to Type A uncertainty evaluation for a number n of observations leads to the impractical consequence that n must be at least equal to 4, thus presenting a difficulty for many metrologists. This paper presents a Bayesian analysis of Type A uncertainty evaluation that applies for all n ≥slant 2 , as in the frequentist analysis in the current GUM. The analysis is based on assuming that the observations are drawn from a normal distribution (as in the conventional objective Bayesian analysis), but uses an informative prior based on lower and upper bounds for the standard deviation of the sampling distribution for the quantity under consideration. The main outcome of the analysis is a closed-form mathematical expression for the factor by which the standard deviation of the mean observation should be multiplied to calculate the required standard uncertainty. Metrological examples are used to illustrate the approach, which is straightforward to apply using a formula or look-up table.

Attention in a Bayesian Framework

PubMed Central

Whiteley, Louise; Sahani, Maneesh

2012-01-01

The behavioral phenomena of sensory attention are thought to reflect the allocation of a limited processing resource, but there is little consensus on the nature of the resource or why it should be limited. Here we argue that a fundamental bottleneck emerges naturally within Bayesian models of perception, and use this observation to frame a new computational account of the need for, and action of, attention – unifying diverse attentional phenomena in a way that goes beyond previous inferential, probabilistic and Bayesian models. Attentional effects are most evident in cluttered environments, and include both selective phenomena, where attention is invoked by cues that point to particular stimuli, and integrative phenomena, where attention is invoked dynamically by endogenous processing. However, most previous Bayesian accounts of attention have focused on describing relatively simple experimental settings, where cues shape expectations about a small number of upcoming stimuli and thus convey “prior” information about clearly defined objects. While operationally consistent with the experiments it seeks to describe, this view of attention as prior seems to miss many essential elements of both its selective and integrative roles, and thus cannot be easily extended to complex environments. We suggest that the resource bottleneck stems from the computational intractability of exact perceptual inference in complex settings, and that attention reflects an evolved mechanism for approximate inference which can be shaped to refine the local accuracy of perception. We show that this approach extends the simple picture of attention as prior, so as to provide a unified and computationally driven account of both selective and integrative attentional phenomena. PMID:22712010

Analysis of capture-recapture models with individual covariates using data augmentation

USGS Publications Warehouse

Royle, J. Andrew

2009-01-01

I consider the analysis of capture-recapture models with individual covariates that influence detection probability. Bayesian analysis of the joint likelihood is carried out using a flexible data augmentation scheme that facilitates analysis by Markov chain Monte Carlo methods, and a simple and straightforward implementation in freely available software. This approach is applied to a study of meadow voles (Microtus pennsylvanicus) in which auxiliary data on a continuous covariate (body mass) are recorded, and it is thought that detection probability is related to body mass. In a second example, the model is applied to an aerial waterfowl survey in which a double-observer protocol is used. The fundamental unit of observation is the cluster of individual birds, and the size of the cluster (a discrete covariate) is used as a covariate on detection probability.

Maximum Entropy Discrimination Poisson Regression for Software Reliability Modeling.

PubMed

Chatzis, Sotirios P; Andreou, Andreas S

2015-11-01

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

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

ERIC Educational Resources Information Center

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

2006-01-01

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

Characterization of background concentrations of contaminants using a mixture of normal distributions.

PubMed

Qian, Song S; Lyons, Regan E

2006-10-01

We present a Bayesian approach for characterizing background contaminant concentration distributions using data from sites that may have been contaminated. Our method, focused on estimation, resolves several technical problems of the existing methods sanctioned by the U.S. Environmental Protection Agency (USEPA) (a hypothesis testing based method), resulting in a simple and quick procedure for estimating background contaminant concentrations. The proposed Bayesian method is applied to two data sets from a federal facility regulated under the Resource Conservation and Restoration Act. The results are compared to background distributions identified using existing methods recommended by the USEPA. The two data sets represent low and moderate levels of censorship in the data. Although an unbiased estimator is elusive, we show that the proposed Bayesian estimation method will have a smaller bias than the EPA recommended method.

Learning Negotiation Policies Using IB3 and Bayesian Networks

NASA Astrophysics Data System (ADS)

Nalepa, Gislaine M.; Ávila, Bráulio C.; Enembreck, Fabrício; Scalabrin, Edson E.

This paper presents an intelligent offer policy in a negotiation environment, in which each agent involved learns the preferences of its opponent in order to improve its own performance. Each agent must also be able to detect drifts in the opponent's preferences so as to quickly adjust itself to their new offer policy. For this purpose, two simple learning techniques were first evaluated: (i) based on instances (IB3) and (ii) based on Bayesian Networks. Additionally, as its known that in theory group learning produces better results than individual/single learning, the efficiency of IB3 and Bayesian classifier groups were also analyzed. Finally, each decision model was evaluated in moments of concept drift, being the drift gradual, moderate or abrupt. Results showed that both groups of classifiers were able to effectively detect drifts in the opponent's preferences.

Practical differences among probabilities, possibilities, and credibilities

NASA Astrophysics Data System (ADS)

Grandin, Jean-Francois; Moulin, Caroline

2002-03-01

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

A comprehensive probabilistic analysis model of oil pipelines network based on Bayesian network

NASA Astrophysics Data System (ADS)

Zhang, C.; Qin, T. X.; Jiang, B.; Huang, C.

2018-02-01

Oil pipelines network is one of the most important facilities of energy transportation. But oil pipelines network accident may result in serious disasters. Some analysis models for these accidents have been established mainly based on three methods, including event-tree, accident simulation and Bayesian network. Among these methods, Bayesian network is suitable for probabilistic analysis. But not all the important influencing factors are considered and the deployment rule of the factors has not been established. This paper proposed a probabilistic analysis model of oil pipelines network based on Bayesian network. Most of the important influencing factors, including the key environment condition and emergency response are considered in this model. Moreover, the paper also introduces a deployment rule for these factors. The model can be used in probabilistic analysis and sensitive analysis of oil pipelines network accident.

Using SPM 12’s Second-Level Bayesian Inference Procedure for fMRI Analysis: Practical Guidelines for End Users

PubMed Central

Han, Hyemin; Park, Joonsuk

2018-01-01

Recent debates about the conventional traditional threshold used in the fields of neuroscience and psychology, namely P < 0.05, have spurred researchers to consider alternative ways to analyze fMRI data. A group of methodologists and statisticians have considered Bayesian inference as a candidate methodology. However, few previous studies have attempted to provide end users of fMRI analysis tools, such as SPM 12, with practical guidelines about how to conduct Bayesian inference. In the present study, we aim to demonstrate how to utilize Bayesian inference, Bayesian second-level inference in particular, implemented in SPM 12 by analyzing fMRI data available to public via NeuroVault. In addition, to help end users understand how Bayesian inference actually works in SPM 12, we examine outcomes from Bayesian second-level inference implemented in SPM 12 by comparing them with those from classical second-level inference. Finally, we provide practical guidelines about how to set the parameters for Bayesian inference and how to interpret the results, such as Bayes factors, from the inference. We also discuss the practical and philosophical benefits of Bayesian inference and directions for future research. PMID:29456498

An introduction to Bayesian statistics in health psychology.

PubMed

Depaoli, Sarah; Rus, Holly M; Clifton, James P; van de Schoot, Rens; Tiemensma, Jitske

2017-09-01

The aim of the current article is to provide a brief introduction to Bayesian statistics within the field of health psychology. Bayesian methods are increasing in prevalence in applied fields, and they have been shown in simulation research to improve the estimation accuracy of structural equation models, latent growth curve (and mixture) models, and hierarchical linear models. Likewise, Bayesian methods can be used with small sample sizes since they do not rely on large sample theory. In this article, we discuss several important components of Bayesian statistics as they relate to health-based inquiries. We discuss the incorporation and impact of prior knowledge into the estimation process and the different components of the analysis that should be reported in an article. We present an example implementing Bayesian estimation in the context of blood pressure changes after participants experienced an acute stressor. We conclude with final thoughts on the implementation of Bayesian statistics in health psychology, including suggestions for reviewing Bayesian manuscripts and grant proposals. We have also included an extensive amount of online supplementary material to complement the content presented here, including Bayesian examples using many different software programmes and an extensive sensitivity analysis examining the impact of priors.

Uncertainty aggregation and reduction in structure-material performance prediction

NASA Astrophysics Data System (ADS)

Hu, Zhen; Mahadevan, Sankaran; Ao, Dan

2018-02-01

An uncertainty aggregation and reduction framework is presented for structure-material performance prediction. Different types of uncertainty sources, structural analysis model, and material performance prediction model are connected through a Bayesian network for systematic uncertainty aggregation analysis. To reduce the uncertainty in the computational structure-material performance prediction model, Bayesian updating using experimental observation data is investigated based on the Bayesian network. It is observed that the Bayesian updating results will have large error if the model cannot accurately represent the actual physics, and that this error will be propagated to the predicted performance distribution. To address this issue, this paper proposes a novel uncertainty reduction method by integrating Bayesian calibration with model validation adaptively. The observation domain of the quantity of interest is first discretized into multiple segments. An adaptive algorithm is then developed to perform model validation and Bayesian updating over these observation segments sequentially. Only information from observation segments where the model prediction is highly reliable is used for Bayesian updating; this is found to increase the effectiveness and efficiency of uncertainty reduction. A composite rotorcraft hub component fatigue life prediction model, which combines a finite element structural analysis model and a material damage model, is used to demonstrate the proposed method.

A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study

ERIC Educational Resources Information Center

Kaplan, David; Chen, Jianshen

2012-01-01

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for…

Probability, statistics, and computational science.

PubMed

Beerenwinkel, Niko; Siebourg, Juliane

2012-01-01

In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent chapters.

New phiomorph rodents from the latest Eocene of Egypt, and the impact of Bayesian "clock"-based phylogenetic methods on estimates of basal hystricognath relationships and biochronology.

PubMed

Sallam, Hesham M; Seiffert, Erik R

2016-01-01

The Fayum Depression of Egypt has yielded fossils of hystricognathous rodents from multiple Eocene and Oligocene horizons that range in age from ∼37 to ∼30 Ma and document several phases in the early evolution of crown Hystricognathi and one of its major subclades, Phiomorpha. Here we describe two new genera and species of basal phiomorphs, Birkamys korai and Mubhammys vadumensis, based on rostra and maxillary and mandibular remains from the terminal Eocene (∼34 Ma) Fayum Locality 41 (L-41). Birkamys is the smallest known Paleogene hystricognath, has very simple molars, and, like derived Oligocene-to-Recent phiomorphs (but unlike contemporaneous and older taxa) apparently retained dP(4)∕4 late into life, with no evidence for P(4)∕4 eruption or formation. Mubhammys is very similar in dental morphology to Birkamys, and also shows no evidence for P(4)∕4 formation or eruption, but is considerably larger. Though parsimony analysis with all characters equally weighted places Birkamys and Mubhammys as sister taxa of extant Thryonomys to the exclusion of much younger relatives of that genus, all other methods (standard Bayesian inference, Bayesian "tip-dating," and parsimony analysis with scaled transitions between "fixed" and polymorphic states) place these species in more basal positions within Hystricognathi, as sister taxa of Oligocene-to-Recent phiomorphs. We also employ tip-dating as a means for estimating the ages of early hystricognath-bearing localities, many of which are not well-constrained by geological, geochronological, or biostratigraphic evidence. By simultaneously taking into account phylogeny, evolutionary rates, and uniform priors that appropriately encompass the range of possible ages for fossil localities, dating of tips in this Bayesian framework allows paleontologists to move beyond vague and assumption-laden "stage of evolution" arguments in biochronology to provide relatively rigorous age assessments of poorly-constrained faunas. This approach should become increasingly robust as estimates are combined from multiple independent analyses of distantly related clades, and is broadly applicable across the tree of life; as such it is deserving of paleontologists' close attention. Notably, in the example provided here, hystricognathous rodents from Libya and Namibia that are controversially considered to be of middle Eocene age are instead estimated to be of late Eocene and late Oligocene age, respectively. Finally, we reconstruct the evolution of first lower molar size among Paleogene African hystricognaths using a Bayesian approach; the results of this analysis reconstruct a rapid latest Eocene dwarfing event along the lineage leading to Birkamys.

Prior elicitation and Bayesian analysis of the Steroids for Corneal Ulcers Trial.

PubMed

See, Craig W; Srinivasan, Muthiah; Saravanan, Somu; Oldenburg, Catherine E; Esterberg, Elizabeth J; Ray, Kathryn J; Glaser, Tanya S; Tu, Elmer Y; Zegans, Michael E; McLeod, Stephen D; Acharya, Nisha R; Lietman, Thomas M

2012-12-01

To elicit expert opinion on the use of adjunctive corticosteroid therapy in bacterial corneal ulcers. To perform a Bayesian analysis of the Steroids for Corneal Ulcers Trial (SCUT), using expert opinion as a prior probability. The SCUT was a placebo-controlled trial assessing visual outcomes in patients receiving topical corticosteroids or placebo as adjunctive therapy for bacterial keratitis. Questionnaires were conducted at scientific meetings in India and North America to gauge expert consensus on the perceived benefit of corticosteroids as adjunct treatment. Bayesian analysis, using the questionnaire data as a prior probability and the primary outcome of SCUT as a likelihood, was performed. For comparison, an additional Bayesian analysis was performed using the results of the SCUT pilot study as a prior distribution. Indian respondents believed there to be a 1.21 Snellen line improvement, and North American respondents believed there to be a 1.24 line improvement with corticosteroid therapy. The SCUT primary outcome found a non-significant 0.09 Snellen line benefit with corticosteroid treatment. The results of the Bayesian analysis estimated a slightly greater benefit than did the SCUT primary analysis (0.19 lines verses 0.09 lines). Indian and North American experts had similar expectations on the effectiveness of corticosteroids in bacterial corneal ulcers; that corticosteroids would markedly improve visual outcomes. Bayesian analysis produced results very similar to those produced by the SCUT primary analysis. The similarity in result is likely due to the large sample size of SCUT and helps validate the results of SCUT.

Evolution of Associative Learning in Chemical Networks

PubMed Central

McGregor, Simon; Vasas, Vera; Husbands, Phil; Fernando, Chrisantha

2012-01-01

Organisms that can learn about their environment and modify their behaviour appropriately during their lifetime are more likely to survive and reproduce than organisms that do not. While associative learning – the ability to detect correlated features of the environment – has been studied extensively in nervous systems, where the underlying mechanisms are reasonably well understood, mechanisms within single cells that could allow associative learning have received little attention. Here, using in silico evolution of chemical networks, we show that there exists a diversity of remarkably simple and plausible chemical solutions to the associative learning problem, the simplest of which uses only one core chemical reaction. We then asked to what extent a linear combination of chemical concentrations in the network could approximate the ideal Bayesian posterior of an environment given the stimulus history so far? This Bayesian analysis revealed the ‘memory traces’ of the chemical network. The implication of this paper is that there is little reason to believe that a lack of suitable phenotypic variation would prevent associative learning from evolving in cell signalling, metabolic, gene regulatory, or a mixture of these networks in cells. PMID:23133353

Careful with Those Priors: A Note on Bayesian Estimation in Two-Parameter Logistic Item Response Theory Models

ERIC Educational Resources Information Center

Marcoulides, Katerina M.

2018-01-01

This study examined the use of Bayesian analysis methods for the estimation of item parameters in a two-parameter logistic item response theory model. Using simulated data under various design conditions with both informative and non-informative priors, the parameter recovery of Bayesian analysis methods were examined. Overall results showed that…

A bayesian approach to classification criteria for spectacled eiders

USGS Publications Warehouse

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

1996-01-01

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

Genetic biasing through cultural transmission: do simple Bayesian models of language evolution generalize?

PubMed

Dediu, Dan

2009-08-07

The recent Bayesian approaches to language evolution and change seem to suggest that genetic biases can impact on the characteristics of language, but, at the same time, that its cultural transmission can partially free it from these same genetic constraints. One of the current debates centres on the striking differences between sampling and a posteriori maximising Bayesian learners, with the first converging on the prior bias while the latter allows a certain freedom to language evolution. The present paper shows that this difference disappears if populations more complex than a single teacher and a single learner are considered, with the resulting behaviours more similar to the sampler. This suggests that generalisations based on the language produced by Bayesian agents in such homogeneous single agent chains are not warranted. It is not clear which of the assumptions in such models are responsible, but these findings seem to support the rising concerns on the validity of the "acquisitionist" assumption, whereby the locus of language change and evolution is taken to be the first language acquirers (children) as opposed to the competent language users (the adults).

Bayesian data analysis in observational comparative effectiveness research: rationale and examples.

PubMed

Olson, William H; Crivera, Concetta; Ma, Yi-Wen; Panish, Jessica; Mao, Lian; Lynch, Scott M

2013-11-01

Many comparative effectiveness research and patient-centered outcomes research studies will need to be observational for one or both of two reasons: first, randomized trials are expensive and time-consuming; and second, only observational studies can answer some research questions. It is generally recognized that there is a need to increase the scientific validity and efficiency of observational studies. Bayesian methods for the design and analysis of observational studies are scientifically valid and offer many advantages over frequentist methods, including, importantly, the ability to conduct comparative effectiveness research/patient-centered outcomes research more efficiently. Bayesian data analysis is being introduced into outcomes studies that we are conducting. Our purpose here is to describe our view of some of the advantages of Bayesian methods for observational studies and to illustrate both realized and potential advantages by describing studies we are conducting in which various Bayesian methods have been or could be implemented.

Non-ignorable missingness in logistic regression.

PubMed

Wang, Joanna J J; Bartlett, Mark; Ryan, Louise

2017-08-30

Nonresponses and missing data are common in observational studies. Ignoring or inadequately handling missing data may lead to biased parameter estimation, incorrect standard errors and, as a consequence, incorrect statistical inference and conclusions. We present a strategy for modelling non-ignorable missingness where the probability of nonresponse depends on the outcome. Using a simple case of logistic regression, we quantify the bias in regression estimates and show the observed likelihood is non-identifiable under non-ignorable missing data mechanism. We then adopt a selection model factorisation of the joint distribution as the basis for a sensitivity analysis to study changes in estimated parameters and the robustness of study conclusions against different assumptions. A Bayesian framework for model estimation is used as it provides a flexible approach for incorporating different missing data assumptions and conducting sensitivity analysis. Using simulated data, we explore the performance of the Bayesian selection model in correcting for bias in a logistic regression. We then implement our strategy using survey data from the 45 and Up Study to investigate factors associated with worsening health from the baseline to follow-up survey. Our findings have practical implications for the use of the 45 and Up Study data to answer important research questions relating to health and quality-of-life. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Norris, Jay P.; Jackson, Brad; Chiang, James

2013-01-01

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it-an improved and generalized version of Bayesian Blocks [Scargle 1998]-that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piece- wise linear and piecewise exponential representations, multivariate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by [Arias-Castro, Donoho and Huo 2003]. In the spirit of Reproducible Research [Donoho et al. (2008)] all of the code and data necessary to reproduce all of the figures in this paper are included as auxiliary material.

Using Bayesian analysis in repeated preclinical in vivo studies for a more effective use of animals.

PubMed

Walley, Rosalind; Sherington, John; Rastrick, Joe; Detrait, Eric; Hanon, Etienne; Watt, Gillian

2016-05-01

Whilst innovative Bayesian approaches are increasingly used in clinical studies, in the preclinical area Bayesian methods appear to be rarely used in the reporting of pharmacology data. This is particularly surprising in the context of regularly repeated in vivo studies where there is a considerable amount of data from historical control groups, which has potential value. This paper describes our experience with introducing Bayesian analysis for such studies using a Bayesian meta-analytic predictive approach. This leads naturally either to an informative prior for a control group as part of a full Bayesian analysis of the next study or using a predictive distribution to replace a control group entirely. We use quality control charts to illustrate study-to-study variation to the scientists and describe informative priors in terms of their approximate effective numbers of animals. We describe two case studies of animal models: the lipopolysaccharide-induced cytokine release model used in inflammation and the novel object recognition model used to screen cognitive enhancers, both of which show the advantage of a Bayesian approach over the standard frequentist analysis. We conclude that using Bayesian methods in stable repeated in vivo studies can result in a more effective use of animals, either by reducing the total number of animals used or by increasing the precision of key treatment differences. This will lead to clearer results and supports the "3Rs initiative" to Refine, Reduce and Replace animals in research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Approximate Bayesian evaluations of measurement uncertainty

NASA Astrophysics Data System (ADS)

Possolo, Antonio; Bodnar, Olha

2018-04-01

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

Bayesian linkage and segregation analysis: factoring the problem.

PubMed

Matthysse, S

2000-01-01

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

Development and comparison of Bayesian modularization method in uncertainty assessment of hydrological models

NASA Astrophysics Data System (ADS)

Li, L.; Xu, C.-Y.; Engeland, K.

2012-04-01

With respect to model calibration, parameter estimation and analysis of uncertainty sources, different approaches have been used in hydrological models. Bayesian method is one of the most widely used methods for uncertainty assessment of hydrological models, which incorporates different sources of information into a single analysis through Bayesian theorem. However, none of these applications can well treat the uncertainty in extreme flows of hydrological models' simulations. This study proposes a Bayesian modularization method approach in uncertainty assessment of conceptual hydrological models by considering the extreme flows. It includes a comprehensive comparison and evaluation of uncertainty assessments by a new Bayesian modularization method approach and traditional Bayesian models using the Metropolis Hasting (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions are used in combination with traditional Bayesian: the AR (1) plus Normal and time period independent model (Model 1), the AR (1) plus Normal and time period dependent model (Model 2) and the AR (1) plus multi-normal model (Model 3). The results reveal that (1) the simulations derived from Bayesian modularization method are more accurate with the highest Nash-Sutcliffe efficiency value, and (2) the Bayesian modularization method performs best in uncertainty estimates of entire flows and in terms of the application and computational efficiency. The study thus introduces a new approach for reducing the extreme flow's effect on the discharge uncertainty assessment of hydrological models via Bayesian. Keywords: extreme flow, uncertainty assessment, Bayesian modularization, hydrological model, WASMOD

A Primer on Bayesian Analysis for Experimental Psychopathologists

PubMed Central

Krypotos, Angelos-Miltiadis; Blanken, Tessa F.; Arnaudova, Inna; Matzke, Dora; Beckers, Tom

2016-01-01

The principal goals of experimental psychopathology (EPP) research are to offer insights into the pathogenic mechanisms of mental disorders and to provide a stable ground for the development of clinical interventions. The main message of the present article is that those goals are better served by the adoption of Bayesian statistics than by the continued use of null-hypothesis significance testing (NHST). In the first part of the article we list the main disadvantages of NHST and explain why those disadvantages limit the conclusions that can be drawn from EPP research. Next, we highlight the advantages of Bayesian statistics. To illustrate, we then pit NHST and Bayesian analysis against each other using an experimental data set from our lab. Finally, we discuss some challenges when adopting Bayesian statistics. We hope that the present article will encourage experimental psychopathologists to embrace Bayesian statistics, which could strengthen the conclusions drawn from EPP research. PMID:28748068

Testing students' e-learning via Facebook through Bayesian structural equation modeling.

PubMed

Salarzadeh Jenatabadi, Hashem; Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students' intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods' results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated.

Testing students’ e-learning via Facebook through Bayesian structural equation modeling

PubMed Central

Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students’ intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods’ results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated. PMID:28886019

Hypothesis testing on the fractal structure of behavioral sequences: the Bayesian assessment of scaling methodology.

PubMed

Moscoso del Prado Martín, Fermín

2013-12-01

I introduce the Bayesian assessment of scaling (BAS), a simple but powerful Bayesian hypothesis contrast methodology that can be used to test hypotheses on the scaling regime exhibited by a sequence of behavioral data. Rather than comparing parametric models, as typically done in previous approaches, the BAS offers a direct, nonparametric way to test whether a time series exhibits fractal scaling. The BAS provides a simpler and faster test than do previous methods, and the code for making the required computations is provided. The method also enables testing of finely specified hypotheses on the scaling indices, something that was not possible with the previously available methods. I then present 4 simulation studies showing that the BAS methodology outperforms the other methods used in the psychological literature. I conclude with a discussion of methodological issues on fractal analyses in experimental psychology. PsycINFO Database Record (c) 2014 APA, all rights reserved.

Bayesian median regression for temporal gene expression data

NASA Astrophysics Data System (ADS)

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

2007-09-01

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

Individual and population pharmacokinetic compartment analysis: a graphic procedure for quantification of predictive performance.

PubMed

Eksborg, Staffan

2013-01-01

Pharmacokinetic studies are important for optimizing of drug dosing, but requires proper validation of the used pharmacokinetic procedures. However, simple and reliable statistical methods suitable for evaluation of the predictive performance of pharmacokinetic analysis are essentially lacking. The aim of the present study was to construct and evaluate a graphic procedure for quantification of predictive performance of individual and population pharmacokinetic compartment analysis. Original data from previously published pharmacokinetic compartment analyses after intravenous, oral, and epidural administration, and digitized data, obtained from published scatter plots of observed vs predicted drug concentrations from population pharmacokinetic studies using the NPEM algorithm and NONMEM computer program and Bayesian forecasting procedures, were used for estimating the predictive performance according to the proposed graphical method and by the method of Sheiner and Beal. The graphical plot proposed in the present paper proved to be a useful tool for evaluation of predictive performance of both individual and population compartment pharmacokinetic analysis. The proposed method is simple to use and gives valuable information concerning time- and concentration-dependent inaccuracies that might occur in individual and population pharmacokinetic compartment analysis. Predictive performance can be quantified by the fraction of concentration ratios within arbitrarily specified ranges, e.g. within the range 0.8-1.2.

Evaluation of Bayesian Sequential Proportion Estimation Using Analyst Labels

NASA Technical Reports Server (NTRS)

Lennington, R. K.; Abotteen, K. M. (Principal Investigator)

1980-01-01

The author has identified the following significant results. A total of ten Large Area Crop Inventory Experiment Phase 3 blind sites and analyst-interpreter labels were used in a study to compare proportional estimates obtained by the Bayes sequential procedure with estimates obtained from simple random sampling and from Procedure 1. The analyst error rate using the Bayes technique was shown to be no greater than that for the simple random sampling. Also, the segment proportion estimates produced using this technique had smaller bias and mean squared errors than the estimates produced using either simple random sampling or Procedure 1.

Prior Elicitation and Bayesian Analysis of the Steroids for Corneal Ulcers Trial

PubMed Central

See, Craig W.; Srinivasan, Muthiah; Saravanan, Somu; Oldenburg, Catherine E.; Esterberg, Elizabeth J.; Ray, Kathryn J.; Glaser, Tanya S.; Tu, Elmer Y.; Zegans, Michael E.; McLeod, Stephen D.; Acharya, Nisha R.; Lietman, Thomas M.

2013-01-01

Purpose To elicit expert opinion on the use of adjunctive corticosteroid therapy in bacterial corneal ulcers. To perform a Bayesian analysis of the Steroids for Corneal Ulcers Trial (SCUT), using expert opinion as a prior probability. Methods The SCUT was a placebo-controlled trial assessing visual outcomes in patients receiving topical corticosteroids or placebo as adjunctive therapy for bacterial keratitis. Questionnaires were conducted at scientific meetings in India and North America to gauge expert consensus on the perceived benefit of corticosteroids as adjunct treatment. Bayesian analysis, using the questionnaire data as a prior probability and the primary outcome of SCUT as a likelihood, was performed. For comparison, an additional Bayesian analysis was performed using the results of the SCUT pilot study as a prior distribution. Results Indian respondents believed there to be a 1.21 Snellen line improvement, and North American respondents believed there to be a 1.24 line improvement with corticosteroid therapy. The SCUT primary outcome found a non-significant 0.09 Snellen line benefit with corticosteroid treatment. The results of the Bayesian analysis estimated a slightly greater benefit than did the SCUT primary analysis (0.19 lines verses 0.09 lines). Conclusion Indian and North American experts had similar expectations on the effectiveness of corticosteroids in bacterial corneal ulcers; that corticosteroids would markedly improve visual outcomes. Bayesian analysis produced results very similar to those produced by the SCUT primary analysis. The similarity in result is likely due to the large sample size of SCUT and helps validate the results of SCUT. PMID:23171211

Bayesian Methods for the Physical Sciences. Learning from Examples in Astronomy and Physics.

NASA Astrophysics Data System (ADS)

Andreon, Stefano; Weaver, Brian

2015-05-01

Chapter 1: This chapter presents some basic steps for performing a good statistical analysis, all summarized in about one page. Chapter 2: This short chapter introduces the basics of probability theory inan intuitive fashion using simple examples. It also illustrates, again with examples, how to propagate errors and the difference between marginal and profile likelihoods. Chapter 3: This chapter introduces the computational tools and methods that we use for sampling from the posterior distribution. Since all numerical computations, and Bayesian ones are no exception, may end in errors, we also provide a few tips to check that the numerical computation is sampling from the posterior distribution. Chapter 4: Many of the concepts of building, running, and summarizing the resultsof a Bayesian analysis are described with this step-by-step guide using a basic (Gaussian) model. The chapter also introduces examples using Poisson and Binomial likelihoods, and how to combine repeated independent measurements. Chapter 5: All statistical analyses make assumptions, and Bayesian analyses are no exception. This chapter emphasizes that results depend on data and priors (assumptions). We illustrate this concept with examples where the prior plays greatly different roles, from major to negligible. We also provide some advice on how to look for information useful for sculpting the prior. Chapter 6: In this chapter we consider examples for which we want to estimate more than a single parameter. These common problems include estimating location and spread. We also consider examples that require the modeling of two populations (one we are interested in and a nuisance population) or averaging incompatible measurements. We also introduce quite complex examples dealing with upper limits and with a larger-than-expected scatter. Chapter 7: Rarely is a sample randomly selected from the population we wish to study. Often, samples are affected by selection effects, e.g., easier-to-collect events or objects are over-represented in samples and difficult-to-collect are under-represented if not missing altogether. In this chapter we show how to account for non-random data collection to infer the properties of the population from the studied sample. Chapter 8: In this chapter we introduce regression models, i.e., how to fit (regress) one, or more quantities, against each other through a functional relationship and estimate any unknown parameters that dictate this relationship. Questions of interest include: how to deal with samples affected by selection effects? How does a rich data structure influence the fitted parameters? And what about non-linear multiple-predictor fits, upper/lower limits, measurements errors of different amplitudes and an intrinsic variety in the studied populations or an extra source of variability? A number of examples illustrate how to answer these questions and how to predict the value of an unavailable quantity by exploiting the existence of a trend with another, available, quantity. Chapter 9: This chapter provides some advice on how the careful scientist should perform model checking and sensitivity analysis, i.e., how to answer the following questions: is the considered model at odds with the current available data (the fitted data), for example because it is over-simplified compared to some specific complexity pointed out by the data? Furthermore, are the data informative about the quantity being measured or are results sensibly dependent on details of the fitted model? And, finally, what about if assumptions are uncertain? A number of examples illustrate how to answer these questions. Chapter 10: This chapter compares the performance of Bayesian methods against simple, non-Bayesian alternatives, such as maximum likelihood, minimal chi square, ordinary and weighted least square, bivariate correlated errors and intrinsic scatter, and robust estimates of location and scale. Performances are evaluated in terms of quality of the prediction, accuracy of the estimates, and fairness and noisiness of the quoted errors. We also focus on three failures of maximum likelihood methods occurring with small samples, with mixtures, and with regressions with errors in the predictor quantity.

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.

Simple summation rule for optimal fixation selection in visual search.

PubMed

Najemnik, Jiri; Geisler, Wilson S

2009-06-01

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

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

NASA Astrophysics Data System (ADS)

Paulin, M. G.

2005-09-01

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

Improved Analysis of Earth System Models and Observations using Simple Climate Models

NASA Astrophysics Data System (ADS)

Nadiga, B. T.; Urban, N. M.

2016-12-01

Earth system models (ESM) are the most comprehensive tools we have to study climate change and develop climate projections. However, the computational infrastructure required and the cost incurred in running such ESMs precludes direct use of such models in conjunction with a wide variety of tools that can further our understanding of climate. Here we are referring to tools that range from dynamical systems tools that give insight into underlying flow structure and topology to tools that come from various applied mathematical and statistical techniques and are central to quantifying stability, sensitivity, uncertainty and predictability to machine learning tools that are now being rapidly developed or improved. Our approach to facilitate the use of such models is to analyze output of ESM experiments (cf. CMIP) using a range of simpler models that consider integral balances of important quantities such as mass and/or energy in a Bayesian framework.We highlight the use of this approach in the context of the uptake of heat by the world oceans in the ongoing global warming. Indeed, since in excess of 90% of the anomalous radiative forcing due greenhouse gas emissions is sequestered in the world oceans, the nature of ocean heat uptake crucially determines the surface warming that is realized (cf. climate sensitivity). Nevertheless, ESMs themselves are never run long enough to directly assess climate sensitivity. So, we consider a range of models based on integral balances--balances that have to be realized in all first-principles based models of the climate system including the most detailed state-of-the art climate simulations. The models range from simple models of energy balance to those that consider dynamically important ocean processes such as the conveyor-belt circulation (Meridional Overturning Circulation, MOC), North Atlantic Deep Water (NADW) formation, Antarctic Circumpolar Current (ACC) and eddy mixing. Results from Bayesian analysis of such models using both ESM experiments and actual observations are presented. One such result points to the importance of direct sequestration of heat below 700 m, a process that is not allowed for in the simple models that have been traditionally used to deduce climate sensitivity.

RECONSTRUCTING EXPOSURE SCENARIOS USING DOSE BIOMARKERS - AN APPLICATION OF BAYESIAN UNCERTAINTY ANALYSIS

EPA Science Inventory

We use Bayesian uncertainty analysis to explore how to estimate pollutant exposures from biomarker concentrations. The growing number of national databases with exposure data makes such an analysis possible. They contain datasets of pharmacokinetic biomarkers for many polluta...

Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics

NASA Astrophysics Data System (ADS)

Abe, Sumiyoshi

2014-11-01

The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown, in particular, how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.

IMAGINE: Interstellar MAGnetic field INference Engine

NASA Astrophysics Data System (ADS)

Steininger, Theo

2018-03-01

IMAGINE (Interstellar MAGnetic field INference Engine) performs inference on generic parametric models of the Galaxy. The modular open source framework uses highly optimized tools and technology such as the MultiNest sampler (ascl:1109.006) and the information field theory framework NIFTy (ascl:1302.013) to create an instance of the Milky Way based on a set of parameters for physical observables, using Bayesian statistics to judge the mismatch between measured data and model prediction. The flexibility of the IMAGINE framework allows for simple refitting for newly available data sets and makes state-of-the-art Bayesian methods easily accessible particularly for random components of the Galactic magnetic field.

Bayesian network learning for natural hazard assessments

NASA Astrophysics Data System (ADS)

Vogel, Kristin

2016-04-01

Even though quite different in occurrence and consequences, from a modelling perspective many natural hazards share similar properties and challenges. Their complex nature as well as lacking knowledge about their driving forces and potential effects make their analysis demanding. On top of the uncertainty about the modelling framework, inaccurate or incomplete event observations and the intrinsic randomness of the natural phenomenon add up to different interacting layers of uncertainty, which require a careful handling. Thus, for reliable natural hazard assessments it is crucial not only to capture and quantify involved uncertainties, but also to express and communicate uncertainties in an intuitive way. Decision-makers, who often find it difficult to deal with uncertainties, might otherwise return to familiar (mostly deterministic) proceedings. In the scope of the DFG research training group „NatRiskChange" we apply the probabilistic framework of Bayesian networks for diverse natural hazard and vulnerability studies. The great potential of Bayesian networks was already shown in previous natural hazard assessments. Treating each model component as random variable, Bayesian networks aim at capturing the joint distribution of all considered variables. Hence, each conditional distribution of interest (e.g. the effect of precautionary measures on damage reduction) can be inferred. The (in-)dependencies between the considered variables can be learned purely data driven or be given by experts. Even a combination of both is possible. By translating the (in-)dependences into a graph structure, Bayesian networks provide direct insights into the workings of the system and allow to learn about the underlying processes. Besides numerous studies on the topic, learning Bayesian networks from real-world data remains challenging. In previous studies, e.g. on earthquake induced ground motion and flood damage assessments, we tackled the problems arising with continuous variables and incomplete observations. Further studies rise the challenge of relying on very small data sets. Since parameter estimates for complex models based on few observations are unreliable, it is necessary to focus on simplified, yet still meaningful models. A so called Markov Blanket approach is developed to identify the most relevant model components and to construct a simple Bayesian network based on those findings. Since the proceeding is completely data driven, it can easily be transferred to various applications in natural hazard domains. This study is funded by the Deutsche Forschungsgemeinschaft (DFG) within the research training programme GRK 2043/1 "NatRiskChange - Natural hazards and risks in a changing world" at Potsdam University.

Bayesian network representing system dynamics in risk analysis of nuclear systems

NASA Astrophysics Data System (ADS)

Varuttamaseni, Athi

2011-12-01

A dynamic Bayesian network (DBN) model is used in conjunction with the alternating conditional expectation (ACE) regression method to analyze the risk associated with the loss of feedwater accident coupled with a subsequent initiation of the feed and bleed operation in the Zion-1 nuclear power plant. The use of the DBN allows the joint probability distribution to be factorized, enabling the analysis to be done on many simpler network structures rather than on one complicated structure. The construction of the DBN model assumes conditional independence relations among certain key reactor parameters. The choice of parameter to model is based on considerations of the macroscopic balance statements governing the behavior of the reactor under a quasi-static assumption. The DBN is used to relate the peak clad temperature to a set of independent variables that are known to be important in determining the success of the feed and bleed operation. A simple linear relationship is then used to relate the clad temperature to the core damage probability. To obtain a quantitative relationship among different nodes in the DBN, surrogates of the RELAP5 reactor transient analysis code are used. These surrogates are generated by applying the ACE algorithm to output data obtained from about 50 RELAP5 cases covering a wide range of the selected independent variables. These surrogates allow important safety parameters such as the fuel clad temperature to be expressed as a function of key reactor parameters such as the coolant temperature and pressure together with important independent variables such as the scram delay time. The time-dependent core damage probability is calculated by sampling the independent variables from their probability distributions and propagate the information up through the Bayesian network to give the clad temperature. With the knowledge of the clad temperature and the assumption that the core damage probability has a one-to-one relationship to it, we have calculated the core damage probably as a function of transient time. The use of the DBN model in combination with ACE allows risk analysis to be performed with much less effort than if the analysis were done using the standard techniques.

Bayesian Factor Analysis as a Variable Selection Problem: Alternative Priors and Consequences

PubMed Central

Lu, Zhao-Hua; Chow, Sy-Miin; Loken, Eric

2016-01-01

Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, a Bayesian structural equation modeling (BSEM) approach (Muthén & Asparouhov, 2012) has been proposed as a way to explore the presence of cross-loadings in CFA models. We show that the issue of determining factor loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov’s approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike and slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set (Byrne, 2012; Pettegrew & Wolf, 1982) is used to demonstrate our approach. PMID:27314566

Application of a data-mining method based on Bayesian networks to lesion-deficit analysis

NASA Technical Reports Server (NTRS)

Herskovits, Edward H.; Gerring, Joan P.

2003-01-01

Although lesion-deficit analysis (LDA) has provided extensive information about structure-function associations in the human brain, LDA has suffered from the difficulties inherent to the analysis of spatial data, i.e., there are many more variables than subjects, and data may be difficult to model using standard distributions, such as the normal distribution. We herein describe a Bayesian method for LDA; this method is based on data-mining techniques that employ Bayesian networks to represent structure-function associations. These methods are computationally tractable, and can represent complex, nonlinear structure-function associations. When applied to the evaluation of data obtained from a study of the psychiatric sequelae of traumatic brain injury in children, this method generates a Bayesian network that demonstrates complex, nonlinear associations among lesions in the left caudate, right globus pallidus, right side of the corpus callosum, right caudate, and left thalamus, and subsequent development of attention-deficit hyperactivity disorder, confirming and extending our previous statistical analysis of these data. Furthermore, analysis of simulated data indicates that methods based on Bayesian networks may be more sensitive and specific for detecting associations among categorical variables than methods based on chi-square and Fisher exact statistics.

Diagnostic accuracy of a bayesian latent group analysis for the detection of malingering-related poor effort.

PubMed

Ortega, Alonso; Labrenz, Stephan; Markowitsch, Hans J; Piefke, Martina

2013-01-01

In the last decade, different statistical techniques have been introduced to improve assessment of malingering-related poor effort. In this context, we have recently shown preliminary evidence that a Bayesian latent group model may help to optimize classification accuracy using a simulation research design. In the present study, we conducted two analyses. Firstly, we evaluated how accurately this Bayesian approach can distinguish between participants answering in an honest way (honest response group) and participants feigning cognitive impairment (experimental malingering group). Secondly, we tested the accuracy of our model in the differentiation between patients who had real cognitive deficits (cognitively impaired group) and participants who belonged to the experimental malingering group. All Bayesian analyses were conducted using the raw scores of a visual recognition forced-choice task (2AFC), the Test of Memory Malingering (TOMM, Trial 2), and the Word Memory Test (WMT, primary effort subtests). The first analysis showed 100% accuracy for the Bayesian model in distinguishing participants of both groups with all effort measures. The second analysis showed outstanding overall accuracy of the Bayesian model when estimates were obtained from the 2AFC and the TOMM raw scores. Diagnostic accuracy of the Bayesian model diminished when using the WMT total raw scores. Despite, overall diagnostic accuracy can still be considered excellent. The most plausible explanation for this decrement is the low performance in verbal recognition and fluency tasks of some patients of the cognitively impaired group. Additionally, the Bayesian model provides individual estimates, p(zi |D), of examinees' effort levels. In conclusion, both high classification accuracy levels and Bayesian individual estimates of effort may be very useful for clinicians when assessing for effort in medico-legal settings.

The impact of using informative priors in a Bayesian cost-effectiveness analysis: an application of endovascular versus open surgical repair for abdominal aortic aneurysms in high-risk patients.

PubMed

McCarron, C Elizabeth; Pullenayegum, Eleanor M; Thabane, Lehana; Goeree, Ron; Tarride, Jean-Eric

2013-04-01

Bayesian methods have been proposed as a way of synthesizing all available evidence to inform decision making. However, few practical applications of the use of Bayesian methods for combining patient-level data (i.e., trial) with additional evidence (e.g., literature) exist in the cost-effectiveness literature. The objective of this study was to compare a Bayesian cost-effectiveness analysis using informative priors to a standard non-Bayesian nonparametric method to assess the impact of incorporating additional information into a cost-effectiveness analysis. Patient-level data from a previously published nonrandomized study were analyzed using traditional nonparametric bootstrap techniques and bivariate normal Bayesian models with vague and informative priors. Two different types of informative priors were considered to reflect different valuations of the additional evidence relative to the patient-level data (i.e., "face value" and "skeptical"). The impact of using different distributions and valuations was assessed in a sensitivity analysis. Models were compared in terms of incremental net monetary benefit (INMB) and cost-effectiveness acceptability frontiers (CEAFs). The bootstrapping and Bayesian analyses using vague priors provided similar results. The most pronounced impact of incorporating the informative priors was the increase in estimated life years in the control arm relative to what was observed in the patient-level data alone. Consequently, the incremental difference in life years originally observed in the patient-level data was reduced, and the INMB and CEAF changed accordingly. The results of this study demonstrate the potential impact and importance of incorporating additional information into an analysis of patient-level data, suggesting this could alter decisions as to whether a treatment should be adopted and whether more information should be acquired.

Single-Case Time Series with Bayesian Analysis: A Practitioner's Guide.

ERIC Educational Resources Information Center

Jones, W. Paul

2003-01-01

This article illustrates a simplified time series analysis for use by the counseling researcher practitioner in single-case baseline plus intervention studies with a Bayesian probability analysis to integrate findings from replications. The C statistic is recommended as a primary analysis tool with particular relevance in the context of actual…

Daniel Goodman’s empirical approach to Bayesian statistics

USGS Publications Warehouse

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

2016-01-01

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

Robust Bayesian Factor Analysis

ERIC Educational Resources Information Center

Hayashi, Kentaro; Yuan, Ke-Hai

2003-01-01

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

Bayesian Meta-Analysis of Coefficient Alpha

ERIC Educational Resources Information Center

Brannick, Michael T.; Zhang, Nanhua

2013-01-01

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

Resolution analysis of marine seismic full waveform data by Bayesian inversion

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Bayesian learning and the psychology of rule induction

PubMed Central

Endress, Ansgar D.

2014-01-01

In recent years, Bayesian learning models have been applied to an increasing variety of domains. While such models have been criticized on theoretical grounds, the underlying assumptions and predictions are rarely made concrete and tested experimentally. Here, I use Frank and Tenenbaum's (2011) Bayesian model of rule-learning as a case study to spell out the underlying assumptions, and to confront them with the empirical results Frank and Tenenbaum (2011) propose to simulate, as well as with novel experiments. While rule-learning is arguably well suited to rational Bayesian approaches, I show that their models are neither psychologically plausible nor ideal observer models. Further, I show that their central assumption is unfounded: humans do not always preferentially learn more specific rules, but, at least in some situations, those rules that happen to be more salient. Even when granting the unsupported assumptions, I show that all of the experiments modeled by Frank and Tenenbaum (2011) either contradict their models, or have a large number of more plausible interpretations. I provide an alternative account of the experimental data based on simple psychological mechanisms, and show that this account both describes the data better, and is easier to falsify. I conclude that, despite the recent surge in Bayesian models of cognitive phenomena, psychological phenomena are best understood by developing and testing psychological theories rather than models that can be fit to virtually any data. PMID:23454791

Branch length estimation and divergence dating: estimates of error in Bayesian and maximum likelihood frameworks.

PubMed

Schwartz, Rachel S; Mueller, Rachel L

2010-01-11

Estimates of divergence dates between species improve our understanding of processes ranging from nucleotide substitution to speciation. Such estimates are frequently based on molecular genetic differences between species; therefore, they rely on accurate estimates of the number of such differences (i.e. substitutions per site, measured as branch length on phylogenies). We used simulations to determine the effects of dataset size, branch length heterogeneity, branch depth, and analytical framework on branch length estimation across a range of branch lengths. We then reanalyzed an empirical dataset for plethodontid salamanders to determine how inaccurate branch length estimation can affect estimates of divergence dates. The accuracy of branch length estimation varied with branch length, dataset size (both number of taxa and sites), branch length heterogeneity, branch depth, dataset complexity, and analytical framework. For simple phylogenies analyzed in a Bayesian framework, branches were increasingly underestimated as branch length increased; in a maximum likelihood framework, longer branch lengths were somewhat overestimated. Longer datasets improved estimates in both frameworks; however, when the number of taxa was increased, estimation accuracy for deeper branches was less than for tip branches. Increasing the complexity of the dataset produced more misestimated branches in a Bayesian framework; however, in an ML framework, more branches were estimated more accurately. Using ML branch length estimates to re-estimate plethodontid salamander divergence dates generally resulted in an increase in the estimated age of older nodes and a decrease in the estimated age of younger nodes. Branch lengths are misestimated in both statistical frameworks for simulations of simple datasets. However, for complex datasets, length estimates are quite accurate in ML (even for short datasets), whereas few branches are estimated accurately in a Bayesian framework. Our reanalysis of empirical data demonstrates the magnitude of effects of Bayesian branch length misestimation on divergence date estimates. Because the length of branches for empirical datasets can be estimated most reliably in an ML framework when branches are <1 substitution/site and datasets are > or =1 kb, we suggest that divergence date estimates using datasets, branch lengths, and/or analytical techniques that fall outside of these parameters should be interpreted with caution.

Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors

PubMed Central

van de Schoot, Rens; Broere, Joris J.; Perryck, Koen H.; Zondervan-Zwijnenburg, Mariëlle; van Loey, Nancy E.

2015-01-01

Background The analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation. Methods First, we show how to specify prior distributions and by means of a sensitivity analysis we demonstrate how to check the exact influence of the prior (mis-) specification. Thereafter, we show by means of a simulation the situations in which the Bayesian approach outperforms the default, maximum likelihood and approach. Finally, we re-analyze empirical data on burn survivors which provided preliminary evidence of an aversive influence of a period of mechanical ventilation on the course of PTSS following burns. Results Not suprisingly, maximum likelihood estimation showed insufficient coverage as well as power with very small samples. Only when Bayesian analysis, in conjunction with informative priors, was used power increased to acceptable levels. As expected, we showed that the smaller the sample size the more the results rely on the prior specification. Conclusion We show that two issues often encountered during analysis of small samples, power and biased parameters, can be solved by including prior information into Bayesian analysis. We argue that the use of informative priors should always be reported together with a sensitivity analysis. PMID:25765534

Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors.

PubMed

van de Schoot, Rens; Broere, Joris J; Perryck, Koen H; Zondervan-Zwijnenburg, Mariëlle; van Loey, Nancy E

2015-01-01

Background : The analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation. Methods : First, we show how to specify prior distributions and by means of a sensitivity analysis we demonstrate how to check the exact influence of the prior (mis-) specification. Thereafter, we show by means of a simulation the situations in which the Bayesian approach outperforms the default, maximum likelihood and approach. Finally, we re-analyze empirical data on burn survivors which provided preliminary evidence of an aversive influence of a period of mechanical ventilation on the course of PTSS following burns. Results : Not suprisingly, maximum likelihood estimation showed insufficient coverage as well as power with very small samples. Only when Bayesian analysis, in conjunction with informative priors, was used power increased to acceptable levels. As expected, we showed that the smaller the sample size the more the results rely on the prior specification. Conclusion : We show that two issues often encountered during analysis of small samples, power and biased parameters, can be solved by including prior information into Bayesian analysis. We argue that the use of informative priors should always be reported together with a sensitivity analysis.

Bayesian dose-response analysis for epidemiological studies with complex uncertainty in dose estimation.

PubMed

Kwon, Deukwoo; Hoffman, F Owen; Moroz, Brian E; Simon, Steven L

2016-02-10

Most conventional risk analysis methods rely on a single best estimate of exposure per person, which does not allow for adjustment for exposure-related uncertainty. Here, we propose a Bayesian model averaging method to properly quantify the relationship between radiation dose and disease outcomes by accounting for shared and unshared uncertainty in estimated dose. Our Bayesian risk analysis method utilizes multiple realizations of sets (vectors) of doses generated by a two-dimensional Monte Carlo simulation method that properly separates shared and unshared errors in dose estimation. The exposure model used in this work is taken from a study of the risk of thyroid nodules among a cohort of 2376 subjects who were exposed to fallout from nuclear testing in Kazakhstan. We assessed the performance of our method through an extensive series of simulations and comparisons against conventional regression risk analysis methods. When the estimated doses contain relatively small amounts of uncertainty, the Bayesian method using multiple a priori plausible draws of dose vectors gave similar results to the conventional regression-based methods of dose-response analysis. However, when large and complex mixtures of shared and unshared uncertainties are present, the Bayesian method using multiple dose vectors had significantly lower relative bias than conventional regression-based risk analysis methods and better coverage, that is, a markedly increased capability to include the true risk coefficient within the 95% credible interval of the Bayesian-based risk estimate. An evaluation of the dose-response using our method is presented for an epidemiological study of thyroid disease following radiation exposure. Copyright © 2015 John Wiley & Sons, Ltd.

Honest Importance Sampling with Multiple Markov Chains

PubMed Central

Tan, Aixin; Doss, Hani; Hobert, James P.

2017-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π1 is replaced by a Harris ergodic Markov chain with invariant density π1, then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π1, …, πk, are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection. PMID:28701855

Honest Importance Sampling with Multiple Markov Chains.

PubMed

Tan, Aixin; Doss, Hani; Hobert, James P

2015-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection.

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.

Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum

2006-01-01

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…

Bayesian Data-Model Fit Assessment for Structural Equation Modeling

ERIC Educational Resources Information Center

Levy, Roy

2011-01-01

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…

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…

New phiomorph rodents from the latest Eocene of Egypt, and the impact of Bayesian “clock”-based phylogenetic methods on estimates of basal hystricognath relationships and biochronology

PubMed Central

2016-01-01

The Fayum Depression of Egypt has yielded fossils of hystricognathous rodents from multiple Eocene and Oligocene horizons that range in age from ∼37 to ∼30 Ma and document several phases in the early evolution of crown Hystricognathi and one of its major subclades, Phiomorpha. Here we describe two new genera and species of basal phiomorphs, Birkamys korai and Mubhammys vadumensis, based on rostra and maxillary and mandibular remains from the terminal Eocene (∼34 Ma) Fayum Locality 41 (L-41). Birkamys is the smallest known Paleogene hystricognath, has very simple molars, and, like derived Oligocene-to-Recent phiomorphs (but unlike contemporaneous and older taxa) apparently retained dP4∕4 late into life, with no evidence for P4∕4 eruption or formation. Mubhammys is very similar in dental morphology to Birkamys, and also shows no evidence for P4∕4 formation or eruption, but is considerably larger. Though parsimony analysis with all characters equally weighted places Birkamys and Mubhammys as sister taxa of extant Thryonomys to the exclusion of much younger relatives of that genus, all other methods (standard Bayesian inference, Bayesian “tip-dating,” and parsimony analysis with scaled transitions between “fixed” and polymorphic states) place these species in more basal positions within Hystricognathi, as sister taxa of Oligocene-to-Recent phiomorphs. We also employ tip-dating as a means for estimating the ages of early hystricognath-bearing localities, many of which are not well-constrained by geological, geochronological, or biostratigraphic evidence. By simultaneously taking into account phylogeny, evolutionary rates, and uniform priors that appropriately encompass the range of possible ages for fossil localities, dating of tips in this Bayesian framework allows paleontologists to move beyond vague and assumption-laden “stage of evolution” arguments in biochronology to provide relatively rigorous age assessments of poorly-constrained faunas. This approach should become increasingly robust as estimates are combined from multiple independent analyses of distantly related clades, and is broadly applicable across the tree of life; as such it is deserving of paleontologists’ close attention. Notably, in the example provided here, hystricognathous rodents from Libya and Namibia that are controversially considered to be of middle Eocene age are instead estimated to be of late Eocene and late Oligocene age, respectively. Finally, we reconstruct the evolution of first lower molar size among Paleogene African hystricognaths using a Bayesian approach; the results of this analysis reconstruct a rapid latest Eocene dwarfing event along the lineage leading to Birkamys. PMID:26966657

Development and comparison in uncertainty assessment based Bayesian modularization method in hydrological modeling

NASA Astrophysics Data System (ADS)

Li, Lu; Xu, Chong-Yu; Engeland, Kolbjørn

2013-04-01

SummaryWith respect to model calibration, parameter estimation and analysis of uncertainty sources, various regression and probabilistic approaches are used in hydrological modeling. A family of Bayesian methods, which incorporates different sources of information into a single analysis through Bayes' theorem, is widely used for uncertainty assessment. However, none of these approaches can well treat the impact of high flows in hydrological modeling. This study proposes a Bayesian modularization uncertainty assessment approach in which the highest streamflow observations are treated as suspect information that should not influence the inference of the main bulk of the model parameters. This study includes a comprehensive comparison and evaluation of uncertainty assessments by our new Bayesian modularization method and standard Bayesian methods using the Metropolis-Hastings (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions were used in combination with standard Bayesian method: the AR(1) plus Normal model independent of time (Model 1), the AR(1) plus Normal model dependent on time (Model 2) and the AR(1) plus Multi-normal model (Model 3). The results reveal that the Bayesian modularization method provides the most accurate streamflow estimates measured by the Nash-Sutcliffe efficiency and provide the best in uncertainty estimates for low, medium and entire flows compared to standard Bayesian methods. The study thus provides a new approach for reducing the impact of high flows on the discharge uncertainty assessment of hydrological models via Bayesian method.

Bayesian correction for covariate measurement error: A frequentist evaluation and comparison with regression calibration.

PubMed

Bartlett, Jonathan W; Keogh, Ruth H

2018-06-01

Bayesian approaches for handling covariate measurement error are well established and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper, we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration, arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to regression calibration and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next, we describe the closely related maximum likelihood and multiple imputation approaches and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of regression calibration and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey.

Genetic diversity of Pinus nigra Arn. populations in Southern Spain and Northern Morocco revealed by inter-simple sequence repeat profiles.

PubMed

Rubio-Moraga, Angela; Candel-Perez, David; Lucas-Borja, Manuel E; Tiscar, Pedro A; Viñegla, Benjamin; Linares, Juan C; Gómez-Gómez, Lourdes; Ahrazem, Oussama

2012-01-01

Eight Pinus nigra Arn. populations from Southern Spain and Northern Morocco were examined using inter-simple sequence repeat markers to characterize the genetic variability amongst populations. Pair-wise population genetic distance ranged from 0.031 to 0.283, with a mean of 0.150 between populations. The highest inter-population average distance was between PaCU from Cuenca and YeCA from Cazorla, while the lowest distance was between TaMO from Morocco and MA Sierra Mágina populations. Analysis of molecular variance (AMOVA) and Nei's genetic diversity analyses revealed higher genetic variation within the same population than among different populations. Genetic differentiation (Gst) was 0.233. Cuenca showed the highest Nei's genetic diversity followed by the Moroccan region, Sierra Mágina, and Cazorla region. However, clustering of populations was not in accordance with their geographical locations. Principal component analysis showed the presence of two major groups-Group 1 contained all populations from Cuenca while Group 2 contained populations from Cazorla, Sierra Mágina and Morocco-while Bayesian analysis revealed the presence of three clusters. The low genetic diversity observed in PaCU and YeCA is probably a consequence of inappropriate management since no estimation of genetic variability was performed before the silvicultural treatments. Data indicates that the inter-simple sequence repeat (ISSR) method is sufficiently informative and powerful to assess genetic variability among populations of P. nigra.

Genetic Diversity of Pinus nigra Arn. Populations in Southern Spain and Northern Morocco Revealed By Inter-Simple Sequence Repeat Profiles †

PubMed Central

Rubio-Moraga, Angela; Candel-Perez, David; Lucas-Borja, Manuel E.; Tiscar, Pedro A.; Viñegla, Benjamin; Linares, Juan C.; Gómez-Gómez, Lourdes; Ahrazem, Oussama

2012-01-01

Eight Pinus nigra Arn. populations from Southern Spain and Northern Morocco were examined using inter-simple sequence repeat markers to characterize the genetic variability amongst populations. Pair-wise population genetic distance ranged from 0.031 to 0.283, with a mean of 0.150 between populations. The highest inter-population average distance was between PaCU from Cuenca and YeCA from Cazorla, while the lowest distance was between TaMO from Morocco and MA Sierra Mágina populations. Analysis of molecular variance (AMOVA) and Nei’s genetic diversity analyses revealed higher genetic variation within the same population than among different populations. Genetic differentiation (Gst) was 0.233. Cuenca showed the highest Nei’s genetic diversity followed by the Moroccan region, Sierra Mágina, and Cazorla region. However, clustering of populations was not in accordance with their geographical locations. Principal component analysis showed the presence of two major groups—Group 1 contained all populations from Cuenca while Group 2 contained populations from Cazorla, Sierra Mágina and Morocco—while Bayesian analysis revealed the presence of three clusters. The low genetic diversity observed in PaCU and YeCA is probably a consequence of inappropriate management since no estimation of genetic variability was performed before the silvicultural treatments. Data indicates that the inter-simple sequence repeat (ISSR) method is sufficiently informative and powerful to assess genetic variability among populations of P. nigra. PMID:22754321

Enhancing the Modeling of PFOA Pharmacokinetics with Bayesian Analysis

EPA Science Inventory

The detail sufficient to describe the pharmacokinetics (PK) for perfluorooctanoic acid (PFOA) and the methods necessary to combine information from multiple data sets are both subjects of ongoing investigation. Bayesian analysis provides tools to accommodate these goals. We exa...

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation.

PubMed

Cornuet, Jean-Marie; Santos, Filipe; Beaumont, Mark A; Robert, Christian P; Marin, Jean-Michel; Balding, David J; Guillemaud, Thomas; Estoup, Arnaud

2008-12-01

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC. The software DIY ABC is freely available at http://www.montpellier.inra.fr/CBGP/diyabc.

A note on the efficiencies of sampling strategies in two-stage Bayesian regional fine mapping of a quantitative trait.

PubMed

Chen, Zhijian; Craiu, Radu V; Bull, Shelley B

2014-11-01

In focused studies designed to follow up associations detected in a genome-wide association study (GWAS), investigators can proceed to fine-map a genomic region by targeted sequencing or dense genotyping of all variants in the region, aiming to identify a functional sequence variant. For the analysis of a quantitative trait, we consider a Bayesian approach to fine-mapping study design that incorporates stratification according to a promising GWAS tag SNP in the same region. Improved cost-efficiency can be achieved when the fine-mapping phase incorporates a two-stage design, with identification of a smaller set of more promising variants in a subsample taken in stage 1, followed by their evaluation in an independent stage 2 subsample. To avoid the potential negative impact of genetic model misspecification on inference we incorporate genetic model selection based on posterior probabilities for each competing model. Our simulation study shows that, compared to simple random sampling that ignores genetic information from GWAS, tag-SNP-based stratified sample allocation methods reduce the number of variants continuing to stage 2 and are more likely to promote the functional sequence variant into confirmation studies. © 2014 WILEY PERIODICALS, INC.

Phylogenetic Analyses: A Toolbox Expanding towards Bayesian Methods

PubMed Central

Aris-Brosou, Stéphane; Xia, Xuhua

2008-01-01

The reconstruction of phylogenies is becoming an increasingly simple activity. This is mainly due to two reasons: the democratization of computing power and the increased availability of sophisticated yet user-friendly software. This review describes some of the latest additions to the phylogenetic toolbox, along with some of their theoretical and practical limitations. It is shown that Bayesian methods are under heavy development, as they offer the possibility to solve a number of long-standing issues and to integrate several steps of the phylogenetic analyses into a single framework. Specific topics include not only phylogenetic reconstruction, but also the comparison of phylogenies, the detection of adaptive evolution, and the estimation of divergence times between species. PMID:18483574

INFERRING THE ECCENTRICITY DISTRIBUTION

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

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

2010-12-20

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

Bayesian statistics: estimating plant demographic parameters

Treesearch

James S. Clark; Michael Lavine

2001-01-01

There are times when external information should be brought tobear on an ecological analysis. experiments are never conducted in a knowledge-free context. The inference we draw from an observation may depend on everything else we know about the process. Bayesian analysis is a method that brings outside evidence into the analysis of experimental and observational data...

Spatial Dependence and Heterogeneity in Bayesian Factor Analysis: A Cross-National Investigation of Schwartz Values

ERIC Educational Resources Information Center

Stakhovych, Stanislav; Bijmolt, Tammo H. A.; Wedel, Michel

2012-01-01

In this article, we present a Bayesian spatial factor analysis model. We extend previous work on confirmatory factor analysis by including geographically distributed latent variables and accounting for heterogeneity and spatial autocorrelation. The simulation study shows excellent recovery of the model parameters and demonstrates the consequences…

Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory

ERIC Educational Resources Information Center

Muthen, Bengt; Asparouhov, Tihomir

2012-01-01

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed…

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

PubMed

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

2016-10-21

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

Introduction to Bayesian statistical approaches to compositional analyses of transgenic crops 1. Model validation and setting the stage.

PubMed

Harrison, Jay M; Breeze, Matthew L; Harrigan, George G

2011-08-01

Statistical comparisons of compositional data generated on genetically modified (GM) crops and their near-isogenic conventional (non-GM) counterparts typically rely on classical significance testing. This manuscript presents an introduction to Bayesian methods for compositional analysis along with recommendations for model validation. The approach is illustrated using protein and fat data from two herbicide tolerant GM soybeans (MON87708 and MON87708×MON89788) and a conventional comparator grown in the US in 2008 and 2009. Guidelines recommended by the US Food and Drug Administration (FDA) in conducting Bayesian analyses of clinical studies on medical devices were followed. This study is the first Bayesian approach to GM and non-GM compositional comparisons. The evaluation presented here supports a conclusion that a Bayesian approach to analyzing compositional data can provide meaningful and interpretable results. We further describe the importance of method validation and approaches to model checking if Bayesian approaches to compositional data analysis are to be considered viable by scientists involved in GM research and regulation. Copyright © 2011 Elsevier Inc. All rights reserved.

Quantifying the uncertainty in discharge data using hydraulic knowledge and uncertain gaugings: a Bayesian method named BaRatin

NASA Astrophysics Data System (ADS)

Le Coz, Jérôme; Renard, Benjamin; Bonnifait, Laurent; Branger, Flora; Le Boursicaud, Raphaël; Horner, Ivan; Mansanarez, Valentin; Lang, Michel; Vigneau, Sylvain

2015-04-01

River discharge is a crucial variable for Hydrology: as the output variable of most hydrologic models, it is used for sensitivity analyses, model structure identification, parameter estimation, data assimilation, prediction, etc. A major difficulty stems from the fact that river discharge is not measured continuously. Instead, discharge time series used by hydrologists are usually based on simple stage-discharge relations (rating curves) calibrated using a set of direct stage-discharge measurements (gaugings). In this presentation, we present a Bayesian approach (cf. Le Coz et al., 2014) to build such hydrometric rating curves, to estimate the associated uncertainty and to propagate this uncertainty to discharge time series. The three main steps of this approach are described: (1) Hydraulic analysis: identification of the hydraulic controls that govern the stage-discharge relation, identification of the rating curve equation and specification of prior distributions for the rating curve parameters; (2) Rating curve estimation: Bayesian inference of the rating curve parameters, accounting for the individual uncertainties of available gaugings, which often differ according to the discharge measurement procedure and the flow conditions; (3) Uncertainty propagation: quantification of the uncertainty in discharge time series, accounting for both the rating curve uncertainties and the uncertainty of recorded stage values. The rating curve uncertainties combine the parametric uncertainties and the remnant uncertainties that reflect the limited accuracy of the mathematical model used to simulate the physical stage-discharge relation. In addition, we also discuss current research activities, including the treatment of non-univocal stage-discharge relationships (e.g. due to hydraulic hysteresis, vegetation growth, sudden change of the geometry of the section, etc.). An operational version of the BaRatin software and its graphical interface are made available free of charge on request to the authors. J. Le Coz, B. Renard, L. Bonnifait, F. Branger, R. Le Boursicaud (2014). Combining hydraulic knowledge and uncertain gaugings in the estimation of hydrometric rating curves: a Bayesian approach, Journal of Hydrology, 509, 573-587.

Developing a new Bayesian Risk Index for risk evaluation of soil contamination.

PubMed

Albuquerque, M T D; Gerassis, S; Sierra, C; Taboada, J; Martín, J E; Antunes, I M H R; Gallego, J R

2017-12-15

Industrial and agricultural activities heavily constrain soil quality. Potentially Toxic Elements (PTEs) are a threat to public health and the environment alike. In this regard, the identification of areas that require remediation is crucial. In the herein research a geochemical dataset (230 samples) comprising 14 elements (Cu, Pb, Zn, Ag, Ni, Mn, Fe, As, Cd, V, Cr, Ti, Al and S) was gathered throughout eight different zones distinguished by their main activity, namely, recreational, agriculture/livestock and heavy industry in the Avilés Estuary (North of Spain). Then a stratified systematic sampling method was used at short, medium, and long distances from each zone to obtain a representative picture of the total variability of the selected attributes. The information was then combined in four risk classes (Low, Moderate, High, Remediation) following reference values from several sediment quality guidelines (SQGs). A Bayesian analysis, inferred for each zone, allowed the characterization of PTEs correlations, the unsupervised learning network technique proving to be the best fit. Based on the Bayesian network structure obtained, Pb, As and Mn were selected as key contamination parameters. For these 3 elements, the conditional probability obtained was allocated to each observed point, and a simple, direct index (Bayesian Risk Index-BRI) was constructed as a linear rating of the pre-defined risk classes weighted by the previously obtained probability. Finally, the BRI underwent geostatistical modeling. One hundred Sequential Gaussian Simulations (SGS) were computed. The Mean Image and the Standard Deviation maps were obtained, allowing the definition of High/Low risk clusters (Local G clustering) and the computation of spatial uncertainty. High-risk clusters are mainly distributed within the area with the highest altitude (agriculture/livestock) showing an associated low spatial uncertainty, clearly indicating the need for remediation. Atmospheric emissions, mainly derived from the metallurgical industry, contribute to soil contamination by PTEs. Copyright © 2017 Elsevier B.V. All rights reserved.

Bayesian analysis of rare events

NASA Astrophysics Data System (ADS)

Straub, Daniel; Papaioannou, Iason; Betz, Wolfgang

2016-06-01

In many areas of engineering and science there is an interest in predicting the probability of rare events, in particular in applications related to safety and security. Increasingly, such predictions are made through computer models of physical systems in an uncertainty quantification framework. Additionally, with advances in IT, monitoring and sensor technology, an increasing amount of data on the performance of the systems is collected. This data can be used to reduce uncertainty, improve the probability estimates and consequently enhance the management of rare events and associated risks. Bayesian analysis is the ideal method to include the data into the probabilistic model. It ensures a consistent probabilistic treatment of uncertainty, which is central in the prediction of rare events, where extrapolation from the domain of observation is common. We present a framework for performing Bayesian updating of rare event probabilities, termed BUS. It is based on a reinterpretation of the classical rejection-sampling approach to Bayesian analysis, which enables the use of established methods for estimating probabilities of rare events. By drawing upon these methods, the framework makes use of their computational efficiency. These methods include the First-Order Reliability Method (FORM), tailored importance sampling (IS) methods and Subset Simulation (SuS). In this contribution, we briefly review these methods in the context of the BUS framework and investigate their applicability to Bayesian analysis of rare events in different settings. We find that, for some applications, FORM can be highly efficient and is surprisingly accurate, enabling Bayesian analysis of rare events with just a few model evaluations. In a general setting, BUS implemented through IS and SuS is more robust and flexible.

A guide to Bayesian model selection for ecologists

USGS Publications Warehouse

Hooten, Mevin B.; Hobbs, N.T.

2015-01-01

The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

A Bayesian approach to estimate evoked potentials.

PubMed

Sparacino, Giovanni; Milani, Stefano; Arslan, Edoardo; Cobelli, Claudio

2002-06-01

Several approaches, based on different assumptions and with various degree of theoretical sophistication and implementation complexity, have been developed for improving the measurement of evoked potentials (EP) performed by conventional averaging (CA). In many of these methods, one of the major challenges is the exploitation of a priori knowledge. In this paper, we present a new method where the 2nd-order statistical information on the background EEG and on the unknown EP, necessary for the optimal filtering of each sweep in a Bayesian estimation framework, is, respectively, estimated from pre-stimulus data and obtained through a multiple integration of a white noise process model. The latter model is flexible (i.e. it can be employed for a large class of EP) and simple enough to be easily identifiable from the post-stimulus data thanks to a smoothing criterion. The mean EP is determined as the weighted average of the filtered sweeps, where each weight is inversely proportional to the expected value of the norm of the correspondent filter error, a quantity determinable thanks to the employment of the Bayesian approach. The performance of the new approach is shown on both simulated and real auditory EP. A signal-to-noise ratio enhancement is obtained that can allow the (possibly automatic) identification of peak latencies and amplitudes with less sweeps than those required by CA. For cochlear EP, the method also allows the audiology investigator to gather new and clinically important information. The possibility of handling single-sweep analysis with further development of the method is also addressed.

How to interpret the results of medical time series data analysis: Classical statistical approaches versus dynamic Bayesian network modeling.

PubMed

Onisko, Agnieszka; Druzdzel, Marek J; Austin, R Marshall

2016-01-01

Classical statistics is a well-established approach in the analysis of medical data. While the medical community seems to be familiar with the concept of a statistical analysis and its interpretation, the Bayesian approach, argued by many of its proponents to be superior to the classical frequentist approach, is still not well-recognized in the analysis of medical data. The goal of this study is to encourage data analysts to use the Bayesian approach, such as modeling with graphical probabilistic networks, as an insightful alternative to classical statistical analysis of medical data. This paper offers a comparison of two approaches to analysis of medical time series data: (1) classical statistical approach, such as the Kaplan-Meier estimator and the Cox proportional hazards regression model, and (2) dynamic Bayesian network modeling. Our comparison is based on time series cervical cancer screening data collected at Magee-Womens Hospital, University of Pittsburgh Medical Center over 10 years. The main outcomes of our comparison are cervical cancer risk assessments produced by the three approaches. However, our analysis discusses also several aspects of the comparison, such as modeling assumptions, model building, dealing with incomplete data, individualized risk assessment, results interpretation, and model validation. Our study shows that the Bayesian approach is (1) much more flexible in terms of modeling effort, and (2) it offers an individualized risk assessment, which is more cumbersome for classical statistical approaches.

Spatiotemporal Bayesian analysis of Lyme disease in New York state, 1990-2000.

PubMed

Chen, Haiyan; Stratton, Howard H; Caraco, Thomas B; White, Dennis J

2006-07-01

Mapping ordinarily increases our understanding of nontrivial spatial and temporal heterogeneities in disease rates. However, the large number of parameters required by the corresponding statistical models often complicates detailed analysis. This study investigates the feasibility of a fully Bayesian hierarchical regression approach to the problem and identifies how it outperforms two more popular methods: crude rate estimates (CRE) and empirical Bayes standardization (EBS). In particular, we apply a fully Bayesian approach to the spatiotemporal analysis of Lyme disease incidence in New York state for the period 1990-2000. These results are compared with those obtained by CRE and EBS in Chen et al. (2005). We show that the fully Bayesian regression model not only gives more reliable estimates of disease rates than the other two approaches but also allows for tractable models that can accommodate more numerous sources of variation and unknown parameters.

A Tutorial on Multiple Testing: False Discovery Control

NASA Astrophysics Data System (ADS)

Chatelain, F.

2016-09-01

This paper presents an overview of criteria and methods in multiple testing, with an emphasis on the false discovery rate control. The popular Benjamini and Hochberg procedure is described. The rationale for this approach is explained through a simple Bayesian interpretation. Some state-of-the-art variations and extensions are also presented.

The Counter-Intuitive Non-Informative Prior for the Bernoulli Family

ERIC Educational Resources Information Center

Zhu, Mu; Lu, Arthur Y.

2004-01-01

In Bayesian statistics, the choice of the prior distribution is often controversial. Different rules for selecting priors have been suggested in the literature, which, sometimes, produce priors that are difficult for the students to understand intuitively. In this article, we use a simple heuristic to illustrate to the students the rather…

A Bayesian Attractor Model for Perceptual Decision Making

PubMed Central

Bitzer, Sebastian; Bruineberg, Jelle; Kiebel, Stefan J.

2015-01-01

Even for simple perceptual decisions, the mechanisms that the brain employs are still under debate. Although current consensus states that the brain accumulates evidence extracted from noisy sensory information, open questions remain about how this simple model relates to other perceptual phenomena such as flexibility in decisions, decision-dependent modulation of sensory gain, or confidence about a decision. We propose a novel approach of how perceptual decisions are made by combining two influential formalisms into a new model. Specifically, we embed an attractor model of decision making into a probabilistic framework that models decision making as Bayesian inference. We show that the new model can explain decision making behaviour by fitting it to experimental data. In addition, the new model combines for the first time three important features: First, the model can update decisions in response to switches in the underlying stimulus. Second, the probabilistic formulation accounts for top-down effects that may explain recent experimental findings of decision-related gain modulation of sensory neurons. Finally, the model computes an explicit measure of confidence which we relate to recent experimental evidence for confidence computations in perceptual decision tasks. PMID:26267143

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

PubMed

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

2017-01-01

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

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

PubMed

Guo, Xuan; Liu, Bing; Chen, Le; Chen, Guantao; Pan, Yi; Zhang, Jing

2016-01-01

This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come.

Detection and recognition of simple spatial forms

NASA Technical Reports Server (NTRS)

Watson, A. B.

1983-01-01

A model of human visual sensitivity to spatial patterns is constructed. The model predicts the visibility and discriminability of arbitrary two-dimensional monochrome images. The image is analyzed by a large array of linear feature sensors, which differ in spatial frequency, phase, orientation, and position in the visual field. All sensors have one octave frequency bandwidths, and increase in size linearly with eccentricity. Sensor responses are processed by an ideal Bayesian classifier, subject to uncertainty. The performance of the model is compared to that of the human observer in detecting and discriminating some simple images.

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

Karabatsos, George

2017-02-01

Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected functionals and values of covariates. The software is illustrated through the BNP regression analysis of real data.

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

PubMed

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

2013-01-01

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

Bayesian Exploratory Factor Analysis

PubMed Central

Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.; Piatek, Rémi

2014-01-01

This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates from a high dimensional set of psychological measurements. PMID:25431517

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

A fast combination method in DSmT and its application to recommender system

PubMed Central

Liu, Yihai

2018-01-01

In many applications involving epistemic uncertainties usually modeled by belief functions, it is often necessary to approximate general (non-Bayesian) basic belief assignments (BBAs) to subjective probabilities (called Bayesian BBAs). This necessity occurs if one needs to embed the fusion result in a system based on the probabilistic framework and Bayesian inference (e.g. tracking systems), or if one needs to make a decision in the decision making problems. In this paper, we present a new fast combination method, called modified rigid coarsening (MRC), to obtain the final Bayesian BBAs based on hierarchical decomposition (coarsening) of the frame of discernment. Regarding this method, focal elements with probabilities are coarsened efficiently to reduce computational complexity in the process of combination by using disagreement vector and a simple dichotomous approach. In order to prove the practicality of our approach, this new approach is applied to combine users’ soft preferences in recommender systems (RSs). Additionally, in order to make a comprehensive performance comparison, the proportional conflict redistribution rule #6 (PCR6) is regarded as a baseline in a range of experiments. According to the results of experiments, MRC is more effective in accuracy of recommendations compared to original Rigid Coarsening (RC) method and comparable in computational time. PMID:29351297

Receptive Field Inference with Localized Priors

PubMed Central

Park, Mijung; Pillow, Jonathan W.

2011-01-01

The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets. PMID:22046110

Applying Bayesian Modeling and Receiver Operating Characteristic Methodologies for Test Utility Analysis

ERIC Educational Resources Information Center

Wang, Qiu; Diemer, Matthew A.; Maier, Kimberly S.

2013-01-01

This study integrated Bayesian hierarchical modeling and receiver operating characteristic analysis (BROCA) to evaluate how interest strength (IS) and interest differentiation (ID) predicted low–socioeconomic status (SES) youth's interest-major congruence (IMC). Using large-scale Kuder Career Search online-assessment data, this study fit three…

Metrics for evaluating performance and uncertainty of Bayesian network models

Treesearch

Bruce G. Marcot

2012-01-01

This paper presents a selected set of existing and new metrics for gauging Bayesian network model performance and uncertainty. Selected existing and new metrics are discussed for conducting model sensitivity analysis (variance reduction, entropy reduction, case file simulation); evaluating scenarios (influence analysis); depicting model complexity (numbers of model...

Monte Carlo Algorithms for a Bayesian Analysis of the Cosmic Microwave Background

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Eriksen, H. K.; ODwyer, I. J.; Wandelt, B. D.; Gorski, K.; Knox, L.; Chu, M.

2006-01-01

A viewgraph presentation on the review of Bayesian approach to Cosmic Microwave Background (CMB) analysis, numerical implementation with Gibbs sampling, a summary of application to WMAP I and work in progress with generalizations to polarization, foregrounds, asymmetric beams, and 1/f noise is given.

Bayesian analysis of rare events

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

Straub, Daniel, E-mail: straub@tum.de; Papaioannou, Iason; Betz, Wolfgang

2016-06-01

In many areas of engineering and science there is an interest in predicting the probability of rare events, in particular in applications related to safety and security. Increasingly, such predictions are made through computer models of physical systems in an uncertainty quantification framework. Additionally, with advances in IT, monitoring and sensor technology, an increasing amount of data on the performance of the systems is collected. This data can be used to reduce uncertainty, improve the probability estimates and consequently enhance the management of rare events and associated risks. Bayesian analysis is the ideal method to include the data into themore » probabilistic model. It ensures a consistent probabilistic treatment of uncertainty, which is central in the prediction of rare events, where extrapolation from the domain of observation is common. We present a framework for performing Bayesian updating of rare event probabilities, termed BUS. It is based on a reinterpretation of the classical rejection-sampling approach to Bayesian analysis, which enables the use of established methods for estimating probabilities of rare events. By drawing upon these methods, the framework makes use of their computational efficiency. These methods include the First-Order Reliability Method (FORM), tailored importance sampling (IS) methods and Subset Simulation (SuS). In this contribution, we briefly review these methods in the context of the BUS framework and investigate their applicability to Bayesian analysis of rare events in different settings. We find that, for some applications, FORM can be highly efficient and is surprisingly accurate, enabling Bayesian analysis of rare events with just a few model evaluations. In a general setting, BUS implemented through IS and SuS is more robust and flexible.« less

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

PubMed

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

2016-12-20

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

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

PubMed

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

2013-10-01

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

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

PubMed Central

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

2013-01-01

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

Age estimation by assessment of pulp chamber volume: a Bayesian network for the evaluation of dental evidence.

PubMed

Sironi, Emanuele; Taroni, Franco; Baldinotti, Claudio; Nardi, Cosimo; Norelli, Gian-Aristide; Gallidabino, Matteo; Pinchi, Vilma

2017-11-14

The present study aimed to investigate the performance of a Bayesian method in the evaluation of dental age-related evidence collected by means of a geometrical approximation procedure of the pulp chamber volume. Measurement of this volume was based on three-dimensional cone beam computed tomography images. The Bayesian method was applied by means of a probabilistic graphical model, namely a Bayesian network. Performance of that method was investigated in terms of accuracy and bias of the decisional outcomes. Influence of an informed elicitation of the prior belief of chronological age was also studied by means of a sensitivity analysis. Outcomes in terms of accuracy were adequate with standard requirements for forensic adult age estimation. Findings also indicated that the Bayesian method does not show a particular tendency towards under- or overestimation of the age variable. Outcomes of the sensitivity analysis showed that results on estimation are improved with a ration elicitation of the prior probabilities of age.

A Permutation Approach for Selecting the Penalty Parameter in Penalized Model Selection

PubMed Central

Sabourin, Jeremy A; Valdar, William; Nobel, Andrew B

2015-01-01

Summary We describe a simple, computationally effcient, permutation-based procedure for selecting the penalty parameter in LASSO penalized regression. The procedure, permutation selection, is intended for applications where variable selection is the primary focus, and can be applied in a variety of structural settings, including that of generalized linear models. We briefly discuss connections between permutation selection and existing theory for the LASSO. In addition, we present a simulation study and an analysis of real biomedical data sets in which permutation selection is compared with selection based on the following: cross-validation (CV), the Bayesian information criterion (BIC), Scaled Sparse Linear Regression, and a selection method based on recently developed testing procedures for the LASSO. PMID:26243050

Next Steps in Bayesian Structural Equation Models: Comments on, Variations of, and Extensions to Muthen and Asparouhov (2012)

ERIC Educational Resources Information Center

Rindskopf, David

2012-01-01

Muthen and Asparouhov (2012) made a strong case for the advantages of Bayesian methodology in factor analysis and structural equation models. I show additional extensions and adaptations of their methods and show how non-Bayesians can take advantage of many (though not all) of these advantages by using interval restrictions on parameters. By…

A Bayesian Approach to Person Fit Analysis in Item Response Theory Models. Research Report.

ERIC Educational Resources Information Center

Glas, Cees A. W.; Meijer, Rob R.

A Bayesian approach to the evaluation of person fit in item response theory (IRT) models is presented. In a posterior predictive check, the observed value on a discrepancy variable is positioned in its posterior distribution. In a Bayesian framework, a Markov Chain Monte Carlo procedure can be used to generate samples of the posterior distribution…

Bayesian Latent Class Analysis Tutorial.

PubMed

Li, Yuelin; Lord-Bessen, Jennifer; Shiyko, Mariya; Loeb, Rebecca

2018-01-01

This article is a how-to guide on Bayesian computation using Gibbs sampling, demonstrated in the context of Latent Class Analysis (LCA). It is written for students in quantitative psychology or related fields who have a working knowledge of Bayes Theorem and conditional probability and have experience in writing computer programs in the statistical language R . The overall goals are to provide an accessible and self-contained tutorial, along with a practical computation tool. We begin with how Bayesian computation is typically described in academic articles. Technical difficulties are addressed by a hypothetical, worked-out example. We show how Bayesian computation can be broken down into a series of simpler calculations, which can then be assembled together to complete a computationally more complex model. The details are described much more explicitly than what is typically available in elementary introductions to Bayesian modeling so that readers are not overwhelmed by the mathematics. Moreover, the provided computer program shows how Bayesian LCA can be implemented with relative ease. The computer program is then applied in a large, real-world data set and explained line-by-line. We outline the general steps in how to extend these considerations to other methodological applications. We conclude with suggestions for further readings.

Nuclear data correlation between different isotopes via integral information

NASA Astrophysics Data System (ADS)

Rochman, Dimitri A.; Bauge, Eric; Vasiliev, Alexander; Ferroukhi, Hakim; Perret, Gregory

2018-05-01

This paper presents a Bayesian approach based on integral experiments to create correlations between different isotopes which do not appear with differential data. A simple Bayesian set of equations is presented with random nuclear data, similarly to the usual methods applied with differential data. As a consequence, updated nuclear data (cross sections, ν‾, fission neutron spectra and covariance matrices) are obtained, leading to better integral results. An example for 235U and 238U is proposed taking into account the Bigten criticality benchmark.

A nonparametric method to generate synthetic populations to adjust for complex sampling design features.

PubMed

Dong, Qi; Elliott, Michael R; Raghunathan, Trivellore E

2014-06-01

Outside of the survey sampling literature, samples are often assumed to be generated by a simple random sampling process that produces independent and identically distributed (IID) samples. Many statistical methods are developed largely in this IID world. Application of these methods to data from complex sample surveys without making allowance for the survey design features can lead to erroneous inferences. Hence, much time and effort have been devoted to develop the statistical methods to analyze complex survey data and account for the sample design. This issue is particularly important when generating synthetic populations using finite population Bayesian inference, as is often done in missing data or disclosure risk settings, or when combining data from multiple surveys. By extending previous work in finite population Bayesian bootstrap literature, we propose a method to generate synthetic populations from a posterior predictive distribution in a fashion inverts the complex sampling design features and generates simple random samples from a superpopulation point of view, making adjustment on the complex data so that they can be analyzed as simple random samples. We consider a simulation study with a stratified, clustered unequal-probability of selection sample design, and use the proposed nonparametric method to generate synthetic populations for the 2006 National Health Interview Survey (NHIS), and the Medical Expenditure Panel Survey (MEPS), which are stratified, clustered unequal-probability of selection sample designs.

A nonparametric method to generate synthetic populations to adjust for complex sampling design features

PubMed Central

Dong, Qi; Elliott, Michael R.; Raghunathan, Trivellore E.

2017-01-01

Outside of the survey sampling literature, samples are often assumed to be generated by a simple random sampling process that produces independent and identically distributed (IID) samples. Many statistical methods are developed largely in this IID world. Application of these methods to data from complex sample surveys without making allowance for the survey design features can lead to erroneous inferences. Hence, much time and effort have been devoted to develop the statistical methods to analyze complex survey data and account for the sample design. This issue is particularly important when generating synthetic populations using finite population Bayesian inference, as is often done in missing data or disclosure risk settings, or when combining data from multiple surveys. By extending previous work in finite population Bayesian bootstrap literature, we propose a method to generate synthetic populations from a posterior predictive distribution in a fashion inverts the complex sampling design features and generates simple random samples from a superpopulation point of view, making adjustment on the complex data so that they can be analyzed as simple random samples. We consider a simulation study with a stratified, clustered unequal-probability of selection sample design, and use the proposed nonparametric method to generate synthetic populations for the 2006 National Health Interview Survey (NHIS), and the Medical Expenditure Panel Survey (MEPS), which are stratified, clustered unequal-probability of selection sample designs. PMID:29200608

Bayesian multimodel inference for dose-response studies

USGS Publications Warehouse

Link, W.A.; Albers, P.H.

2007-01-01

Statistical inference in dose?response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose?response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

Bayesian B-spline mapping for dynamic quantitative traits.

PubMed

Xing, Jun; Li, Jiahan; Yang, Runqing; Zhou, Xiaojing; Xu, Shizhong

2012-04-01

Owing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located.

A Simple Effect Size Estimator for Single Case Designs Using WinBUGS

ERIC Educational Resources Information Center

Rindskopf, David; Shadish, William; Hedges, Larry V.

2012-01-01

This conference presentation demonstrates a multilevel model for analyzing single case designs. The model is implemented in the Bayesian program WinBUGS. The authors show how it is possible to estimate a d-statistic like the one in Hedges, Pustejovsky and Shadish (2012) in this program. Results are demonstrated on an example.

A comparison of analytic and bayesian approaches for characterizing thermal hysteresis in cattle using algebraic and geometric distances

USDA-ARS?s Scientific Manuscript database

A high ambient temperature poses a serious threat to cattle. Above a certain threshold, an animal’s body temperature (Tb) appears to be driven by the hot cyclic air temperature (Ta) and hysteresis occurs. Elliptical hysteresis describes the output of a process in response to a simple harmonic input,...

Boosting Bayesian parameter inference of stochastic differential equation models with methods from statistical physics

NASA Astrophysics Data System (ADS)

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Measured time-series of both precipitation and runoff are known to exhibit highly non-trivial statistical properties. For making reliable probabilistic predictions in hydrology, it is therefore desirable to have stochastic models with output distributions that share these properties. When parameters of such models have to be inferred from data, we also need to quantify the associated parametric uncertainty. For non-trivial stochastic models, however, this latter step is typically very demanding, both conceptually and numerically, and always never done in hydrology. Here, we demonstrate that methods developed in statistical physics make a large class of stochastic differential equation (SDE) models amenable to a full-fledged Bayesian parameter inference. For concreteness we demonstrate these methods by means of a simple yet non-trivial toy SDE model. We consider a natural catchment that can be described by a linear reservoir, at the scale of observation. All the neglected processes are assumed to happen at much shorter time-scales and are therefore modeled with a Gaussian white noise term, the standard deviation of which is assumed to scale linearly with the system state (water volume in the catchment). Even for constant input, the outputs of this simple non-linear SDE model show a wealth of desirable statistical properties, such as fat-tailed distributions and long-range correlations. Standard algorithms for Bayesian inference fail, for models of this kind, because their likelihood functions are extremely high-dimensional intractable integrals over all possible model realizations. The use of Kalman filters is illegitimate due to the non-linearity of the model. Particle filters could be used but become increasingly inefficient with growing number of data points. Hamiltonian Monte Carlo algorithms allow us to translate this inference problem to the problem of simulating the dynamics of a statistical mechanics system and give us access to most sophisticated methods that have been developed in the statistical physics community over the last few decades. We demonstrate that such methods, along with automated differentiation algorithms, allow us to perform a full-fledged Bayesian inference, for a large class of SDE models, in a highly efficient and largely automatized manner. Furthermore, our algorithm is highly parallelizable. For our toy model, discretized with a few hundred points, a full Bayesian inference can be performed in a matter of seconds on a standard PC.

Bayesian inference for psychology. Part II: Example applications with JASP.

PubMed

Wagenmakers, Eric-Jan; Love, Jonathon; Marsman, Maarten; Jamil, Tahira; Ly, Alexander; Verhagen, Josine; Selker, Ravi; Gronau, Quentin F; Dropmann, Damian; Boutin, Bruno; Meerhoff, Frans; Knight, Patrick; Raj, Akash; van Kesteren, Erik-Jan; van Doorn, Johnny; Šmíra, Martin; Epskamp, Sacha; Etz, Alexander; Matzke, Dora; de Jong, Tim; van den Bergh, Don; Sarafoglou, Alexandra; Steingroever, Helen; Derks, Koen; Rouder, Jeffrey N; Morey, Richard D

2018-02-01

Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder's BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

Applying Bayesian statistics to the study of psychological trauma: A suggestion for future research.

PubMed

Yalch, Matthew M

2016-03-01

Several contemporary researchers have noted the virtues of Bayesian methods of data analysis. Although debates continue about whether conventional or Bayesian statistics is the "better" approach for researchers in general, there are reasons why Bayesian methods may be well suited to the study of psychological trauma in particular. This article describes how Bayesian statistics offers practical solutions to the problems of data non-normality, small sample size, and missing data common in research on psychological trauma. After a discussion of these problems and the effects they have on trauma research, this article explains the basic philosophical and statistical foundations of Bayesian statistics and how it provides solutions to these problems using an applied example. Results of the literature review and the accompanying example indicates the utility of Bayesian statistics in addressing problems common in trauma research. Bayesian statistics provides a set of methodological tools and a broader philosophical framework that is useful for trauma researchers. Methodological resources are also provided so that interested readers can learn more. (c) 2016 APA, all rights reserved).

Laban Movement Analysis towards Behavior Patterns

NASA Astrophysics Data System (ADS)

Santos, Luís; Dias, Jorge

This work presents a study about the use of Laban Movement Analysis (LMA) as a robust tool to describe human basic behavior patterns, to be applied in human-machine interaction. LMA is a language used to describe and annotate dancing movements and is divided in components [1]: Body, Space, Shape and Effort. Despite its general framework is widely used in physical and mental therapy [2], it has found little application in the engineering domain. Rett J. [3] proposed to implement LMA using Bayesian Networks. However LMA component models have not yet been fully implemented. A study on how to approach behavior using LMA is presented. Behavior is a complex feature and movement chain, but we believe that most basic behavior primitives can be discretized in simple features. Correctly identifying Laban parameters and the movements the authors feel that good patterns can be found within a specific set of basic behavior semantics.

Sewer deterioration modeling with condition data lacking historical records.

PubMed

Egger, C; Scheidegger, A; Reichert, P; Maurer, M

2013-11-01

Accurate predictions of future conditions of sewer systems are needed for efficient rehabilitation planning. For this purpose, a range of sewer deterioration models has been proposed which can be improved by calibration with observed sewer condition data. However, if datasets lack historical records, calibration requires a combination of deterioration and sewer rehabilitation models, as the current state of the sewer network reflects the combined effect of both processes. Otherwise, physical sewer lifespans are overestimated as pipes in poor condition that were rehabilitated are no longer represented in the dataset. We therefore propose the combination of a sewer deterioration model with a simple rehabilitation model which can be calibrated with datasets lacking historical information. We use Bayesian inference for parameter estimation due to the limited information content of the data and limited identifiability of the model parameters. A sensitivity analysis gives an insight into the model's robustness against the uncertainty of the prior. The analysis reveals that the model results are principally sensitive to the means of the priors of specific model parameters, which should therefore be elicited with care. The importance sampling technique applied for the sensitivity analysis permitted efficient implementation for regional sensitivity analysis with reasonable computational outlay. Application of the combined model with both simulated and real data shows that it effectively compensates for the bias induced by a lack of historical data. Thus, the novel approach makes it possible to calibrate sewer pipe deterioration models even when historical condition records are lacking. Since at least some prior knowledge of the model parameters is available, the strength of Bayesian inference is particularly evident in the case of small datasets. Copyright © 2013 Elsevier Ltd. All rights reserved.

Bayesian Network Meta-Analysis for Unordered Categorical Outcomes with Incomplete Data

ERIC Educational Resources Information Center

Schmid, Christopher H.; Trikalinos, Thomas A.; Olkin, Ingram

2014-01-01

We develop a Bayesian multinomial network meta-analysis model for unordered (nominal) categorical outcomes that allows for partially observed data in which exact event counts may not be known for each category. This model properly accounts for correlations of counts in mutually exclusive categories and enables proper comparison and ranking of…

A Comparison of Imputation Methods for Bayesian Factor Analysis Models

ERIC Educational Resources Information Center

Merkle, Edgar C.

2011-01-01

Imputation methods are popular for the handling of missing data in psychology. The methods generally consist of predicting missing data based on observed data, yielding a complete data set that is amiable to standard statistical analyses. In the context of Bayesian factor analysis, this article compares imputation under an unrestricted…

Modeling Associations among Multivariate Longitudinal Categorical Variables in Survey Data: A Semiparametric Bayesian Approach

ERIC Educational Resources Information Center

Tchumtchoua, Sylvie; Dey, Dipak K.

2012-01-01

This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the…

Bayesian Meta-Analysis of Cronbach's Coefficient Alpha to Evaluate Informative Hypotheses

ERIC Educational Resources Information Center

Okada, Kensuke

2015-01-01

This paper proposes a new method to evaluate informative hypotheses for meta-analysis of Cronbach's coefficient alpha using a Bayesian approach. The coefficient alpha is one of the most widely used reliability indices. In meta-analyses of reliability, researchers typically form specific informative hypotheses beforehand, such as "alpha of…

Assessment of Matrix Multiplication Learning with a Rule-Based Analytical Model--"A Bayesian Network Representation"

ERIC Educational Resources Information Center

Zhang, Zhidong

2016-01-01

This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model,…

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…

Application of Multiple Imputation for Missing Values in Three-Way Three-Mode Multi-Environment Trial Data

PubMed Central

Tian, Ting; McLachlan, Geoffrey J.; Dieters, Mark J.; Basford, Kaye E.

2015-01-01

It is a common occurrence in plant breeding programs to observe missing values in three-way three-mode multi-environment trial (MET) data. We proposed modifications of models for estimating missing observations for these data arrays, and developed a novel approach in terms of hierarchical clustering. Multiple imputation (MI) was used in four ways, multiple agglomerative hierarchical clustering, normal distribution model, normal regression model, and predictive mean match. The later three models used both Bayesian analysis and non-Bayesian analysis, while the first approach used a clustering procedure with randomly selected attributes and assigned real values from the nearest neighbour to the one with missing observations. Different proportions of data entries in six complete datasets were randomly selected to be missing and the MI methods were compared based on the efficiency and accuracy of estimating those values. The results indicated that the models using Bayesian analysis had slightly higher accuracy of estimation performance than those using non-Bayesian analysis but they were more time-consuming. However, the novel approach of multiple agglomerative hierarchical clustering demonstrated the overall best performances. PMID:26689369

Application of Multiple Imputation for Missing Values in Three-Way Three-Mode Multi-Environment Trial Data.

PubMed

Tian, Ting; McLachlan, Geoffrey J; Dieters, Mark J; Basford, Kaye E

2015-01-01

It is a common occurrence in plant breeding programs to observe missing values in three-way three-mode multi-environment trial (MET) data. We proposed modifications of models for estimating missing observations for these data arrays, and developed a novel approach in terms of hierarchical clustering. Multiple imputation (MI) was used in four ways, multiple agglomerative hierarchical clustering, normal distribution model, normal regression model, and predictive mean match. The later three models used both Bayesian analysis and non-Bayesian analysis, while the first approach used a clustering procedure with randomly selected attributes and assigned real values from the nearest neighbour to the one with missing observations. Different proportions of data entries in six complete datasets were randomly selected to be missing and the MI methods were compared based on the efficiency and accuracy of estimating those values. The results indicated that the models using Bayesian analysis had slightly higher accuracy of estimation performance than those using non-Bayesian analysis but they were more time-consuming. However, the novel approach of multiple agglomerative hierarchical clustering demonstrated the overall best performances.

Approximate string matching algorithms for limited-vocabulary OCR output correction

NASA Astrophysics Data System (ADS)

Lasko, Thomas A.; Hauser, Susan E.

2000-12-01

Five methods for matching words mistranslated by optical character recognition to their most likely match in a reference dictionary were tested on data from the archives of the National Library of Medicine. The methods, including an adaptation of the cross correlation algorithm, the generic edit distance algorithm, the edit distance algorithm with a probabilistic substitution matrix, Bayesian analysis, and Bayesian analysis on an actively thinned reference dictionary were implemented and their accuracy rates compared. Of the five, the Bayesian algorithm produced the most correct matches (87%), and had the advantage of producing scores that have a useful and practical interpretation.

Bayesian conditional-independence modeling of the AIDS epidemic in England and Wales

NASA Astrophysics Data System (ADS)

Gilks, Walter R.; De Angelis, Daniela; Day, Nicholas E.

We describe the use of conditional-independence modeling, Bayesian inference and Markov chain Monte Carlo, to model and project the HIV-AIDS epidemic in homosexual/bisexual males in England and Wales. Complexity in this analysis arises through selectively missing data, indirectly observed underlying processes, and measurement error. Our emphasis is on presentation and discussion of the concepts, not on the technicalities of this analysis, which can be found elsewhere [D. De Angelis, W.R. Gilks, N.E. Day, Bayesian projection of the the acquired immune deficiency syndrome epidemic (with discussion), Applied Statistics, in press].

Time-varying nonstationary multivariate risk analysis using a dynamic Bayesian copula

NASA Astrophysics Data System (ADS)

Sarhadi, Ali; Burn, Donald H.; Concepción Ausín, María.; Wiper, Michael P.

2016-03-01

A time-varying risk analysis is proposed for an adaptive design framework in nonstationary conditions arising from climate change. A Bayesian, dynamic conditional copula is developed for modeling the time-varying dependence structure between mixed continuous and discrete multiattributes of multidimensional hydrometeorological phenomena. Joint Bayesian inference is carried out to fit the marginals and copula in an illustrative example using an adaptive, Gibbs Markov Chain Monte Carlo (MCMC) sampler. Posterior mean estimates and credible intervals are provided for the model parameters and the Deviance Information Criterion (DIC) is used to select the model that best captures different forms of nonstationarity over time. This study also introduces a fully Bayesian, time-varying joint return period for multivariate time-dependent risk analysis in nonstationary environments. The results demonstrate that the nature and the risk of extreme-climate multidimensional processes are changed over time under the impact of climate change, and accordingly the long-term decision making strategies should be updated based on the anomalies of the nonstationary environment.

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

PubMed Central

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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

PubMed

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

2013-12-01

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

Accounting for shared and unshared dosimetric uncertainties in the dose response for ultrasound-detected thyroid nodules after exposure to radioactive fallout.

PubMed

Land, Charles E; Kwon, Deukwoo; Hoffman, F Owen; Moroz, Brian; Drozdovitch, Vladimir; Bouville, André; Beck, Harold; Luckyanov, Nicholas; Weinstock, Robert M; Simon, Steven L

2015-02-01

Dosimetic uncertainties, particularly those that are shared among subgroups of a study population, can bias, distort or reduce the slope or significance of a dose response. Exposure estimates in studies of health risks from environmental radiation exposures are generally highly uncertain and thus, susceptible to these methodological limitations. An analysis was published in 2008 concerning radiation-related thyroid nodule prevalence in a study population of 2,994 villagers under the age of 21 years old between August 1949 and September 1962 and who lived downwind from the Semipalatinsk Nuclear Test Site in Kazakhstan. This dose-response analysis identified a statistically significant association between thyroid nodule prevalence and reconstructed doses of fallout-related internal and external radiation to the thyroid gland; however, the effects of dosimetric uncertainty were not evaluated since the doses were simple point "best estimates". In this work, we revised the 2008 study by a comprehensive treatment of dosimetric uncertainties. Our present analysis improves upon the previous study, specifically by accounting for shared and unshared uncertainties in dose estimation and risk analysis, and differs from the 2008 analysis in the following ways: 1. The study population size was reduced from 2,994 to 2,376 subjects, removing 618 persons with uncertain residence histories; 2. Simulation of multiple population dose sets (vectors) was performed using a two-dimensional Monte Carlo dose estimation method; and 3. A Bayesian model averaging approach was employed for evaluating the dose response, explicitly accounting for large and complex uncertainty in dose estimation. The results were compared against conventional regression techniques. The Bayesian approach utilizes 5,000 independent realizations of population dose vectors, each of which corresponds to a set of conditional individual median internal and external doses for the 2,376 subjects. These 5,000 population dose vectors reflect uncertainties in dosimetric parameters, partly shared and partly independent, among individual members of the study population. Risk estimates for thyroid nodules from internal irradiation were higher than those published in 2008, which results, to the best of our knowledge, from explicitly accounting for dose uncertainty. In contrast to earlier findings, the use of Bayesian methods led to the conclusion that the biological effectiveness for internal and external dose was similar. Estimates of excess relative risk per unit dose (ERR/Gy) for males (177 thyroid nodule cases) were almost 30 times those for females (571 cases) and were similar to those reported for thyroid cancers related to childhood exposures to external and internal sources in other studies. For confirmed cases of papillary thyroid cancers (3 in males, 18 in females), the ERR/Gy was also comparable to risk estimates from other studies, but not significantly different from zero. These findings represent the first reported dose response for a radiation epidemiologic study considering all known sources of shared and unshared errors in dose estimation and using a Bayesian model averaging (BMA) method for analysis of the dose response.

Reliability of a Bayesian network to predict an elevated aldosterone-to-renin ratio.

PubMed

Ducher, Michel; Mounier-Véhier, Claire; Lantelme, Pierre; Vaisse, Bernard; Baguet, Jean-Philippe; Fauvel, Jean-Pierre

2015-05-01

Resistant hypertension is common, mainly idiopathic, but sometimes related to primary aldosteronism. Thus, most hypertension specialists recommend screening for primary aldosteronism. To optimize the selection of patients whose aldosterone-to-renin ratio (ARR) is elevated from simple clinical and biological characteristics. Data from consecutive patients referred between 1 June 2008 and 30 May 2009 were collected retrospectively from five French 'European excellence hypertension centres' institutional registers. Patients were included if they had at least one of: onset of hypertension before age 40 years, resistant hypertension, history of hypokalaemia, efficient treatment by spironolactone, and potassium supplementation. An ARR>32 ng/L and aldosterone>160 ng/L in patients treated without agents altering the renin-angiotensin system was considered as elevated. Bayesian network and stepwise logistic regression were used to predict an elevated ARR. Of 334 patients, 89 were excluded (31 for incomplete data, 32 for taking agents that alter the renin-angiotensin system and 26 for other reasons). Among 245 included patients, 110 had an elevated ARR. Sensitivity reached 100% or 63.3% using Bayesian network or logistic regression, respectively, and specificity reached 89.6% or 67.2%, respectively. The area under the receiver-operating-characteristic curve obtained with the Bayesian network was significantly higher than that obtained by stepwise regression (0.93±0.02 vs. 0.70±0.03; P<0.001). In hypertension centres, Bayesian network efficiently detected patients with an elevated ARR. An external validation study is required before use in primary clinical settings. Copyright © 2015 Elsevier Masson SAS. All rights reserved.

Evaluating impacts using a BACI design, ratios, and a Bayesian approach with a focus on restoration.

PubMed

Conner, Mary M; Saunders, W Carl; Bouwes, Nicolaas; Jordan, Chris

2015-10-01

Before-after-control-impact (BACI) designs are an effective method to evaluate natural and human-induced perturbations on ecological variables when treatment sites cannot be randomly chosen. While effect sizes of interest can be tested with frequentist methods, using Bayesian Markov chain Monte Carlo (MCMC) sampling methods, probabilities of effect sizes, such as a ≥20 % increase in density after restoration, can be directly estimated. Although BACI and Bayesian methods are used widely for assessing natural and human-induced impacts for field experiments, the application of hierarchal Bayesian modeling with MCMC sampling to BACI designs is less common. Here, we combine these approaches and extend the typical presentation of results with an easy to interpret ratio, which provides an answer to the main study question-"How much impact did a management action or natural perturbation have?" As an example of this approach, we evaluate the impact of a restoration project, which implemented beaver dam analogs, on survival and density of juvenile steelhead. Results indicated the probabilities of a ≥30 % increase were high for survival and density after the dams were installed, 0.88 and 0.99, respectively, while probabilities for a higher increase of ≥50 % were variable, 0.17 and 0.82, respectively. This approach demonstrates a useful extension of Bayesian methods that can easily be generalized to other study designs from simple (e.g., single factor ANOVA, paired t test) to more complicated block designs (e.g., crossover, split-plot). This approach is valuable for estimating the probabilities of restoration impacts or other management actions.

Bayesian classification for the selection of in vitro human embryos using morphological and clinical data.

PubMed

Morales, Dinora Araceli; Bengoetxea, Endika; Larrañaga, Pedro; García, Miguel; Franco, Yosu; Fresnada, Mónica; Merino, Marisa

2008-05-01

In vitro fertilization (IVF) is a medically assisted reproduction technique that enables infertile couples to achieve successful pregnancy. Given the uncertainty of the treatment, we propose an intelligent decision support system based on supervised classification by Bayesian classifiers to aid to the selection of the most promising embryos that will form the batch to be transferred to the woman's uterus. The aim of the supervised classification system is to improve overall success rate of each IVF treatment in which a batch of embryos is transferred each time, where the success is achieved when implantation (i.e. pregnancy) is obtained. Due to ethical reasons, different legislative restrictions apply in every country on this technique. In Spain, legislation allows a maximum of three embryos to form each transfer batch. As a result, clinicians prefer to select the embryos by non-invasive embryo examination based on simple methods and observation focused on morphology and dynamics of embryo development after fertilization. This paper proposes the application of Bayesian classifiers to this embryo selection problem in order to provide a decision support system that allows a more accurate selection than with the actual procedures which fully rely on the expertise and experience of embryologists. For this, we propose to take into consideration a reduced subset of feature variables related to embryo morphology and clinical data of patients, and from this data to induce Bayesian classification models. Results obtained applying a filter technique to choose the subset of variables, and the performance of Bayesian classifiers using them, are presented.

Path integration mediated systematic search: a Bayesian model.

PubMed

Vickerstaff, Robert J; Merkle, Tobias

2012-08-21

The systematic search behaviour is a backup system that increases the chances of desert ants finding their nest entrance after foraging when the path integrator has failed to guide them home accurately enough. Here we present a mathematical model of the systematic search that is based on extensive behavioural studies in North African desert ants Cataglyphis fortis. First, a simple search heuristic utilising Bayesian inference and a probability density function is developed. This model, which optimises the short-term nest detection probability, is then compared to three simpler search heuristics and to recorded search patterns of Cataglyphis ants. To compare the different searches a method to quantify search efficiency is established as well as an estimate of the error rate in the ants' path integrator. We demonstrate that the Bayesian search heuristic is able to automatically adapt to increasing levels of positional uncertainty to produce broader search patterns, just as desert ants do, and that it outperforms the three other search heuristics tested. The searches produced by it are also arguably the most similar in appearance to the ant's searches. Copyright © 2012 Elsevier Ltd. All rights reserved.

Statistical inference with quantum measurements: methodologies for nitrogen vacancy centers in diamond

NASA Astrophysics Data System (ADS)

Hincks, Ian; Granade, Christopher; Cory, David G.

2018-01-01

The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (e.g. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NV spin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramér-Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straightforward error propagation into more complex experiments. This is illustrated on experimental data, where quantum Hamiltonian learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

PubMed Central

Cornuet, Jean-Marie; Santos, Filipe; Beaumont, Mark A.; Robert, Christian P.; Marin, Jean-Michel; Balding, David J.; Guillemaud, Thomas; Estoup, Arnaud

2008-01-01

Summary: Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC. Availability: The software DIY ABC is freely available at http://www.montpellier.inra.fr/CBGP/diyabc. Contact: j.cornuet@imperial.ac.uk Supplementary information: Supplementary data are also available at http://www.montpellier.inra.fr/CBGP/diyabc PMID:18842597

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

Disaster Response on September 11, 2001 Through the Lens of Statistical Network Analysis.

PubMed

Schweinberger, Michael; Petrescu-Prahova, Miruna; Vu, Duy Quang

2014-05-01

The rescue and relief operations triggered by the September 11, 2001 attacks on the World Trade Center in New York City demanded collaboration among hundreds of organisations. To shed light on the response to the September 11, 2001 attacks and help to plan and prepare the response to future disasters, we study the inter-organisational network that emerged in response to the attacks. Studying the inter-organisational network can help to shed light on (1) whether some organisations dominated the inter-organisational network and facilitated communication and coordination of the disaster response; (2) whether the dominating organisations were supposed to coordinate disaster response or emerged as coordinators in the wake of the disaster; and (3) the degree of network redundancy and sensitivity of the inter-organisational network to disturbances following the initial disaster. We introduce a Bayesian framework which can answer the substantive questions of interest while being as simple and parsimonious as possible. The framework allows organisations to have varying propensities to collaborate, while taking covariates into account, and allows to assess whether the inter-organisational network had network redundancy-in the form of transitivity-by using a test which may be regarded as a Bayesian score test. We discuss implications in terms of disaster management.

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors.

PubMed

Li, Dan; Wang, Xia; Dey, Dipak K

2016-09-01

Our present work proposes a new survival model in a Bayesian context to analyze right-censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region-specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A Bayesian approach to truncated data sets: An application to Malmquist bias in Supernova Cosmology

NASA Astrophysics Data System (ADS)

March, Marisa Cristina

2018-01-01

A problem commonly encountered in statistical analysis of data is that of truncated data sets. A truncated data set is one in which a number of data points are completely missing from a sample, this is in contrast to a censored sample in which partial information is missing from some data points. In astrophysics this problem is commonly seen in a magnitude limited survey such that the survey is incomplete at fainter magnitudes, that is, certain faint objects are simply not observed. The effect of this `missing data' is manifested as Malmquist bias and can result in biases in parameter inference if it is not accounted for. In Frequentist methodologies the Malmquist bias is often corrected for by analysing many simulations and computing the appropriate correction factors. One problem with this methodology is that the corrections are model dependent. In this poster we derive a Bayesian methodology for accounting for truncated data sets in problems of parameter inference and model selection. We first show the methodology for a simple Gaussian linear model and then go on to show the method for accounting for a truncated data set in the case for cosmological parameter inference with a magnitude limited supernova Ia survey.

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 simplified gross primary production and evapotranspiration model for boreal coniferous forests - is a generic calibration sufficient?

NASA Astrophysics Data System (ADS)

Minunno, F.; Peltoniemi, M.; Launiainen, S.; Aurela, M.; Lindroth, A.; Lohila, A.; Mammarella, I.; Minkkinen, K.; Mäkelä, A.

2015-07-01

The problem of model complexity has been lively debated in environmental sciences as well as in the forest modelling community. Simple models are less input demanding and their calibration involves a lower number of parameters, but they might be suitable only at local scale. In this work we calibrated a simplified ecosystem process model (PRELES) to data from multiple sites and we tested if PRELES can be used at regional scale to estimate the carbon and water fluxes of Boreal conifer forests. We compared a multi-site (M-S) with site-specific (S-S) calibrations. Model calibrations and evaluations were carried out by the means of the Bayesian method; Bayesian calibration (BC) and Bayesian model comparison (BMC) were used to quantify the uncertainty in model parameters and model structure. To evaluate model performances BMC results were combined with more classical analysis of model-data mismatch (M-DM). Evapotranspiration (ET) and gross primary production (GPP) measurements collected in 10 sites of Finland and Sweden were used in the study. Calibration results showed that similar estimates were obtained for the parameters at which model outputs are most sensitive. No significant differences were encountered in the predictions of the multi-site and site-specific versions of PRELES with exception of a site with agricultural history (Alkkia). Although PRELES predicted GPP better than evapotranspiration, we concluded that the model can be reliably used at regional scale to simulate carbon and water fluxes of Boreal forests. Our analyses underlined also the importance of using long and carefully collected flux datasets in model calibration. In fact, even a single site can provide model calibrations that can be applied at a wider spatial scale, since it covers a wide range of variability in climatic conditions.

The Bayesian approach to reporting GSR analysis results: some first-hand experiences

NASA Astrophysics Data System (ADS)

Charles, Sebastien; Nys, Bart

2010-06-01

The use of Bayesian principles in the reporting of forensic findings has been a matter of interest for some years. Recently, also the GSR community is gradually exploring the advantages of this method, or rather approach, for writing reports. Since last year, our GSR group is adapting reporting procedures to the use of Bayesian principles. The police and magistrates find the reports more directly accessible and useful in their part of the criminal investigation. In the lab we find that, through applying the Bayesian principles, unnecessary analyses can be eliminated and thus time can be freed on the instruments.

Analysis of mitochondrial genetic diversity of Ustilago maydis in Mexico.

PubMed

Jiménez-Becerril, María F; Hernández-Delgado, Sanjuana; Solís-Oba, Myrna; González Prieto, Juan M

2018-01-01

The current understanding of the genetic diversity of the phytopathogenic fungus Ustilago maydis is limited. To determine the genetic diversity and structure of U. maydis, 48 fungal isolates were analyzed using mitochondrial simple sequence repeats (SSRs). Tumours (corn smut or 'huitlacoche') were collected from different Mexican states with diverse environmental conditions. Using bioinformatic tools, five microsatellites were identified within intergenic regions of the U. maydis mitochondrial genome. SSRMUM4 was the most polymorphic marker. The most common repeats were hexanucleotides. A total of 12 allelic variants were identified, with a mean of 2.4 alleles per locus. An estimate of the genetic diversity using analysis of molecular variance (AMOVA) revealed that the highest variance component is within states (84%), with moderate genetic differentiation between states (16%) (F ST  = 0.158). A dendrogram generated using the unweighted paired-grouping method with arithmetic averages (UPGMA) and the Bayesian analysis of population structure grouped the U. maydis isolates into two subgroups (K = 2) based on their shared SSRs.

Bayesian Analysis of Multidimensional Item Response Theory Models: A Discussion and Illustration of Three Response Style Models

ERIC Educational Resources Information Center

Leventhal, Brian C.; Stone, Clement A.

2018-01-01

Interest in Bayesian analysis of item response theory (IRT) models has grown tremendously due to the appeal of the paradigm among psychometricians, advantages of these methods when analyzing complex models, and availability of general-purpose software. Possible models include models which reflect multidimensionality due to designed test structure,…

Symptoms of Depression and Challenging Behaviours in People with Intellectual Disability: A Bayesian Analysis. Brief Report

ERIC Educational Resources Information Center

Tsiouris, John; Mann, Rachel; Patti, Paul; Sturmey, Peter

2004-01-01

Clinicians need to know the likelihood of a condition given a positive or negative diagnostic test. In this study a Bayesian analysis of the Clinical Behavior Checklist for Persons with Intellectual Disabilities (CBCPID) to predict depression in people with intellectual disability was conducted. The CBCPID was administered to 92 adults with…

Bayesian analysis of heterogeneous treatment effects for patient-centered outcomes research.

PubMed

Henderson, Nicholas C; Louis, Thomas A; Wang, Chenguang; Varadhan, Ravi

2016-01-01

Evaluation of heterogeneity of treatment effect (HTE) is an essential aspect of personalized medicine and patient-centered outcomes research. Our goal in this article is to promote the use of Bayesian methods for subgroup analysis and to lower the barriers to their implementation by describing the ways in which the companion software beanz can facilitate these types of analyses. To advance this goal, we describe several key Bayesian models for investigating HTE and outline the ways in which they are well-suited to address many of the commonly cited challenges in the study of HTE. Topics highlighted include shrinkage estimation, model choice, sensitivity analysis, and posterior predictive checking. A case study is presented in which we demonstrate the use of the methods discussed.

Predictors of Outcome in Traumatic Brain Injury: New Insight Using Receiver Operating Curve Indices and Bayesian Network Analysis.

PubMed

Zador, Zsolt; Sperrin, Matthew; King, Andrew T

2016-01-01

Traumatic brain injury remains a global health problem. Understanding the relative importance of outcome predictors helps optimize our treatment strategies by informing assessment protocols, clinical decisions and trial designs. In this study we establish importance ranking for outcome predictors based on receiver operating indices to identify key predictors of outcome and create simple predictive models. We then explore the associations between key outcome predictors using Bayesian networks to gain further insight into predictor importance. We analyzed the corticosteroid randomization after significant head injury (CRASH) trial database of 10008 patients and included patients for whom demographics, injury characteristics, computer tomography (CT) findings and Glasgow Outcome Scale (GCS) were recorded (total of 13 predictors, which would be available to clinicians within a few hours following the injury in 6945 patients). Predictions of clinical outcome (death or severe disability at 6 months) were performed using logistic regression models with 5-fold cross validation. Predictive performance was measured using standardized partial area (pAUC) under the receiver operating curve (ROC) and we used Delong test for comparisons. Variable importance ranking was based on pAUC targeted at specificity (pAUCSP) and sensitivity (pAUCSE) intervals of 90-100%. Probabilistic associations were depicted using Bayesian networks. Complete AUC analysis showed very good predictive power (AUC = 0.8237, 95% CI: 0.8138-0.8336) for the complete model. Specificity focused importance ranking highlighted age, pupillary, motor responses, obliteration of basal cisterns/3rd ventricle and midline shift. Interestingly when targeting model sensitivity, the highest-ranking variables were age, severe extracranial injury, verbal response, hematoma on CT and motor response. Simplified models, which included only these key predictors, had similar performance (pAUCSP = 0.6523, 95% CI: 0.6402-0.6641 and pAUCSE = 0.6332, 95% CI: 0.62-0.6477) compared to the complete models (pAUCSP = 0.6664, 95% CI: 0.6543-0.679, pAUCSE = 0.6436, 95% CI: 0.6289-0.6585, de Long p value 0.1165 and 0.3448 respectively). Bayesian networks showed the predictors that did not feature in the simplified models were associated with those that did. We demonstrate that importance based variable selection allows simplified predictive models to be created while maintaining prediction accuracy. Variable selection targeting specificity confirmed key components of clinical assessment in TBI whereas sensitivity based ranking suggested extracranial injury as one of the important predictors. These results help refine our approach to head injury assessment, decision-making and outcome prediction targeted at model sensitivity and specificity. Bayesian networks proved to be a comprehensive tool for depicting probabilistic associations for key predictors giving insight into why the simplified model has maintained accuracy.

Estimating size and scope economies in the Portuguese water sector using the Bayesian stochastic frontier analysis.

PubMed

Carvalho, Pedro; Marques, Rui Cunha

2016-02-15

This study aims to search for economies of size and scope in the Portuguese water sector applying Bayesian and classical statistics to make inference in stochastic frontier analysis (SFA). This study proves the usefulness and advantages of the application of Bayesian statistics for making inference in SFA over traditional SFA which just uses classical statistics. The resulting Bayesian methods allow overcoming some problems that arise in the application of the traditional SFA, such as the bias in small samples and skewness of residuals. In the present case study of the water sector in Portugal, these Bayesian methods provide more plausible and acceptable results. Based on the results obtained we found that there are important economies of output density, economies of size, economies of vertical integration and economies of scope in the Portuguese water sector, pointing out to the huge advantages in undertaking mergers by joining the retail and wholesale components and by joining the drinking water and wastewater services. Copyright © 2015 Elsevier B.V. All rights reserved.

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

Context-dependent decision-making: a simple Bayesian model

PubMed Central

Lloyd, Kevin; Leslie, David S.

2013-01-01

Many phenomena in animal learning can be explained by a context-learning process whereby an animal learns about different patterns of relationship between environmental variables. Differentiating between such environmental regimes or ‘contexts’ allows an animal to rapidly adapt its behaviour when context changes occur. The current work views animals as making sequential inferences about current context identity in a world assumed to be relatively stable but also capable of rapid switches to previously observed or entirely new contexts. We describe a novel decision-making model in which contexts are assumed to follow a Chinese restaurant process with inertia and full Bayesian inference is approximated by a sequential-sampling scheme in which only a single hypothesis about current context is maintained. Actions are selected via Thompson sampling, allowing uncertainty in parameters to drive exploration in a straightforward manner. The model is tested on simple two-alternative choice problems with switching reinforcement schedules and the results compared with rat behavioural data from a number of T-maze studies. The model successfully replicates a number of important behavioural effects: spontaneous recovery, the effect of partial reinforcement on extinction and reversal, the overtraining reversal effect, and serial reversal-learning effects. PMID:23427101

Context-dependent decision-making: a simple Bayesian model.

PubMed

Lloyd, Kevin; Leslie, David S

2013-05-06

Many phenomena in animal learning can be explained by a context-learning process whereby an animal learns about different patterns of relationship between environmental variables. Differentiating between such environmental regimes or 'contexts' allows an animal to rapidly adapt its behaviour when context changes occur. The current work views animals as making sequential inferences about current context identity in a world assumed to be relatively stable but also capable of rapid switches to previously observed or entirely new contexts. We describe a novel decision-making model in which contexts are assumed to follow a Chinese restaurant process with inertia and full Bayesian inference is approximated by a sequential-sampling scheme in which only a single hypothesis about current context is maintained. Actions are selected via Thompson sampling, allowing uncertainty in parameters to drive exploration in a straightforward manner. The model is tested on simple two-alternative choice problems with switching reinforcement schedules and the results compared with rat behavioural data from a number of T-maze studies. The model successfully replicates a number of important behavioural effects: spontaneous recovery, the effect of partial reinforcement on extinction and reversal, the overtraining reversal effect, and serial reversal-learning effects.

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

PubMed Central

Wong, Tony E.; Keller, Klaus

2017-01-01

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

Analyzing the relationship between sequence divergence and nodal support using Bayesian phylogenetic analyses.

PubMed

Makowsky, Robert; Cox, Christian L; Roelke, Corey; Chippindale, Paul T

2010-11-01

Determining the appropriate gene for phylogeny reconstruction can be a difficult process. Rapidly evolving genes tend to resolve recent relationships, but suffer from alignment issues and increased homoplasy among distantly related species. Conversely, slowly evolving genes generally perform best for deeper relationships, but lack sufficient variation to resolve recent relationships. We determine the relationship between sequence divergence and Bayesian phylogenetic reconstruction ability using both natural and simulated datasets. The natural data are based on 28 well-supported relationships within the subphylum Vertebrata. Sequences of 12 genes were acquired and Bayesian analyses were used to determine phylogenetic support for correct relationships. Simulated datasets were designed to determine whether an optimal range of sequence divergence exists across extreme phylogenetic conditions. Across all genes we found that an optimal range of divergence for resolving the correct relationships does exist, although this level of divergence expectedly depends on the distance metric. Simulated datasets show that an optimal range of sequence divergence exists across diverse topologies and models of evolution. We determine that a simple to measure property of genetic sequences (genetic distance) is related to phylogenic reconstruction ability in Bayesian analyses. This information should be useful for selecting the most informative gene to resolve any relationships, especially those that are difficult to resolve, as well as minimizing both cost and confounding information during project design. Copyright © 2010. Published by Elsevier Inc.

A Bayesian framework for infrasound location

NASA Astrophysics Data System (ADS)

Modrak, Ryan T.; Arrowsmith, Stephen J.; Anderson, Dale N.

2010-04-01

We develop a framework for location of infrasound events using backazimuth and infrasonic arrival times from multiple arrays. Bayesian infrasonic source location (BISL) developed here estimates event location and associated credibility regions. BISL accounts for unknown source-to-array path or phase by formulating infrasonic group velocity as random. Differences between observed and predicted source-to-array traveltimes are partitioned into two additive Gaussian sources, measurement error and model error, the second of which accounts for the unknown influence of wind and temperature on path. By applying the technique to both synthetic tests and ground-truth events, we highlight the complementary nature of back azimuths and arrival times for estimating well-constrained event locations. BISL is an extension to methods developed earlier by Arrowsmith et al. that provided simple bounds on location using a grid-search technique.

Bayesian geostatistics in health cartography: the perspective of malaria.

PubMed

Patil, Anand P; Gething, Peter W; Piel, Frédéric B; Hay, Simon I

2011-06-01

Maps of parasite prevalences and other aspects of infectious diseases that vary in space are widely used in parasitology. However, spatial parasitological datasets rarely, if ever, have sufficient coverage to allow exact determination of such maps. Bayesian geostatistics (BG) is a method for finding a large sample of maps that can explain a dataset, in which maps that do a better job of explaining the data are more likely to be represented. This sample represents the knowledge that the analyst has gained from the data about the unknown true map. BG provides a conceptually simple way to convert these samples to predictions of features of the unknown map, for example regional averages. These predictions account for each map in the sample, yielding an appropriate level of predictive precision.

Bayesian geostatistics in health cartography: the perspective of malaria

PubMed Central

Patil, Anand P.; Gething, Peter W.; Piel, Frédéric B.; Hay, Simon I.

2011-01-01

Maps of parasite prevalences and other aspects of infectious diseases that vary in space are widely used in parasitology. However, spatial parasitological datasets rarely, if ever, have sufficient coverage to allow exact determination of such maps. Bayesian geostatistics (BG) is a method for finding a large sample of maps that can explain a dataset, in which maps that do a better job of explaining the data are more likely to be represented. This sample represents the knowledge that the analyst has gained from the data about the unknown true map. BG provides a conceptually simple way to convert these samples to predictions of features of the unknown map, for example regional averages. These predictions account for each map in the sample, yielding an appropriate level of predictive precision. PMID:21420361

Bayesian reconstruction of projection reconstruction NMR (PR-NMR).

PubMed

Yoon, Ji Won

2014-11-01

Projection reconstruction nuclear magnetic resonance (PR-NMR) is a technique for generating multidimensional NMR spectra. A small number of projections from lower-dimensional NMR spectra are used to reconstruct the multidimensional NMR spectra. In our previous work, it was shown that multidimensional NMR spectra are efficiently reconstructed using peak-by-peak based reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. We propose an extended and generalized RJMCMC algorithm replacing a simple linear model with a linear mixed model to reconstruct close NMR spectra into true spectra. This statistical method generates samples in a Bayesian scheme. Our proposed algorithm is tested on a set of six projections derived from the three-dimensional 700 MHz HNCO spectrum of a protein HasA. Copyright © 2014 Elsevier Ltd. All rights reserved.

Bayesian Group Bridge for Bi-level Variable Selection.

PubMed

Mallick, Himel; Yi, Nengjun

2017-06-01

A Bayesian bi-level variable selection method (BAGB: Bayesian Analysis of Group Bridge) is developed for regularized regression and classification. This new development is motivated by grouped data, where generic variables can be divided into multiple groups, with variables in the same group being mechanistically related or statistically correlated. As an alternative to frequentist group variable selection methods, BAGB incorporates structural information among predictors through a group-wise shrinkage prior. Posterior computation proceeds via an efficient MCMC algorithm. In addition to the usual ease-of-interpretation of hierarchical linear models, the Bayesian formulation produces valid standard errors, a feature that is notably absent in the frequentist framework. Empirical evidence of the attractiveness of the method is illustrated by extensive Monte Carlo simulations and real data analysis. Finally, several extensions of this new approach are presented, providing a unified framework for bi-level variable selection in general models with flexible penalties.

Bayesian analysis of CCDM models

NASA Astrophysics Data System (ADS)

Jesus, J. F.; Valentim, R.; Andrade-Oliveira, F.

2017-09-01

Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3αH0 model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.

Alveolar ridge preservation after tooth extraction: a Bayesian Network meta-analysis of grafting materials efficacy on prevention of bone height and width reduction.

PubMed

Iocca, Oreste; Farcomeni, Alessio; Pardiñas Lopez, Simon; Talib, Huzefa S

2017-01-01

To conduct a traditional meta-analysis and a Bayesian Network meta-analysis to synthesize the information coming from randomized controlled trials on different socket grafting materials and combine the resulting indirect evidence in order to make inferences on treatments that have not been compared directly. RCTs were identified for inclusion in the systematic review and subsequent statistical analysis. Bone height and width remodelling were selected as the chosen summary measures for comparison. First, a series of pairwise meta-analyses were performed and overall mean difference (MD) in mm with 95% CI was calculated between grafted versus non-grafted sockets. Then, a Bayesian Network meta-analysis was performed to draw indirect conclusions on which grafting materials can be considered most likely the best compared to the others. From the six included studies, seven comparisons were obtained. Traditional meta-analysis showed statistically significant results in favour of grafting the socket compared to no-graft both for height (MD 1.02, 95% CI 0.44-1.59, p value < 0.001) than for width (MD 1.52 95% CI 1.18-1.86, p value <0.000001) remodelling. Bayesian Network meta-analysis allowed to obtain a rank of intervention efficacy. On the basis of the results of the present analysis, socket grafting seems to be more favourable than unassisted socket healing. Moreover, Bayesian Network meta-analysis indicates that freeze-dried bone graft plus membrane is the most likely effective in the reduction of bone height remodelling. Autologous bone marrow resulted the most likely effective when width remodelling was considered. Studies with larger samples and less risk of bias should be conducted in the future in order to further strengthen the results of this analysis. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

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.

Bayesian Correlation Analysis for Sequence Count Data

PubMed Central

Lau, Nelson; Perkins, Theodore J.

2016-01-01

Evaluating the similarity of different measured variables is a fundamental task of statistics, and a key part of many bioinformatics algorithms. Here we propose a Bayesian scheme for estimating the correlation between different entities’ measurements based on high-throughput sequencing data. These entities could be different genes or miRNAs whose expression is measured by RNA-seq, different transcription factors or histone marks whose expression is measured by ChIP-seq, or even combinations of different types of entities. Our Bayesian formulation accounts for both measured signal levels and uncertainty in those levels, due to varying sequencing depth in different experiments and to varying absolute levels of individual entities, both of which affect the precision of the measurements. In comparison with a traditional Pearson correlation analysis, we show that our Bayesian correlation analysis retains high correlations when measurement confidence is high, but suppresses correlations when measurement confidence is low—especially for entities with low signal levels. In addition, we consider the influence of priors on the Bayesian correlation estimate. Perhaps surprisingly, we show that naive, uniform priors on entities’ signal levels can lead to highly biased correlation estimates, particularly when different experiments have widely varying sequencing depths. However, we propose two alternative priors that provably mitigate this problem. We also prove that, like traditional Pearson correlation, our Bayesian correlation calculation constitutes a kernel in the machine learning sense, and thus can be used as a similarity measure in any kernel-based machine learning algorithm. We demonstrate our approach on two RNA-seq datasets and one miRNA-seq dataset. PMID:27701449

Online Variational Bayesian Filtering-Based Mobile Target Tracking in Wireless Sensor Networks

PubMed Central

Zhou, Bingpeng; Chen, Qingchun; Li, Tiffany Jing; Xiao, Pei

2014-01-01

The received signal strength (RSS)-based online tracking for a mobile node in wireless sensor networks (WSNs) is investigated in this paper. Firstly, a multi-layer dynamic Bayesian network (MDBN) is introduced to characterize the target mobility with either directional or undirected movement. In particular, it is proposed to employ the Wishart distribution to approximate the time-varying RSS measurement precision's randomness due to the target movement. It is shown that the proposed MDBN offers a more general analysis model via incorporating the underlying statistical information of both the target movement and observations, which can be utilized to improve the online tracking capability by exploiting the Bayesian statistics. Secondly, based on the MDBN model, a mean-field variational Bayesian filtering (VBF) algorithm is developed to realize the online tracking of a mobile target in the presence of nonlinear observations and time-varying RSS precision, wherein the traditional Bayesian filtering scheme cannot be directly employed. Thirdly, a joint optimization between the real-time velocity and its prior expectation is proposed to enable online velocity tracking in the proposed online tacking scheme. Finally, the associated Bayesian Cramer–Rao Lower Bound (BCRLB) analysis and numerical simulations are conducted. Our analysis unveils that, by exploiting the potential state information via the general MDBN model, the proposed VBF algorithm provides a promising solution to the online tracking of a mobile node in WSNs. In addition, it is shown that the final tracking accuracy linearly scales with its expectation when the RSS measurement precision is time-varying. PMID:25393784

Systemic antibiotics in the treatment of aggressive periodontitis. A systematic review and a Bayesian Network meta-analysis.

PubMed

Rabelo, Cleverton Correa; Feres, Magda; Gonçalves, Cristiane; Figueiredo, Luciene C; Faveri, Marcelo; Tu, Yu-Kang; Chambrone, Leandro

2015-07-01

The aim of this study was to assess the effect of systemic antibiotic therapy on the treatment of aggressive periodontitis (AgP). This study was conducted and reported in accordance with the PRISMA statement. The MEDLINE, EMBASE and CENTRAL databases were searched up to June 2014 for randomized clinical trials comparing the treatment of subjects with AgP with either scaling and root planing (SRP) alone or associated with systemic antibiotics. Bayesian network meta-analysis was prepared using the Bayesian random-effects hierarchical models and the outcomes reported at 6-month post-treatment. Out of 350 papers identified, 14 studies were eligible. Greater gain in clinical attachment (CA) (mean difference [MD]: 1.08 mm; p < 0.0001) and reduction in probing depth (PD) (MD: 1.05 mm; p < 0.00001) were observed for SRP + metronidazole (Mtz), and for SRP + Mtz + amoxicillin (Amx) (MD: 0.45 mm, MD: 0.53 mm, respectively; p < 0.00001) than SRP alone/placebo. Bayesian network meta-analysis showed additional benefits in CA gain and PD reduction when SRP was associated with systemic antibiotics. SRP plus systemic antibiotics led to an additional clinical effect compared with SRP alone in the treatment of AgP. Of the antibiotic protocols available for inclusion into the Bayesian network meta-analysis, Mtz and Mtz/Amx provided to the most beneficial outcomes. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

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

PubMed

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

2016-03-01

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

Maritime Transportation Risk Assessment of Tianjin Port with Bayesian Belief Networks.

PubMed

Zhang, Jinfen; Teixeira, Ângelo P; Guedes Soares, C; Yan, Xinping; Liu, Kezhong

2016-06-01

This article develops a Bayesian belief network model for the prediction of accident consequences in the Tianjin port. The study starts with a statistical analysis of historical accident data of six years from 2008 to 2013. Then a Bayesian belief network is constructed to express the dependencies between the indicator variables and accident consequences. The statistics and expert knowledge are synthesized in the Bayesian belief network model to obtain the probability distribution of the consequences. By a sensitivity analysis, several indicator variables that have influence on the consequences are identified, including navigational area, ship type and time of the day. The results indicate that the consequences are most sensitive to the position where the accidents occurred, followed by time of day and ship length. The results also reflect that the navigational risk of the Tianjin port is at the acceptable level, despite that there is more room of improvement. These results can be used by the Maritime Safety Administration to take effective measures to enhance maritime safety in the Tianjin port. © 2016 Society for Risk Analysis.

Risk Assessment for Mobile Systems Through a Multilayered Hierarchical Bayesian Network.

PubMed

Li, Shancang; Tryfonas, Theo; Russell, Gordon; Andriotis, Panagiotis

2016-08-01

Mobile systems are facing a number of application vulnerabilities that can be combined together and utilized to penetrate systems with devastating impact. When assessing the overall security of a mobile system, it is important to assess the security risks posed by each mobile applications (apps), thus gaining a stronger understanding of any vulnerabilities present. This paper aims at developing a three-layer framework that assesses the potential risks which apps introduce within the Android mobile systems. A Bayesian risk graphical model is proposed to evaluate risk propagation in a layered risk architecture. By integrating static analysis, dynamic analysis, and behavior analysis in a hierarchical framework, the risks and their propagation through each layer are well modeled by the Bayesian risk graph, which can quantitatively analyze risks faced to both apps and mobile systems. The proposed hierarchical Bayesian risk graph model offers a novel way to investigate the security risks in mobile environment and enables users and administrators to evaluate the potential risks. This strategy allows to strengthen both app security as well as the security of the entire system.

Embedding the results of focussed Bayesian fusion into a global context

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael

2014-05-01

Bayesian statistics offers a well-founded and powerful fusion methodology also for the fusion of heterogeneous information sources. However, except in special cases, the needed posterior distribution is not analytically derivable. As consequence, Bayesian fusion may cause unacceptably high computational and storage costs in practice. Local Bayesian fusion approaches aim at reducing the complexity of the Bayesian fusion methodology significantly. This is done by concentrating the actual Bayesian fusion on the potentially most task relevant parts of the domain of the Properties of Interest. Our research on these approaches is motivated by an analogy to criminal investigations where criminalists pursue clues also only locally. This publication follows previous publications on a special local Bayesian fusion technique called focussed Bayesian fusion. Here, the actual calculation of the posterior distribution gets completely restricted to a suitably chosen local context. By this, the global posterior distribution is not completely determined. Strategies for using the results of a focussed Bayesian analysis appropriately are needed. In this publication, we primarily contrast different ways of embedding the results of focussed Bayesian fusion explicitly into a global context. To obtain a unique global posterior distribution, we analyze the application of the Maximum Entropy Principle that has been shown to be successfully applicable in metrology and in different other areas. To address the special need for making further decisions subsequently to the actual fusion task, we further analyze criteria for decision making under partial information.

A Bayesian framework for extracting human gait using strong prior knowledge.

PubMed

Zhou, Ziheng; Prügel-Bennett, Adam; Damper, Robert I

2006-11-01

Extracting full-body motion of walking people from monocular video sequences in complex, real-world environments is an important and difficult problem, going beyond simple tracking, whose satisfactory solution demands an appropriate balance between use of prior knowledge and learning from data. We propose a consistent Bayesian framework for introducing strong prior knowledge into a system for extracting human gait. In this work, the strong prior is built from a simple articulated model having both time-invariant (static) and time-variant (dynamic) parameters. The model is easily modified to cater to situations such as walkers wearing clothing that obscures the limbs. The statistics of the parameters are learned from high-quality (indoor laboratory) data and the Bayesian framework then allows us to "bootstrap" to accurate gait extraction on the noisy images typical of cluttered, outdoor scenes. To achieve automatic fitting, we use a hidden Markov model to detect the phases of images in a walking cycle. We demonstrate our approach on silhouettes extracted from fronto-parallel ("sideways on") sequences of walkers under both high-quality indoor and noisy outdoor conditions. As well as high-quality data with synthetic noise and occlusions added, we also test walkers with rucksacks, skirts, and trench coats. Results are quantified in terms of chamfer distance and average pixel error between automatically extracted body points and corresponding hand-labeled points. No one part of the system is novel in itself, but the overall framework makes it feasible to extract gait from very much poorer quality image sequences than hitherto. This is confirmed by comparing person identification by gait using our method and a well-established baseline recognition algorithm.

Phylogeny of sipunculan worms: A combined analysis of four gene regions and morphology.

PubMed

Schulze, Anja; Cutler, Edward B; Giribet, Gonzalo

2007-01-01

The intra-phyletic relationships of sipunculan worms were analyzed based on DNA sequence data from four gene regions and 58 morphological characters. Initially we analyzed the data under direct optimization using parsimony as optimality criterion. An implied alignment resulting from the direct optimization analysis was subsequently utilized to perform a Bayesian analysis with mixed models for the different data partitions. For this we applied a doublet model for the stem regions of the 18S rRNA. Both analyses support monophyly of Sipuncula and most of the same clades within the phylum. The analyses differ with respect to the relationships among the major groups but whereas the deep nodes in the direct optimization analysis generally show low jackknife support, they are supported by 100% posterior probability in the Bayesian analysis. Direct optimization has been useful for handling sequences of unequal length and generating conservative phylogenetic hypotheses whereas the Bayesian analysis under mixed models provided high resolution in the basal nodes of the tree.

A Bayesian analysis of gene flow from crops to their wild relatives: cultivated (Lactuca sativa L.) and prickly lettuce (L. serriola L.) and the recent expansion of L. serriola in Europe.

PubMed

Uwimana, Brigitte; D'Andrea, Luigi; Felber, François; Hooftman, Danny A P; Den Nijs, Hans C M; Smulders, Marinus J M; Visser, Richard G F; Van De Wiel, Clemens C M

2012-06-01

Interspecific gene flow can lead to the formation of hybrid populations that have a competitive advantage over the parental populations, even for hybrids from a cross between crops and wild relatives. Wild prickly lettuce (Lactuca serriola) has recently expanded in Europe and hybridization with the related crop species (cultivated lettuce, L. sativa) has been hypothesized as one of the mechanisms behind this expansion. In a basically selfing species, such as lettuce, assessing hybridization in natural populations may not be straightforward. Therefore, we analysed a uniquely large data set of plants genotyped with SSR (simple sequence repeat) markers with two programs for Bayesian population genetic analysis, STRUCTURE and NewHybrids. The data set comprised 7738 plants, including a complete genebank collection, which provided a wide coverage of cultivated germplasm and a fair coverage of wild accessions, and a set of wild populations recently sampled across Europe. STRUCTURE analysis inferred the occurrence of hybrids at a level of 7% across Europe. NewHybrids indicated these hybrids to be advanced selfed generations of a hybridization event or of one backcross after such an event, which is according to expectations for a basically selfing species. These advanced selfed generations could not be detected effectively with crop-specific alleles. In the northern part of Europe, where the expansion of L. serriola took place, the fewest putative hybrids were found. Therefore, we conclude that other mechanisms than crop/wild gene flow, such as an increase in disturbed habitats and/or climate warming, are more likely explanations for this expansion. © 2012 Blackwell Publishing Ltd.

Bayesian models: A statistical primer for ecologists

USGS Publications Warehouse

Hobbs, N. Thompson; Hooten, Mevin B.

2015-01-01

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach.Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian models

Semiparametric Thurstonian Models for Recurrent Choices: A Bayesian Analysis

ERIC Educational Resources Information Center

Ansari, Asim; Iyengar, Raghuram

2006-01-01

We develop semiparametric Bayesian Thurstonian models for analyzing repeated choice decisions involving multinomial, multivariate binary or multivariate ordinal data. Our modeling framework has multiple components that together yield considerable flexibility in modeling preference utilities, cross-sectional heterogeneity and parameter-driven…

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

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

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

Deep Learning Neural Networks and Bayesian Neural Networks in Data Analysis

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

PubMed Central

Puig, X; Ginebra, J; Graffelman, J

2017-01-01

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

Uncertainty Analysis and Parameter Estimation For Nearshore Hydrodynamic Models

NASA Astrophysics Data System (ADS)

Ardani, S.; Kaihatu, J. M.

2012-12-01

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

Automated Bayesian model development for frequency detection in biological time series.

PubMed

Granqvist, Emma; Oldroyd, Giles E D; Morris, Richard J

2011-06-24

A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure.

Automated Bayesian model development for frequency detection in biological time series

PubMed Central

2011-01-01

Background A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. Results In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Conclusions Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure. PMID:21702910

Bayesian ensemble refinement by replica simulations and reweighting.

PubMed

Hummer, Gerhard; Köfinger, Jürgen

2015-12-28

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

Bayesian ensemble refinement by replica simulations and reweighting

NASA Astrophysics Data System (ADS)

Hummer, Gerhard; Köfinger, Jürgen

2015-12-01

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

Simple Form of MMSE Estimator for Super-Gaussian Prior Densities

NASA Astrophysics Data System (ADS)

Kittisuwan, Pichid

2015-04-01

The denoising method that become popular in recent years for additive white Gaussian noise (AWGN) are Bayesian estimation techniques e.g., maximum a posteriori (MAP) and minimum mean square error (MMSE). In super-Gaussian prior densities, it is well known that the MMSE estimator in such a case has a complicated form. In this work, we derive the MMSE estimation with Taylor series. We show that the proposed estimator also leads to a simple formula. An extension of this estimator to Pearson type VII prior density is also offered. The experimental result shows that the proposed estimator to the original MMSE nonlinearity is reasonably good.

Making Sense of a Negative Clinical Trial Result: A Bayesian Analysis of a Clinical Trial of Lorazepam and Diazepam for Pediatric Status Epilepticus.

PubMed

Chamberlain, Daniel B; Chamberlain, James M

2017-01-01

We demonstrate the application of a Bayesian approach to a recent negative clinical trial result. A Bayesian analysis of such a trial can provide a more useful interpretation of results and can incorporate previous evidence. This was a secondary analysis of the efficacy and safety results of the Pediatric Seizure Study, a randomized clinical trial of lorazepam versus diazepam for pediatric status epilepticus. We included the published results from the only prospective pediatric study of status in a Bayesian hierarchic model, and we performed sensitivity analyses on the amount of pooling between studies. We evaluated 3 summary analyses for the results: superiority, noninferiority (margin <-10%), and practical equivalence (within ±10%). Consistent with the original study's classic analysis of study results, we did not demonstrate superiority of lorazepam over diazepam. There is a 95% probability that the true efficacy of lorazepam is in the range of 66% to 80%. For both the efficacy and safety outcomes, there was greater than 95% probability that lorazepam is noninferior to diazepam, and there was greater than 90% probability that the 2 medications are practically equivalent. The results were largely driven by the current study because of the sample sizes of our study (n=273) and the previous pediatric study (n=61). Because Bayesian analysis estimates the probability of one or more hypotheses, such an approach can provide more useful information about the meaning of the results of a negative trial outcome. In the case of pediatric status epilepticus, it is highly likely that lorazepam is noninferior and practically equivalent to diazepam. Copyright © 2016 American College of Emergency Physicians. Published by Elsevier Inc. All rights reserved.

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

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Bayesian isotonic density regression

PubMed Central

Wang, Lianming; Dunson, David B.

2011-01-01

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

Estimability and simple dynamical analyses of range (range-rate range-difference) observations to artificial satellites. [laser range observations to LAGEOS using non-Bayesian statistics

NASA Technical Reports Server (NTRS)

Vangelder, B. H. W.

1978-01-01

Non-Bayesian statistics were used in simulation studies centered around laser range observations to LAGEOS. The capabilities of satellite laser ranging especially in connection with relative station positioning are evaluated. The satellite measurement system under investigation may fall short in precise determinations of the earth's orientation (precession and nutation) and earth's rotation as opposed to systems as very long baseline interferometry (VLBI) and lunar laser ranging (LLR). Relative station positioning, determination of (differential) polar motion, positioning of stations with respect to the earth's center of mass and determination of the earth's gravity field should be easily realized by satellite laser ranging (SLR). The last two features should be considered as best (or solely) determinable by SLR in contrast to VLBI and LLR.

A Bayesian Multinomial Probit MODEL FOR THE ANALYSIS OF PANEL CHOICE DATA.

PubMed

Fong, Duncan K H; Kim, Sunghoon; Chen, Zhe; DeSarbo, Wayne S

2016-03-01

A new Bayesian multinomial probit model is proposed for the analysis of panel choice data. Using a parameter expansion technique, we are able to devise a Markov Chain Monte Carlo algorithm to compute our Bayesian estimates efficiently. We also show that the proposed procedure enables the estimation of individual level coefficients for the single-period multinomial probit model even when the available prior information is vague. We apply our new procedure to consumer purchase data and reanalyze a well-known scanner panel dataset that reveals new substantive insights. In addition, we delineate a number of advantageous features of our proposed procedure over several benchmark models. Finally, through a simulation analysis employing a fractional factorial design, we demonstrate that the results from our proposed model are quite robust with respect to differing factors across various conditions.

A fully Bayesian before-after analysis of permeable friction course (PFC) pavement wet weather safety.

PubMed

Buddhavarapu, Prasad; Smit, Andre F; Prozzi, Jorge A

2015-07-01

Permeable friction course (PFC), a porous hot-mix asphalt, is typically applied to improve wet weather safety on high-speed roadways in Texas. In order to warrant expensive PFC construction, a statistical evaluation of its safety benefits is essential. Generally, the literature on the effectiveness of porous mixes in reducing wet-weather crashes is limited and often inconclusive. In this study, the safety effectiveness of PFC was evaluated using a fully Bayesian before-after safety analysis. First, two groups of road segments overlaid with PFC and non-PFC material were identified across Texas; the non-PFC or reference road segments selected were similar to their PFC counterparts in terms of site specific features. Second, a negative binomial data generating process was assumed to model the underlying distribution of crash counts of PFC and reference road segments to perform Bayesian inference on the safety effectiveness. A data-augmentation based computationally efficient algorithm was employed for a fully Bayesian estimation. The statistical analysis shows that PFC is not effective in reducing wet weather crashes. It should be noted that the findings of this study are in agreement with the existing literature, although these studies were not based on a fully Bayesian statistical analysis. Our study suggests that the safety effectiveness of PFC road surfaces, or any other safety infrastructure, largely relies on its interrelationship with the road user. The results suggest that the safety infrastructure must be properly used to reap the benefits of the substantial investments. Copyright © 2015 Elsevier Ltd. All rights reserved.

A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models

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

Xu, Jin; Yu, Yaming; Van Dyk, David A.

2014-10-20

Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use amore » principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.« less

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

NASA Astrophysics Data System (ADS)

Crabtree, Chris; Ganguli, Gurudas; Tejero, Erik

2017-10-01

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

Bayesian just-so stories in psychology and neuroscience.

PubMed

Bowers, Jeffrey S; Davis, Colin J

2012-05-01

According to Bayesian theories in psychology and neuroscience, minds and brains are (near) optimal in solving a wide range of tasks. We challenge this view and argue that more traditional, non-Bayesian approaches are more promising. We make 3 main arguments. First, we show that the empirical evidence for Bayesian theories in psychology is weak. This weakness relates to the many arbitrary ways that priors, likelihoods, and utility functions can be altered in order to account for the data that are obtained, making the models unfalsifiable. It further relates to the fact that Bayesian theories are rarely better at predicting data compared with alternative (and simpler) non-Bayesian theories. Second, we show that the empirical evidence for Bayesian theories in neuroscience is weaker still. There are impressive mathematical analyses showing how populations of neurons could compute in a Bayesian manner but little or no evidence that they do. Third, we challenge the general scientific approach that characterizes Bayesian theorizing in cognitive science. A common premise is that theories in psychology should largely be constrained by a rational analysis of what the mind ought to do. We question this claim and argue that many of the important constraints come from biological, evolutionary, and processing (algorithmic) considerations that have no adaptive relevance to the problem per se. In our view, these factors have contributed to the development of many Bayesian "just so" stories in psychology and neuroscience; that is, mathematical analyses of cognition that can be used to explain almost any behavior as optimal. 2012 APA, all rights reserved.

Evaluation of a Partial Genome Screening of Two Asthma Susceptibility Regions Using Bayesian Network Based Bayesian Multilevel Analysis of Relevance

PubMed Central

Antal, Péter; Kiszel, Petra Sz.; Gézsi, András; Hadadi, Éva; Virág, Viktor; Hajós, Gergely; Millinghoffer, András; Nagy, Adrienne; Kiss, András; Semsei, Ágnes F.; Temesi, Gergely; Melegh, Béla; Kisfali, Péter; Széll, Márta; Bikov, András; Gálffy, Gabriella; Tamási, Lilla; Falus, András; Szalai, Csaba

2012-01-01

Genetic studies indicate high number of potential factors related to asthma. Based on earlier linkage analyses we selected the 11q13 and 14q22 asthma susceptibility regions, for which we designed a partial genome screening study using 145 SNPs in 1201 individuals (436 asthmatic children and 765 controls). The results were evaluated with traditional frequentist methods and we applied a new statistical method, called Bayesian network based Bayesian multilevel analysis of relevance (BN-BMLA). This method uses Bayesian network representation to provide detailed characterization of the relevance of factors, such as joint significance, the type of dependency, and multi-target aspects. We estimated posteriors for these relations within the Bayesian statistical framework, in order to estimate the posteriors whether a variable is directly relevant or its association is only mediated. With frequentist methods one SNP (rs3751464 in the FRMD6 gene) provided evidence for an association with asthma (OR = 1.43(1.2–1.8); p = 3×10−4). The possible role of the FRMD6 gene in asthma was also confirmed in an animal model and human asthmatics. In the BN-BMLA analysis altogether 5 SNPs in 4 genes were found relevant in connection with asthma phenotype: PRPF19 on chromosome 11, and FRMD6, PTGER2 and PTGDR on chromosome 14. In a subsequent step a partial dataset containing rhinitis and further clinical parameters was used, which allowed the analysis of relevance of SNPs for asthma and multiple targets. These analyses suggested that SNPs in the AHNAK and MS4A2 genes were indirectly associated with asthma. This paper indicates that BN-BMLA explores the relevant factors more comprehensively than traditional statistical methods and extends the scope of strong relevance based methods to include partial relevance, global characterization of relevance and multi-target relevance. PMID:22432035

A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study.

PubMed

Kaplan, David; Chen, Jianshen

2012-07-01

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for three methods of implementation: propensity score stratification, weighting, and optimal full matching. Three simulation studies and one case study are presented to elaborate the proposed two-step Bayesian propensity score approach. Results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist-based treatment effect. A slight advantage is shown for the Bayesian approach in small samples. Results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results. However, greater precision around the correct treatment effect parameter yields quite good results, with slight improvement seen with greater precision in the propensity score equation. A comparison of coverage rates for the conventional frequentist approach and proposed Bayesian approach is also provided. The case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non-informative.

Robust Bayesian Analysis of Heavy-tailed Stochastic Volatility Models using Scale Mixtures of Normal Distributions

PubMed Central

Abanto-Valle, C. A.; Bandyopadhyay, D.; Lachos, V. H.; Enriquez, I.

2009-01-01

A Bayesian analysis of stochastic volatility (SV) models using the class of symmetric scale mixtures of normal (SMN) distributions is considered. In the face of non-normality, this provides an appealing robust alternative to the routine use of the normal distribution. Specific distributions examined include the normal, student-t, slash and the variance gamma distributions. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. The methods developed are applied to analyze daily stock returns data on S&P500 index. Bayesian model selection criteria as well as out-of- sample forecasting results reveal that the SV models based on heavy-tailed SMN distributions provide significant improvement in model fit as well as prediction to the S&P500 index data over the usual normal model. PMID:20730043

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

PubMed

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

2017-07-01

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

Bayesian Estimation of the True Prevalence and of the Diagnostic Test Sensitivity and Specificity of Enteropathogenic Yersinia in Finnish Pig Serum Samples.

PubMed

Vilar, M J; Ranta, J; Virtanen, S; Korkeala, H

2015-01-01

Bayesian analysis was used to estimate the pig's and herd's true prevalence of enteropathogenic Yersinia in serum samples collected from Finnish pig farms. The sensitivity and specificity of the diagnostic test were also estimated for the commercially available ELISA which is used for antibody detection against enteropathogenic Yersinia. The Bayesian analysis was performed in two steps; the first step estimated the prior true prevalence of enteropathogenic Yersinia with data obtained from a systematic review of the literature. In the second step, data of the apparent prevalence (cross-sectional study data), prior true prevalence (first step), and estimated sensitivity and specificity of the diagnostic methods were used for building the Bayesian model. The true prevalence of Yersinia in slaughter-age pigs was 67.5% (95% PI 63.2-70.9). The true prevalence of Yersinia in sows was 74.0% (95% PI 57.3-82.4). The estimates of sensitivity and specificity values of the ELISA were 79.5% and 96.9%.

Accounting for Shared and Unshared Dosimetric Uncertainties in the Dose Response for Ultrasound-Detected Thyroid Nodules after Exposure to Radioactive Fallout

PubMed Central

Hoffman, F. Owen; Moroz, Brian; Drozdovitch, Vladimir; Bouville, André; Beck, Harold; Luckyanov, Nicholas; Weinstock, Robert M.; Simon, Steven L.

2015-01-01

Dosimetic uncertainties, particularly those that are shared among subgroups of a study population, can bias, distort or reduce the slope or significance of a dose response. Exposure estimates in studies of health risks from environmental radiation exposures are generally highly uncertain and thus, susceptible to these methodological limitations. An analysis was published in 2008 concerning radiation-related thyroid nodule prevalence in a study population of 2,994 villagers under the age of 21 years old between August 1949 and September 1962 and who lived downwind from the Semi-palatinsk Nuclear Test Site in Kazakhstan. This dose-response analysis identified a statistically significant association between thyroid nodule prevalence and reconstructed doses of fallout-related internal and external radiation to the thyroid gland; however, the effects of dosimetric uncertainty were not evaluated since the doses were simple point “best estimates”. In this work, we revised the 2008 study by a comprehensive treatment of dosimetric uncertainties. Our present analysis improves upon the previous study, specifically by accounting for shared and unshared uncertainties in dose estimation and risk analysis, and differs from the 2008 analysis in the following ways: 1. The study population size was reduced from 2,994 to 2,376 subjects, removing 618 persons with uncertain residence histories; 2. Simulation of multiple population dose sets (vectors) was performed using a two-dimensional Monte Carlo dose estimation method; and 3. A Bayesian model averaging approach was employed for evaluating the dose response, explicitly accounting for large and complex uncertainty in dose estimation. The results were compared against conventional regression techniques. The Bayesian approach utilizes 5,000 independent realizations of population dose vectors, each of which corresponds to a set of conditional individual median internal and external doses for the 2,376 subjects. These 5,000 population dose vectors reflect uncertainties in dosimetric parameters, partly shared and partly independent, among individual members of the study population. Risk estimates for thyroid nodules from internal irradiation were higher than those published in 2008, which results, to the best of our knowledge, from explicitly accounting for dose uncertainty. In contrast to earlier findings, the use of Bayesian methods led to the conclusion that the biological effectiveness for internal and external dose was similar. Estimates of excess relative risk per unit dose (ERR/Gy) for males (177 thyroid nodule cases) were almost 30 times those for females (571 cases) and were similar to those reported for thyroid cancers related to childhood exposures to external and internal sources in other studies. For confirmed cases of papillary thyroid cancers (3 in males, 18 in females), the ERR/Gy was also comparable to risk estimates from other studies, but not significantly different from zero. These findings represent the first reported dose response for a radiation epidemiologic study considering all known sources of shared and unshared errors in dose estimation and using a Bayesian model averaging (BMA) method for analysis of the dose response. PMID:25574587

A Bayesian Approach to a Multiple-Group Latent Class-Profile Analysis: The Timing of Drinking Onset and Subsequent Drinking Behaviors among U.S. Adolescents

ERIC Educational Resources Information Center

Chung, Hwan; Anthony, James C.

2013-01-01

This article presents a multiple-group latent class-profile analysis (LCPA) by taking a Bayesian approach in which a Markov chain Monte Carlo simulation is employed to achieve more robust estimates for latent growth patterns. This article describes and addresses a label-switching problem that involves the LCPA likelihood function, which has…

Bayesian Logic Programs for Plan Recognition and Machine Reading

DTIC Science & Technology

2012-12-01

models is that they can handle both uncertainty and structured/ relational data. As a result, they are widely used in domains like social network...data. As a result, they are widely used in domains like social net- work analysis, biological data analysis, and natural language processing. Bayesian...the Story Understanding data set. (b) The logical representation of the observations. (c) The set of ground rules obtained from logical abduction

Uncertainty plus prior equals rational bias: an intuitive Bayesian probability weighting function.

PubMed

Fennell, John; Baddeley, Roland

2012-10-01

Empirical research has shown that when making choices based on probabilistic options, people behave as if they overestimate small probabilities, underestimate large probabilities, and treat positive and negative outcomes differently. These distortions have been modeled using a nonlinear probability weighting function, which is found in several nonexpected utility theories, including rank-dependent models and prospect theory; here, we propose a Bayesian approach to the probability weighting function and, with it, a psychological rationale. In the real world, uncertainty is ubiquitous and, accordingly, the optimal strategy is to combine probability statements with prior information using Bayes' rule. First, we show that any reasonable prior on probabilities leads to 2 of the observed effects; overweighting of low probabilities and underweighting of high probabilities. We then investigate 2 plausible kinds of priors: informative priors based on previous experience and uninformative priors of ignorance. Individually, these priors potentially lead to large problems of bias and inefficiency, respectively; however, when combined using Bayesian model comparison methods, both forms of prior can be applied adaptively, gaining the efficiency of empirical priors and the robustness of ignorance priors. We illustrate this for the simple case of generic good and bad options, using Internet blogs to estimate the relevant priors of inference. Given this combined ignorant/informative prior, the Bayesian probability weighting function is not only robust and efficient but also matches all of the major characteristics of the distortions found in empirical research. PsycINFO Database Record (c) 2012 APA, all rights reserved.

Bayesian Models for Astrophysical Data Using R, JAGS, Python, and Stan

NASA Astrophysics Data System (ADS)

Hilbe, Joseph M.; de Souza, Rafael S.; Ishida, Emille E. O.

2017-05-01

This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

Toward an ecological analysis of Bayesian inferences: how task characteristics influence responses

PubMed Central

Hafenbrädl, Sebastian; Hoffrage, Ulrich

2015-01-01

In research on Bayesian inferences, the specific tasks, with their narratives and characteristics, are typically seen as exchangeable vehicles that merely transport the structure of the problem to research participants. In the present paper, we explore whether, and possibly how, task characteristics that are usually ignored influence participants’ responses in these tasks. We focus on both quantitative dimensions of the tasks, such as their base rates, hit rates, and false-alarm rates, as well as qualitative characteristics, such as whether the task involves a norm violation or not, whether the stakes are high or low, and whether the focus is on the individual case or on the numbers. Using a data set of 19 different tasks presented to 500 different participants who provided a total of 1,773 responses, we analyze these responses in two ways: first, on the level of the numerical estimates themselves, and second, on the level of various response strategies, Bayesian and non-Bayesian, that might have produced the estimates. We identified various contingencies, and most of the task characteristics had an influence on participants’ responses. Typically, this influence has been stronger when the numerical information in the tasks was presented in terms of probabilities or percentages, compared to natural frequencies – and this effect cannot be fully explained by a higher proportion of Bayesian responses when natural frequencies were used. One characteristic that did not seem to influence participants’ response strategy was the numerical value of the Bayesian solution itself. Our exploratory study is a first step toward an ecological analysis of Bayesian inferences, and highlights new avenues for future research. PMID:26300791

Hip fracture in the elderly: a re-analysis of the EPIDOS study with causal Bayesian networks.

PubMed

Caillet, Pascal; Klemm, Sarah; Ducher, Michel; Aussem, Alexandre; Schott, Anne-Marie

2015-01-01

Hip fractures commonly result in permanent disability, institutionalization or death in elderly. Existing hip-fracture predicting tools are underused in clinical practice, partly due to their lack of intuitive interpretation. By use of a graphical layer, Bayesian network models could increase the attractiveness of fracture prediction tools. Our aim was to study the potential contribution of a causal Bayesian network in this clinical setting. A logistic regression was performed as a standard control approach to check the robustness of the causal Bayesian network approach. EPIDOS is a multicenter study, conducted in an ambulatory care setting in five French cities between 1992 and 1996 and updated in 2010. The study included 7598 women aged 75 years or older, in which fractures were assessed quarterly during 4 years. A causal Bayesian network and a logistic regression were performed on EPIDOS data to describe major variables involved in hip fractures occurrences. Both models had similar association estimations and predictive performances. They detected gait speed and mineral bone density as variables the most involved in the fracture process. The causal Bayesian network showed that gait speed and bone mineral density were directly connected to fracture and seem to mediate the influence of all the other variables included in our model. The logistic regression approach detected multiple interactions involving psychotropic drug use, age and bone mineral density. Both approaches retrieved similar variables as predictors of hip fractures. However, Bayesian network highlighted the whole web of relation between the variables involved in the analysis, suggesting a possible mechanism leading to hip fracture. According to the latter results, intervention focusing concomitantly on gait speed and bone mineral density may be necessary for an optimal prevention of hip fracture occurrence in elderly people.

Quantifying the Uncertainty in Discharge Data Using Hydraulic Knowledge and Uncertain Gaugings

NASA Astrophysics Data System (ADS)

Renard, B.; Le Coz, J.; Bonnifait, L.; Branger, F.; Le Boursicaud, R.; Horner, I.; Mansanarez, V.; Lang, M.

2014-12-01

River discharge is a crucial variable for Hydrology: as the output variable of most hydrologic models, it is used for sensitivity analyses, model structure identification, parameter estimation, data assimilation, prediction, etc. A major difficulty stems from the fact that river discharge is not measured continuously. Instead, discharge time series used by hydrologists are usually based on simple stage-discharge relations (rating curves) calibrated using a set of direct stage-discharge measurements (gaugings). In this presentation, we present a Bayesian approach to build such hydrometric rating curves, to estimate the associated uncertainty and to propagate this uncertainty to discharge time series. The three main steps of this approach are described: (1) Hydraulic analysis: identification of the hydraulic controls that govern the stage-discharge relation, identification of the rating curve equation and specification of prior distributions for the rating curve parameters; (2) Rating curve estimation: Bayesian inference of the rating curve parameters, accounting for the individual uncertainties of available gaugings, which often differ according to the discharge measurement procedure and the flow conditions; (3) Uncertainty propagation: quantification of the uncertainty in discharge time series, accounting for both the rating curve uncertainties and the uncertainty of recorded stage values. In addition, we also discuss current research activities, including the treatment of non-univocal stage-discharge relationships (e.g. due to hydraulic hysteresis, vegetation growth, sudden change of the geometry of the section, etc.).

Banding of NMR-derived Methyl Order Parameters: Implications for Protein Dynamics

PubMed Central

Sharp, Kim A.; Kasinath, Vignesh; Wand, A. Joshua

2014-01-01

Our understanding of protein folding, stability and function has begun to more explicitly incorporate dynamical aspects. Nuclear magnetic resonance has emerged as a powerful experimental method for obtaining comprehensive site-resolved insight into protein motion. It has been observed that methyl-group motion tends to cluster into three “classes” when expressed in terms of the popular Lipari-Szabo model-free squared generalized order parameter. Here the origins of the three classes or bands in the distribution of order parameters are examined. As a first step, a Bayesian based approach, which makes no a priori assumption about the existence or number of bands, is developed to detect the banding of O2axis values derived either from NMR experiments or molecular dynamics simulations. The analysis is applied to seven proteins with extensive molecular dynamics simulations of these proteins in explicit water to examine the relationship between O2 and fine details of the motion of methyl bearing side chains. All of the proteins studied display banding, with some subtle differences. We propose a very simple yet plausible physical mechanism for banding. Finally, our Bayesian method is used to analyze the measured distributions of methyl group motions in the catabolite activating protein and several of its mutants in various liganded states and discuss the functional implications of the observed banding to protein dynamics and function. PMID:24677353

Directed area search using socio-biological vision algorithms and cognitive Bayesian reasoning

NASA Astrophysics Data System (ADS)

Medasani, S.; Owechko, Y.; Allen, D.; Lu, T. C.; Khosla, D.

2010-04-01

Volitional search systems that assist the analyst by searching for specific targets or objects such as vehicles, factories, airports, etc in wide area overhead imagery need to overcome multiple problems present in current manual and automatic approaches. These problems include finding targets hidden in terabytes of information, relatively few pixels on targets, long intervals between interesting regions, time consuming analysis requiring many analysts, no a priori representative examples or templates of interest, detecting multiple classes of objects, and the need for very high detection rates and very low false alarm rates. This paper describes a conceptual analyst-centric framework that utilizes existing technology modules to search and locate occurrences of targets of interest (e.g., buildings, mobile targets of military significance, factories, nuclear plants, etc.), from video imagery of large areas. Our framework takes simple queries from the analyst and finds the queried targets with relatively minimum interaction from the analyst. It uses a hybrid approach that combines biologically inspired bottom up attention, socio-biologically inspired object recognition for volitionally recognizing targets, and hierarchical Bayesian networks for modeling and representing the domain knowledge. This approach has the benefits of high accuracy, low false alarm rate and can handle both low-level visual information and high-level domain knowledge in a single framework. Such a system would be of immense help for search and rescue efforts, intelligence gathering, change detection systems, and other surveillance systems.

Value-based decision-making battery: A Bayesian adaptive approach to assess impulsive and risky behavior.

PubMed

Pooseh, Shakoor; Bernhardt, Nadine; Guevara, Alvaro; Huys, Quentin J M; Smolka, Michael N

2018-02-01

Using simple mathematical models of choice behavior, we present a Bayesian adaptive algorithm to assess measures of impulsive and risky decision making. Practically, these measures are characterized by discounting rates and are used to classify individuals or population groups, to distinguish unhealthy behavior, and to predict developmental courses. However, a constant demand for improved tools to assess these constructs remains unanswered. The algorithm is based on trial-by-trial observations. At each step, a choice is made between immediate (certain) and delayed (risky) options. Then the current parameter estimates are updated by the likelihood of observing the choice, and the next offers are provided from the indifference point, so that they will acquire the most informative data based on the current parameter estimates. The procedure continues for a certain number of trials in order to reach a stable estimation. The algorithm is discussed in detail for the delay discounting case, and results from decision making under risk for gains, losses, and mixed prospects are also provided. Simulated experiments using prescribed parameter values were performed to justify the algorithm in terms of the reproducibility of its parameters for individual assessments, and to test the reliability of the estimation procedure in a group-level analysis. The algorithm was implemented as an experimental battery to measure temporal and probability discounting rates together with loss aversion, and was tested on a healthy participant sample.

Bayesian flood forecasting methods: A review

NASA Astrophysics Data System (ADS)

Han, Shasha; Coulibaly, Paulin

2017-08-01

Over the past few decades, floods have been seen as one of the most common and largely distributed natural disasters in the world. If floods could be accurately forecasted in advance, then their negative impacts could be greatly minimized. It is widely recognized that quantification and reduction of uncertainty associated with the hydrologic forecast is of great importance for flood estimation and rational decision making. Bayesian forecasting system (BFS) offers an ideal theoretic framework for uncertainty quantification that can be developed for probabilistic flood forecasting via any deterministic hydrologic model. It provides suitable theoretical structure, empirically validated models and reasonable analytic-numerical computation method, and can be developed into various Bayesian forecasting approaches. This paper presents a comprehensive review on Bayesian forecasting approaches applied in flood forecasting from 1999 till now. The review starts with an overview of fundamentals of BFS and recent advances in BFS, followed with BFS application in river stage forecasting and real-time flood forecasting, then move to a critical analysis by evaluating advantages and limitations of Bayesian forecasting methods and other predictive uncertainty assessment approaches in flood forecasting, and finally discusses the future research direction in Bayesian flood forecasting. Results show that the Bayesian flood forecasting approach is an effective and advanced way for flood estimation, it considers all sources of uncertainties and produces a predictive distribution of the river stage, river discharge or runoff, thus gives more accurate and reliable flood forecasts. Some emerging Bayesian forecasting methods (e.g. ensemble Bayesian forecasting system, Bayesian multi-model combination) were shown to overcome limitations of single model or fixed model weight and effectively reduce predictive uncertainty. In recent years, various Bayesian flood forecasting approaches have been developed and widely applied, but there is still room for improvements. Future research in the context of Bayesian flood forecasting should be on assimilation of various sources of newly available information and improvement of predictive performance assessment methods.

Bayesian analysis of non-homogeneous Markov chains: application to mental health data.

PubMed

Sung, Minje; Soyer, Refik; Nhan, Nguyen

2007-07-10

In this paper we present a formal treatment of non-homogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the non-homogeneity of transition patterns. In doing so, we introduce a logistic regression set-up for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study. Copyright 2006 John Wiley & Sons, Ltd.

A FAST BAYESIAN METHOD FOR UPDATING AND FORECASTING HOURLY OZONE LEVELS

EPA Science Inventory

A Bayesian hierarchical space-time model is proposed by combining information from real-time ambient AIRNow air monitoring data, and output from a computer simulation model known as the Community Multi-scale Air Quality (Eta-CMAQ) forecast model. A model validation analysis shows...

Uncertainty estimation of a complex water quality model: The influence of Box-Cox transformation on Bayesian approaches and comparison with a non-Bayesian method

NASA Astrophysics Data System (ADS)

Freni, Gabriele; Mannina, Giorgio

In urban drainage modelling, uncertainty analysis is of undoubted necessity. However, uncertainty analysis in urban water-quality modelling is still in its infancy and only few studies have been carried out. Therefore, several methodological aspects still need to be experienced and clarified especially regarding water quality modelling. The use of the Bayesian approach for uncertainty analysis has been stimulated by its rigorous theoretical framework and by the possibility of evaluating the impact of new knowledge on the modelling predictions. Nevertheless, the Bayesian approach relies on some restrictive hypotheses that are not present in less formal methods like the Generalised Likelihood Uncertainty Estimation (GLUE). One crucial point in the application of Bayesian method is the formulation of a likelihood function that is conditioned by the hypotheses made regarding model residuals. Statistical transformations, such as the use of Box-Cox equation, are generally used to ensure the homoscedasticity of residuals. However, this practice may affect the reliability of the analysis leading to a wrong uncertainty estimation. The present paper aims to explore the influence of the Box-Cox equation for environmental water quality models. To this end, five cases were considered one of which was the “real” residuals distributions (i.e. drawn from available data). The analysis was applied to the Nocella experimental catchment (Italy) which is an agricultural and semi-urbanised basin where two sewer systems, two wastewater treatment plants and a river reach were monitored during both dry and wet weather periods. The results show that the uncertainty estimation is greatly affected by residual transformation and a wrong assumption may also affect the evaluation of model uncertainty. The use of less formal methods always provide an overestimation of modelling uncertainty with respect to Bayesian method but such effect is reduced if a wrong assumption is made regarding the residuals distribution. If residuals are not normally distributed, the uncertainty is over-estimated if Box-Cox transformation is not applied or non-calibrated parameter is used.

Using Bayesian Networks and Decision Theory to Model Physical Security

DTIC Science & Technology

2003-02-01

Home automation technologies allow a person to monitor and control various activities within a home or office setting. Cameras, sensors and other...components used along with the simple rules in the home automation software provide an environment where the lights, security and other appliances can be...monitored and controlled. These home automation technologies, however, lack the power to reason under uncertain conditions and thus the system can

A Bayesian Hierarchical Model for Large-Scale Educational Surveys: An Application to the National Assessment of Educational Progress. Research Report. ETS RR-04-38

ERIC Educational Resources Information Center

Johnson, Matthew S.; Jenkins, Frank

2005-01-01

Large-scale educational assessments such as the National Assessment of Educational Progress (NAEP) sample examinees to whom an exam will be administered. In most situations the sampling design is not a simple random sample and must be accounted for in the estimating model. After reviewing the current operational estimation procedure for NAEP, this…

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

DTIC Science & Technology

2009-12-01

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

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

USGS Publications Warehouse

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

2007-01-01

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

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

PubMed

Dokoumetzidis, Aristides; Aarons, Leon

2005-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

Analysis of the Westland Data Set

NASA Technical Reports Server (NTRS)

Wen, Fang; Willett, Peter; Deb, Somnath

2001-01-01

The "Westland" set of empirical accelerometer helicopter data with seeded and labeled faults is analyzed with the aim of condition monitoring. The autoregressive (AR) coefficients from a simple linear model encapsulate a great deal of information in a relatively few measurements; and it has also been found that augmentation of these by harmonic and other parameters call improve classification significantly. Several techniques have been explored, among these restricted Coulomb energy (RCE) networks, learning vector quantization (LVQ), Gaussian mixture classifiers and decision trees. A problem with these approaches, and in common with many classification paradigms, is that augmentation of the feature dimension can degrade classification ability. Thus, we also introduce the Bayesian data reduction algorithm (BDRA), which imposes a Dirichlet prior oil training data and is thus able to quantify probability of error in all exact manner, such that features may be discarded or coarsened appropriately.

Markov Chain Monte Carlo: an introduction for epidemiologists

PubMed Central

Hamra, Ghassan; MacLehose, Richard; Richardson, David

2013-01-01

Markov Chain Monte Carlo (MCMC) methods are increasingly popular among epidemiologists. The reason for this may in part be that MCMC offers an appealing approach to handling some difficult types of analyses. Additionally, MCMC methods are those most commonly used for Bayesian analysis. However, epidemiologists are still largely unfamiliar with MCMC. They may lack familiarity either with he implementation of MCMC or with interpretation of the resultant output. As with tutorials outlining the calculus behind maximum likelihood in previous decades, a simple description of the machinery of MCMC is needed. We provide an introduction to conducting analyses with MCMC, and show that, given the same data and under certain model specifications, the results of an MCMC simulation match those of methods based on standard maximum-likelihood estimation (MLE). In addition, we highlight examples of instances in which MCMC approaches to data analysis provide a clear advantage over MLE. We hope that this brief tutorial will encourage epidemiologists to consider MCMC approaches as part of their analytic tool-kit. PMID:23569196

Pathway analysis of high-throughput biological data within a Bayesian network framework.

PubMed

Isci, Senol; Ozturk, Cengizhan; Jones, Jon; Otu, Hasan H

2011-06-15

Most current approaches to high-throughput biological data (HTBD) analysis either perform individual gene/protein analysis or, gene/protein set enrichment analysis for a list of biologically relevant molecules. Bayesian Networks (BNs) capture linear and non-linear interactions, handle stochastic events accounting for noise, and focus on local interactions, which can be related to causal inference. Here, we describe for the first time an algorithm that models biological pathways as BNs and identifies pathways that best explain given HTBD by scoring fitness of each network. Proposed method takes into account the connectivity and relatedness between nodes of the pathway through factoring pathway topology in its model. Our simulations using synthetic data demonstrated robustness of our approach. We tested proposed method, Bayesian Pathway Analysis (BPA), on human microarray data regarding renal cell carcinoma (RCC) and compared our results with gene set enrichment analysis. BPA was able to find broader and more specific pathways related to RCC. Accompanying BPA software (BPAS) package is freely available for academic use at http://bumil.boun.edu.tr/bpa.

A Bayesian method for using simulator data to enhance human error probabilities assigned by existing HRA methods

DOE PAGES

Groth, Katrina M.; Smith, Curtis L.; Swiler, Laura P.

2014-04-05

In the past several years, several international agencies have begun to collect data on human performance in nuclear power plant simulators [1]. This data provides a valuable opportunity to improve human reliability analysis (HRA), but there improvements will not be realized without implementation of Bayesian methods. Bayesian methods are widely used in to incorporate sparse data into models in many parts of probabilistic risk assessment (PRA), but Bayesian methods have not been adopted by the HRA community. In this article, we provide a Bayesian methodology to formally use simulator data to refine the human error probabilities (HEPs) assigned by existingmore » HRA methods. We demonstrate the methodology with a case study, wherein we use simulator data from the Halden Reactor Project to update the probability assignments from the SPAR-H method. The case study demonstrates the ability to use performance data, even sparse data, to improve existing HRA methods. Furthermore, this paper also serves as a demonstration of the value of Bayesian methods to improve the technical basis of HRA.« less

Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches.

PubMed

Li, Michael; Dushoff, Jonathan; Bolker, Benjamin M

2018-07-01

Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

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

PubMed Central

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

2012-01-01

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

Bayesian approach for counting experiment statistics applied to a neutrino point source analysis

NASA Astrophysics Data System (ADS)

Bose, D.; Brayeur, L.; Casier, M.; de Vries, K. D.; Golup, G.; van Eijndhoven, N.

2013-12-01

In this paper we present a model independent analysis method following Bayesian statistics to analyse data from a generic counting experiment and apply it to the search for neutrinos from point sources. We discuss a test statistic defined following a Bayesian framework that will be used in the search for a signal. In case no signal is found, we derive an upper limit without the introduction of approximations. The Bayesian approach allows us to obtain the full probability density function for both the background and the signal rate. As such, we have direct access to any signal upper limit. The upper limit derivation directly compares with a frequentist approach and is robust in the case of low-counting observations. Furthermore, it allows also to account for previous upper limits obtained by other analyses via the concept of prior information without the need of the ad hoc application of trial factors. To investigate the validity of the presented Bayesian approach, we have applied this method to the public IceCube 40-string configuration data for 10 nearby blazars and we have obtained a flux upper limit, which is in agreement with the upper limits determined via a frequentist approach. Furthermore, the upper limit obtained compares well with the previously published result of IceCube, using the same data set.

Comparing interval estimates for small sample ordinal CFA models

PubMed Central

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research. PMID:26579002

Comparing interval estimates for small sample ordinal CFA models.

PubMed

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research.

A Bayesian Missing Data Framework for Generalized Multiple Outcome Mixed Treatment Comparisons

ERIC Educational Resources Information Center

Hong, Hwanhee; Chu, Haitao; Zhang, Jing; Carlin, Bradley P.

2016-01-01

Bayesian statistical approaches to mixed treatment comparisons (MTCs) are becoming more popular because of their flexibility and interpretability. Many randomized clinical trials report multiple outcomes with possible inherent correlations. Moreover, MTC data are typically sparse (although richer than standard meta-analysis, comparing only two…

Multi-Scale Validation of a Nanodiamond Drug Delivery System and Multi-Scale Engineering Education

ERIC Educational Resources Information Center

Schwalbe, Michelle Kristin

2010-01-01

This dissertation has two primary concerns: (i) evaluating the uncertainty and prediction capabilities of a nanodiamond drug delivery model using Bayesian calibration and bias correction, and (ii) determining conceptual difficulties of multi-scale analysis from an engineering education perspective. A Bayesian uncertainty quantification scheme…

Bayesian Adaptive Lasso for Ordinal Regression with Latent Variables

ERIC Educational Resources Information Center

Feng, Xiang-Nan; Wu, Hao-Tian; Song, Xin-Yuan

2017-01-01

We consider an ordinal regression model with latent variables to investigate the effects of observable and latent explanatory variables on the ordinal responses of interest. Each latent variable is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a Bayesian adaptive lasso procedure to conduct…

IMPLICATIONS OF USING ROBUST BAYESIAN ANALYSIS TO REPRESENT DIVERSE SOURCES OF UNCERTAINTY IN INTEGRATED ASSESSMENT

EPA Science Inventory

In our previous research, we showed that robust Bayesian methods can be used in environmental modeling to define a set of probability distributions for key parameters that captures the effects of expert disagreement, ambiguity, or ignorance. This entire set can then be update...

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…

Large ensemble modeling of last deglacial retreat of the West Antarctic Ice Sheet: comparison of simple and advanced statistical techniques

NASA Astrophysics Data System (ADS)

Pollard, D.; Chang, W.; Haran, M.; Applegate, P.; DeConto, R.

2015-11-01

A 3-D hybrid ice-sheet model is applied to the last deglacial retreat of the West Antarctic Ice Sheet over the last ~ 20 000 years. A large ensemble of 625 model runs is used to calibrate the model to modern and geologic data, including reconstructed grounding lines, relative sea-level records, elevation-age data and uplift rates, with an aggregate score computed for each run that measures overall model-data misfit. Two types of statistical methods are used to analyze the large-ensemble results: simple averaging weighted by the aggregate score, and more advanced Bayesian techniques involving Gaussian process-based emulation and calibration, and Markov chain Monte Carlo. Results for best-fit parameter ranges and envelopes of equivalent sea-level rise with the simple averaging method agree quite well with the more advanced techniques, but only for a large ensemble with full factorial parameter sampling. Best-fit parameter ranges confirm earlier values expected from prior model tuning, including large basal sliding coefficients on modern ocean beds. Each run is extended 5000 years into the "future" with idealized ramped climate warming. In the majority of runs with reasonable scores, this produces grounding-line retreat deep into the West Antarctic interior, and the analysis provides sea-level-rise envelopes with well defined parametric uncertainty bounds.

Moderation analysis with missing data in the predictors.

PubMed

Zhang, Qian; Wang, Lijuan

2017-12-01

The most widely used statistical model for conducting moderation analysis is the moderated multiple regression (MMR) model. In MMR modeling, missing data could pose a challenge, mainly because the interaction term is a product of two or more variables and thus is a nonlinear function of the involved variables. In this study, we consider a simple MMR model, where the effect of the focal predictor X on the outcome Y is moderated by a moderator U. The primary interest is to find ways of estimating and testing the moderation effect with the existence of missing data in X. We mainly focus on cases when X is missing completely at random (MCAR) and missing at random (MAR). Three methods are compared: (a) Normal-distribution-based maximum likelihood estimation (NML); (b) Normal-distribution-based multiple imputation (NMI); and (c) Bayesian estimation (BE). Via simulations, we found that NML and NMI could lead to biased estimates of moderation effects under MAR missingness mechanism. The BE method outperformed NMI and NML for MMR modeling with missing data in the focal predictor, missingness depending on the moderator and/or auxiliary variables, and correctly specified distributions for the focal predictor. In addition, more robust BE methods are needed in terms of the distribution mis-specification problem of the focal predictor. An empirical example was used to illustrate the applications of the methods with a simple sensitivity analysis. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

PubMed

Chen, Bo; Chen, Minhua; Paisley, John; Zaas, Aimee; Woods, Christopher; Ginsburg, Geoffrey S; Hero, Alfred; Lucas, Joseph; Dunson, David; Carin, Lawrence

2010-11-09

Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

CRAFT (complete reduction to amplitude frequency table)--robust and time-efficient Bayesian approach for quantitative mixture analysis by NMR.

PubMed

Krishnamurthy, Krish

2013-12-01

The intrinsic quantitative nature of NMR is increasingly exploited in areas ranging from complex mixture analysis (as in metabolomics and reaction monitoring) to quality assurance/control. Complex NMR spectra are more common than not, and therefore, extraction of quantitative information generally involves significant prior knowledge and/or operator interaction to characterize resonances of interest. Moreover, in most NMR-based metabolomic experiments, the signals from metabolites are normally present as a mixture of overlapping resonances, making quantification difficult. Time-domain Bayesian approaches have been reported to be better than conventional frequency-domain analysis at identifying subtle changes in signal amplitude. We discuss an approach that exploits Bayesian analysis to achieve a complete reduction to amplitude frequency table (CRAFT) in an automated and time-efficient fashion - thus converting the time-domain FID to a frequency-amplitude table. CRAFT uses a two-step approach to FID analysis. First, the FID is digitally filtered and downsampled to several sub FIDs, and secondly, these sub FIDs are then modeled as sums of decaying sinusoids using the Bayesian approach. CRAFT tables can be used for further data mining of quantitative information using fingerprint chemical shifts of compounds of interest and/or statistical analysis of modulation of chemical quantity in a biological study (metabolomics) or process study (reaction monitoring) or quality assurance/control. The basic principles behind this approach as well as results to evaluate the effectiveness of this approach in mixture analysis are presented. Copyright © 2013 John Wiley & Sons, Ltd.

Decision making with epistemic uncertainty under safety constraints: An application to seismic design

USGS Publications Warehouse

Veneziano, D.; Agarwal, A.; Karaca, E.

2009-01-01

The problem of accounting for epistemic uncertainty in risk management decisions is conceptually straightforward, but is riddled with practical difficulties. Simple approximations are often used whereby future variations in epistemic uncertainty are ignored or worst-case scenarios are postulated. These strategies tend to produce sub-optimal decisions. We develop a general framework based on Bayesian decision theory and exemplify it for the case of seismic design of buildings. When temporal fluctuations of the epistemic uncertainties and regulatory safety constraints are included, the optimal level of seismic protection exceeds the normative level at the time of construction. Optimal Bayesian decisions do not depend on the aleatory or epistemic nature of the uncertainties, but only on the total (epistemic plus aleatory) uncertainty and how that total uncertainty varies randomly during the lifetime of the project. ?? 2009 Elsevier Ltd. All rights reserved.

Bayesian coronal seismology

NASA Astrophysics Data System (ADS)

Arregui, Iñigo

2018-01-01

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

Bayesian 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.

A Bayesian Approach for Evaluation of Determinants of Health System Efficiency Using Stochastic Frontier Analysis and Beta Regression.

PubMed

Şenel, Talat; Cengiz, Mehmet Ali

2016-01-01

In today's world, Public expenditures on health are one of the most important issues for governments. These increased expenditures are putting pressure on public budgets. Therefore, health policy makers have focused on the performance of their health systems and many countries have introduced reforms to improve the performance of their health systems. This study investigates the most important determinants of healthcare efficiency for OECD countries using second stage approach for Bayesian Stochastic Frontier Analysis (BSFA). There are two steps in this study. First we measure 29 OECD countries' healthcare efficiency by BSFA using the data from the OECD Health Database. At second stage, we expose the multiple relationships between the healthcare efficiency and characteristics of healthcare systems across OECD countries using Bayesian beta regression.

Aminoglycoside Therapy Manager: An Advanced Computer Program for Decision Support for Drug Dosing and Therapeutic Monitoring

PubMed Central

Lenert, Leslie; Lurie, Jon; Coleman, Robert; Klosterman, Heidrun; Blaschke, Terrence

1990-01-01

In this paper, we will describe an advanced drug dosing program, Aminoglycoside Therapy Manager that reasons using Bayesian pharmacokinetic modeling and symbolic modeling of patient status and drug response. Our design is similar to the design of the Digitalis Therapy Advisor program, but extends previous work by incorporating a Bayesian pharmacokinetic model, a “meta-level” analysis of drug concentrations to identify sampling errors and changes in pharmacokinetics, and including the results of the “meta-level” analysis in reasoning for dosing and therapeutic monitoring recommendations. The program is user friendly and runs on low cost general-purpose hardware. Validation studies show that the program is as accurate in predicting future drug concentrations as an expert using commercial Bayesian forecasting software.

Applications of Bayesian spectrum representation in acoustics

NASA Astrophysics Data System (ADS)

Botts, Jonathan M.

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

Bayesian Sensitivity Analysis of Statistical Models with Missing Data

PubMed Central

ZHU, HONGTU; IBRAHIM, JOSEPH G.; TANG, NIANSHENG

2013-01-01

Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures. PMID:24753718

An efficient Bayesian meta-analysis approach for studying cross-phenotype genetic associations

PubMed Central

Majumdar, Arunabha; Haldar, Tanushree; Bhattacharya, Sourabh; Witte, John S.

2018-01-01

Simultaneous analysis of genetic associations with multiple phenotypes may reveal shared genetic susceptibility across traits (pleiotropy). For a locus exhibiting overall pleiotropy, it is important to identify which specific traits underlie this association. We propose a Bayesian meta-analysis approach (termed CPBayes) that uses summary-level data across multiple phenotypes to simultaneously measure the evidence of aggregate-level pleiotropic association and estimate an optimal subset of traits associated with the risk locus. This method uses a unified Bayesian statistical framework based on a spike and slab prior. CPBayes performs a fully Bayesian analysis by employing the Markov Chain Monte Carlo (MCMC) technique Gibbs sampling. It takes into account heterogeneity in the size and direction of the genetic effects across traits. It can be applied to both cohort data and separate studies of multiple traits having overlapping or non-overlapping subjects. Simulations show that CPBayes can produce higher accuracy in the selection of associated traits underlying a pleiotropic signal than the subset-based meta-analysis ASSET. We used CPBayes to undertake a genome-wide pleiotropic association study of 22 traits in the large Kaiser GERA cohort and detected six independent pleiotropic loci associated with at least two phenotypes. This includes a locus at chromosomal region 1q24.2 which exhibits an association simultaneously with the risk of five different diseases: Dermatophytosis, Hemorrhoids, Iron Deficiency, Osteoporosis and Peripheral Vascular Disease. We provide an R-package ‘CPBayes’ implementing the proposed method. PMID:29432419

The Theory and Practice of Bayesian Image Labeling

DTIC Science & Technology

1988-08-01

simple. The intensity images are the results of many confounding factors - lighting, surface geometry , surface reflectance, and camera characteristics...related through the geometry of the surfaces in view. They are conditionally independent in the following sense: P (g,O Ifp) = P (g Ifl) P(O If,). (6.6a...different spatial resolution and projection geometry , or using DOG-type filters of various scales. We believe that the success of visual integration at

A novel Bayesian change-point algorithm for genome-wide analysis of diverse ChIPseq data types.

PubMed

Xing, Haipeng; Liao, Willey; Mo, Yifan; Zhang, Michael Q

2012-12-10

ChIPseq is a widely used technique for investigating protein-DNA interactions. Read density profiles are generated by using next-sequencing of protein-bound DNA and aligning the short reads to a reference genome. Enriched regions are revealed as peaks, which often differ dramatically in shape, depending on the target protein(1). For example, transcription factors often bind in a site- and sequence-specific manner and tend to produce punctate peaks, while histone modifications are more pervasive and are characterized by broad, diffuse islands of enrichment(2). Reliably identifying these regions was the focus of our work. Algorithms for analyzing ChIPseq data have employed various methodologies, from heuristics(3-5) to more rigorous statistical models, e.g. Hidden Markov Models (HMMs)(6-8). We sought a solution that minimized the necessity for difficult-to-define, ad hoc parameters that often compromise resolution and lessen the intuitive usability of the tool. With respect to HMM-based methods, we aimed to curtail parameter estimation procedures and simple, finite state classifications that are often utilized. Additionally, conventional ChIPseq data analysis involves categorization of the expected read density profiles as either punctate or diffuse followed by subsequent application of the appropriate tool. We further aimed to replace the need for these two distinct models with a single, more versatile model, which can capably address the entire spectrum of data types. To meet these objectives, we first constructed a statistical framework that naturally modeled ChIPseq data structures using a cutting edge advance in HMMs(9), which utilizes only explicit formulas-an innovation crucial to its performance advantages. More sophisticated then heuristic models, our HMM accommodates infinite hidden states through a Bayesian model. We applied it to identifying reasonable change points in read density, which further define segments of enrichment. Our analysis revealed how our Bayesian Change Point (BCP) algorithm had a reduced computational complexity-evidenced by an abridged run time and memory footprint. The BCP algorithm was successfully applied to both punctate peak and diffuse island identification with robust accuracy and limited user-defined parameters. This illustrated both its versatility and ease of use. Consequently, we believe it can be implemented readily across broad ranges of data types and end users in a manner that is easily compared and contrasted, making it a great tool for ChIPseq data analysis that can aid in collaboration and corroboration between research groups. Here, we demonstrate the application of BCP to existing transcription factor(10,11) and epigenetic data(12) to illustrate its usefulness.

A Bayesian Approach for Nonlinear Structural Equation Models with Dichotomous Variables Using Logit and Probit Links

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng

2010-01-01

Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…

Bayesian Statistics in Educational Research: A Look at the Current State of Affairs

ERIC Educational Resources Information Center

König, Christoph; van de Schoot, Rens

2018-01-01

The ability of a scientific discipline to build cumulative knowledge depends on its predominant method of data analysis. A steady accumulation of knowledge requires approaches which allow researchers to consider results from comparable prior research. Bayesian statistics is especially relevant for establishing a cumulative scientific discipline,…

Bayesian Finite Mixtures for Nonlinear Modeling of Educational Data.

ERIC Educational Resources Information Center

Tirri, Henry; And Others

A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…

Bayesian Analysis of Structural Equation Models with Nonlinear Covariates and Latent Variables

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2006-01-01

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…

Evidence of major genes affecting stress response in rainbow trout using Bayesian methods of complex segregation analysis

USDA-ARS?s Scientific Manuscript database

As a first step towards the genetic mapping of quantitative trait loci (QTL) affecting stress response variation in rainbow trout, we performed complex segregation analyses (CSA) fitting mixed inheritance models of plasma cortisol using Bayesian methods in large full-sib families of rainbow trout. ...

A Hierarchical Bayesian Procedure for Two-Mode Cluster Analysis

ERIC Educational Resources Information Center

DeSarbo, Wayne S.; Fong, Duncan K. H.; Liechty, John; Saxton, M. Kim

2004-01-01

This manuscript introduces a new Bayesian finite mixture methodology for the joint clustering of row and column stimuli/objects associated with two-mode asymmetric proximity, dominance, or profile data. That is, common clusters are derived which partition both the row and column stimuli/objects simultaneously into the same derived set of clusters.…

Exact Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data.

PubMed

Lin, Yan; Lipsitz, Stuart R; Sinha, Debajyoti; Fitzmaurice, Garrett; Lipshultz, Steven

2017-01-01

Altham (Altham PME. Exact Bayesian analysis of a 2 × 2 contingency table, and Fisher's "exact" significance test. J R Stat Soc B 1969; 31: 261-269) showed that a one-sided p-value from Fisher's exact test of independence in a 2 × 2 contingency table is equal to the posterior probability of negative association in the 2 × 2 contingency table under a Bayesian analysis using an improper prior. We derive an extension of Fisher's exact test p-value in the presence of missing data, assuming the missing data mechanism is ignorable (i.e., missing at random or completely at random). Further, we propose Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data using alternative priors; we also present results from a simulation study exploring the Type I error rate and power of the proposed exact test p-values. An example, using data on the association between blood pressure and a cardiac enzyme, is presented to illustrate the methods.

Bayesian randomized clinical trials: From fixed to adaptive design.

PubMed

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

2017-08-01

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

Exoplanet Biosignatures: Future Directions

PubMed Central

Bains, William; Cronin, Leroy; DasSarma, Shiladitya; Danielache, Sebastian; Domagal-Goldman, Shawn; Kacar, Betul; Kiang, Nancy Y.; Lenardic, Adrian; Reinhard, Christopher T.; Moore, William; Schwieterman, Edward W.; Shkolnik, Evgenya L.; Smith, Harrison B.

2018-01-01

Abstract We introduce a Bayesian method for guiding future directions for detection of life on exoplanets. We describe empirical and theoretical work necessary to place constraints on the relevant likelihoods, including those emerging from better understanding stellar environment, planetary climate and geophysics, geochemical cycling, the universalities of physics and chemistry, the contingencies of evolutionary history, the properties of life as an emergent complex system, and the mechanisms driving the emergence of life. We provide examples for how the Bayesian formalism could guide future search strategies, including determining observations to prioritize or deciding between targeted searches or larger lower resolution surveys to generate ensemble statistics and address how a Bayesian methodology could constrain the prior probability of life with or without a positive detection. Key Words: Exoplanets—Biosignatures—Life detection—Bayesian analysis. Astrobiology 18, 779–824. PMID:29938538

Population forecasts for Bangladesh, using a Bayesian methodology.

PubMed

Mahsin, Md; Hossain, Syed Shahadat

2012-12-01

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

Exoplanet Biosignatures: Future Directions.

PubMed

Walker, Sara I; Bains, William; Cronin, Leroy; DasSarma, Shiladitya; Danielache, Sebastian; Domagal-Goldman, Shawn; Kacar, Betul; Kiang, Nancy Y; Lenardic, Adrian; Reinhard, Christopher T; Moore, William; Schwieterman, Edward W; Shkolnik, Evgenya L; Smith, Harrison B

2018-06-01

We introduce a Bayesian method for guiding future directions for detection of life on exoplanets. We describe empirical and theoretical work necessary to place constraints on the relevant likelihoods, including those emerging from better understanding stellar environment, planetary climate and geophysics, geochemical cycling, the universalities of physics and chemistry, the contingencies of evolutionary history, the properties of life as an emergent complex system, and the mechanisms driving the emergence of life. We provide examples for how the Bayesian formalism could guide future search strategies, including determining observations to prioritize or deciding between targeted searches or larger lower resolution surveys to generate ensemble statistics and address how a Bayesian methodology could constrain the prior probability of life with or without a positive detection. Key Words: Exoplanets-Biosignatures-Life detection-Bayesian analysis. Astrobiology 18, 779-824.

Use of limited data to construct Bayesian networks for probabilistic risk assessment.

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

Groth, Katrina M.; Swiler, Laura Painton

2013-03-01

Probabilistic Risk Assessment (PRA) is a fundamental part of safety/quality assurance for nuclear power and nuclear weapons. Traditional PRA very effectively models complex hardware system risks using binary probabilistic models. However, traditional PRA models are not flexible enough to accommodate non-binary soft-causal factors, such as digital instrumentation&control, passive components, aging, common cause failure, and human errors. Bayesian Networks offer the opportunity to incorporate these risks into the PRA framework. This report describes the results of an early career LDRD project titled %E2%80%9CUse of Limited Data to Construct Bayesian Networks for Probabilistic Risk Assessment%E2%80%9D. The goal of the work was tomore » establish the capability to develop Bayesian Networks from sparse data, and to demonstrate this capability by producing a data-informed Bayesian Network for use in Human Reliability Analysis (HRA) as part of nuclear power plant Probabilistic Risk Assessment (PRA). This report summarizes the research goal and major products of the research.« less

Applications of Bayesian Statistics to Problems in Gamma-Ray Bursts

NASA Technical Reports Server (NTRS)

Meegan, Charles A.

1997-01-01

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

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

The integration of probabilistic information during sensorimotor estimation is unimpaired in children with Cerebral Palsy

PubMed Central

Sokhey, Taegh; Gaebler-Spira, Deborah; Kording, Konrad P.

2017-01-01

Background It is important to understand the motor deficits of children with Cerebral Palsy (CP). Our understanding of this motor disorder can be enriched by computational models of motor control. One crucial stage in generating movement involves combining uncertain information from different sources, and deficits in this process could contribute to reduced motor function in children with CP. Healthy adults can integrate previously-learned information (prior) with incoming sensory information (likelihood) in a close-to-optimal way when estimating object location, consistent with the use of Bayesian statistics. However, there are few studies investigating how children with CP perform sensorimotor integration. We compare sensorimotor estimation in children with CP and age-matched controls using a model-based analysis to understand the process. Methods and findings We examined Bayesian sensorimotor integration in children with CP, aged between 5 and 12 years old, with Gross Motor Function Classification System (GMFCS) levels 1–3 and compared their estimation behavior with age-matched typically-developing (TD) children. We used a simple sensorimotor estimation task which requires participants to combine probabilistic information from different sources: a likelihood distribution (current sensory information) with a prior distribution (learned target information). In order to examine sensorimotor integration, we quantified how participants weighed statistical information from the two sources (prior and likelihood) and compared this to the statistical optimal weighting. We found that the weighing of statistical information in children with CP was as statistically efficient as that of TD children. Conclusions We conclude that Bayesian sensorimotor integration is not impaired in children with CP and therefore, does not contribute to their motor deficits. Future research has the potential to enrich our understanding of motor disorders by investigating the stages of motor processing set out by computational models. Therapeutic interventions should exploit the ability of children with CP to use statistical information. PMID:29186196

Spatial cluster detection using dynamic programming.

PubMed

Sverchkov, Yuriy; Jiang, Xia; Cooper, Gregory F

2012-03-25

The task of spatial cluster detection involves finding spatial regions where some property deviates from the norm or the expected value. In a probabilistic setting this task can be expressed as finding a region where some event is significantly more likely than usual. Spatial cluster detection is of interest in fields such as biosurveillance, mining of astronomical data, military surveillance, and analysis of fMRI images. In almost all such applications we are interested both in the question of whether a cluster exists in the data, and if it exists, we are interested in finding the most accurate characterization of the cluster. We present a general dynamic programming algorithm for grid-based spatial cluster detection. The algorithm can be used for both Bayesian maximum a-posteriori (MAP) estimation of the most likely spatial distribution of clusters and Bayesian model averaging over a large space of spatial cluster distributions to compute the posterior probability of an unusual spatial clustering. The algorithm is explained and evaluated in the context of a biosurveillance application, specifically the detection and identification of Influenza outbreaks based on emergency department visits. A relatively simple underlying model is constructed for the purpose of evaluating the algorithm, and the algorithm is evaluated using the model and semi-synthetic test data. When compared to baseline methods, tests indicate that the new algorithm can improve MAP estimates under certain conditions: the greedy algorithm we compared our method to was found to be more sensitive to smaller outbreaks, while as the size of the outbreaks increases, in terms of area affected and proportion of individuals affected, our method overtakes the greedy algorithm in spatial precision and recall. The new algorithm performs on-par with baseline methods in the task of Bayesian model averaging. We conclude that the dynamic programming algorithm performs on-par with other available methods for spatial cluster detection and point to its low computational cost and extendability as advantages in favor of further research and use of the algorithm.

Spatial cluster detection using dynamic programming

PubMed Central

2012-01-01

Background The task of spatial cluster detection involves finding spatial regions where some property deviates from the norm or the expected value. In a probabilistic setting this task can be expressed as finding a region where some event is significantly more likely than usual. Spatial cluster detection is of interest in fields such as biosurveillance, mining of astronomical data, military surveillance, and analysis of fMRI images. In almost all such applications we are interested both in the question of whether a cluster exists in the data, and if it exists, we are interested in finding the most accurate characterization of the cluster. Methods We present a general dynamic programming algorithm for grid-based spatial cluster detection. The algorithm can be used for both Bayesian maximum a-posteriori (MAP) estimation of the most likely spatial distribution of clusters and Bayesian model averaging over a large space of spatial cluster distributions to compute the posterior probability of an unusual spatial clustering. The algorithm is explained and evaluated in the context of a biosurveillance application, specifically the detection and identification of Influenza outbreaks based on emergency department visits. A relatively simple underlying model is constructed for the purpose of evaluating the algorithm, and the algorithm is evaluated using the model and semi-synthetic test data. Results When compared to baseline methods, tests indicate that the new algorithm can improve MAP estimates under certain conditions: the greedy algorithm we compared our method to was found to be more sensitive to smaller outbreaks, while as the size of the outbreaks increases, in terms of area affected and proportion of individuals affected, our method overtakes the greedy algorithm in spatial precision and recall. The new algorithm performs on-par with baseline methods in the task of Bayesian model averaging. Conclusions We conclude that the dynamic programming algorithm performs on-par with other available methods for spatial cluster detection and point to its low computational cost and extendability as advantages in favor of further research and use of the algorithm. PMID:22443103

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

PubMed

Wiczling, Paweł; Kaliszan, Roman

2016-01-05

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

The evolutionary relationships and age of Homo naledi: An assessment using dated Bayesian phylogenetic methods.

PubMed

Dembo, Mana; Radovčić, Davorka; Garvin, Heather M; Laird, Myra F; Schroeder, Lauren; Scott, Jill E; Brophy, Juliet; Ackermann, Rebecca R; Musiba, Chares M; de Ruiter, Darryl J; Mooers, Arne Ø; Collard, Mark

2016-08-01

Homo naledi is a recently discovered species of fossil hominin from South Africa. A considerable amount is already known about H. naledi but some important questions remain unanswered. Here we report a study that addressed two of them: "Where does H. naledi fit in the hominin evolutionary tree?" and "How old is it?" We used a large supermatrix of craniodental characters for both early and late hominin species and Bayesian phylogenetic techniques to carry out three analyses. First, we performed a dated Bayesian analysis to generate estimates of the evolutionary relationships of fossil hominins including H. naledi. Then we employed Bayes factor tests to compare the strength of support for hypotheses about the relationships of H. naledi suggested by the best-estimate trees. Lastly, we carried out a resampling analysis to assess the accuracy of the age estimate for H. naledi yielded by the dated Bayesian analysis. The analyses strongly supported the hypothesis that H. naledi forms a clade with the other Homo species and Australopithecus sediba. The analyses were more ambiguous regarding the position of H. naledi within the (Homo, Au. sediba) clade. A number of hypotheses were rejected, but several others were not. Based on the available craniodental data, Homo antecessor, Asian Homo erectus, Homo habilis, Homo floresiensis, Homo sapiens, and Au. sediba could all be the sister taxon of H. naledi. According to the dated Bayesian analysis, the most likely age for H. naledi is 912 ka. This age estimate was supported by the resampling analysis. Our findings have a number of implications. Most notably, they support the assignment of the new specimens to Homo, cast doubt on the claim that H. naledi is simply a variant of H. erectus, and suggest H. naledi is younger than has been previously proposed. Copyright © 2016 Elsevier Ltd. All rights reserved.

Bayesian switching factor analysis for estimating time-varying functional connectivity in fMRI.

PubMed

Taghia, Jalil; Ryali, Srikanth; Chen, Tianwen; Supekar, Kaustubh; Cai, Weidong; Menon, Vinod

2017-07-15

There is growing interest in understanding the dynamical properties of functional interactions between distributed brain regions. However, robust estimation of temporal dynamics from functional magnetic resonance imaging (fMRI) data remains challenging due to limitations in extant multivariate methods for modeling time-varying functional interactions between multiple brain areas. Here, we develop a Bayesian generative model for fMRI time-series within the framework of hidden Markov models (HMMs). The model is a dynamic variant of the static factor analysis model (Ghahramani and Beal, 2000). We refer to this model as Bayesian switching factor analysis (BSFA) as it integrates factor analysis into a generative HMM in a unified Bayesian framework. In BSFA, brain dynamic functional networks are represented by latent states which are learnt from the data. Crucially, BSFA is a generative model which estimates the temporal evolution of brain states and transition probabilities between states as a function of time. An attractive feature of BSFA is the automatic determination of the number of latent states via Bayesian model selection arising from penalization of excessively complex models. Key features of BSFA are validated using extensive simulations on carefully designed synthetic data. We further validate BSFA using fingerprint analysis of multisession resting-state fMRI data from the Human Connectome Project (HCP). Our results show that modeling temporal dependencies in the generative model of BSFA results in improved fingerprinting of individual participants. Finally, we apply BSFA to elucidate the dynamic functional organization of the salience, central-executive, and default mode networks-three core neurocognitive systems with central role in cognitive and affective information processing (Menon, 2011). Across two HCP sessions, we demonstrate a high level of dynamic interactions between these networks and determine that the salience network has the highest temporal flexibility among the three networks. Our proposed methods provide a novel and powerful generative model for investigating dynamic brain connectivity. Copyright © 2017 Elsevier Inc. All rights reserved.

Bayesian cross-validation for model evaluation and selection, with application to the North American Breeding Bird Survey

USGS Publications Warehouse

Link, William; Sauer, John R.

2016-01-01

The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.

Classifying emotion in Twitter using Bayesian network

NASA Astrophysics Data System (ADS)

Surya Asriadie, Muhammad; Syahrul Mubarok, Mohamad; Adiwijaya

2018-03-01

Language is used to express not only facts, but also emotions. Emotions are noticeable from behavior up to the social media statuses written by a person. Analysis of emotions in a text is done in a variety of media such as Twitter. This paper studies classification of emotions on twitter using Bayesian network because of its ability to model uncertainty and relationships between features. The result is two models based on Bayesian network which are Full Bayesian Network (FBN) and Bayesian Network with Mood Indicator (BNM). FBN is a massive Bayesian network where each word is treated as a node. The study shows the method used to train FBN is not very effective to create the best model and performs worse compared to Naive Bayes. F1-score for FBN is 53.71%, while for Naive Bayes is 54.07%. BNM is proposed as an alternative method which is based on the improvement of Multinomial Naive Bayes and has much lower computational complexity compared to FBN. Even though it’s not better compared to FBN, the resulting model successfully improves the performance of Multinomial Naive Bayes. F1-Score for Multinomial Naive Bayes model is 51.49%, while for BNM is 52.14%.

Estimation of parameter uncertainty for an activated sludge model using Bayesian inference: a comparison with the frequentist method.

PubMed

Zonta, Zivko J; Flotats, Xavier; Magrí, Albert

2014-08-01

The procedure commonly used for the assessment of the parameters included in activated sludge models (ASMs) relies on the estimation of their optimal value within a confidence region (i.e. frequentist inference). Once optimal values are estimated, parameter uncertainty is computed through the covariance matrix. However, alternative approaches based on the consideration of the model parameters as probability distributions (i.e. Bayesian inference), may be of interest. The aim of this work is to apply (and compare) both Bayesian and frequentist inference methods when assessing uncertainty for an ASM-type model, which considers intracellular storage and biomass growth, simultaneously. Practical identifiability was addressed exclusively considering respirometric profiles based on the oxygen uptake rate and with the aid of probabilistic global sensitivity analysis. Parameter uncertainty was thus estimated according to both the Bayesian and frequentist inferential procedures. Results were compared in order to evidence the strengths and weaknesses of both approaches. Since it was demonstrated that Bayesian inference could be reduced to a frequentist approach under particular hypotheses, the former can be considered as a more generalist methodology. Hence, the use of Bayesian inference is encouraged for tackling inferential issues in ASM environments.

[Reliability theory based on quality risk network analysis for Chinese medicine injection].

PubMed

Li, Zheng; Kang, Li-Yuan; Fan, Xiao-Hui

2014-08-01

A new risk analysis method based upon reliability theory was introduced in this paper for the quality risk management of Chinese medicine injection manufacturing plants. The risk events including both cause and effect ones were derived in the framework as nodes with a Bayesian network analysis approach. It thus transforms the risk analysis results from failure mode and effect analysis (FMEA) into a Bayesian network platform. With its structure and parameters determined, the network can be used to evaluate the system reliability quantitatively with probabilistic analytical appraoches. Using network analysis tools such as GeNie and AgenaRisk, we are able to find the nodes that are most critical to influence the system reliability. The importance of each node to the system can be quantitatively evaluated by calculating the effect of the node on the overall risk, and minimization plan can be determined accordingly to reduce their influences and improve the system reliability. Using the Shengmai injection manufacturing plant of SZYY Ltd as a user case, we analyzed the quality risk with both static FMEA analysis and dynamic Bayesian Network analysis. The potential risk factors for the quality of Shengmai injection manufacturing were identified with the network analysis platform. Quality assurance actions were further defined to reduce the risk and improve the product quality.

Fuzzy Naive Bayesian model for medical diagnostic decision support.

PubMed

Wagholikar, Kavishwar B; Vijayraghavan, Sundararajan; Deshpande, Ashok W

2009-01-01

This work relates to the development of computational algorithms to provide decision support to physicians. The authors propose a Fuzzy Naive Bayesian (FNB) model for medical diagnosis, which extends the Fuzzy Bayesian approach proposed by Okuda. A physician's interview based method is described to define a orthogonal fuzzy symptom information system, required to apply the model. For the purpose of elaboration and elicitation of characteristics, the algorithm is applied to a simple simulated dataset, and compared with conventional Naive Bayes (NB) approach. As a preliminary evaluation of FNB in real world scenario, the comparison is repeated on a real fuzzy dataset of 81 patients diagnosed with infectious diseases. The case study on simulated dataset elucidates that FNB can be optimal over NB for diagnosing patients with imprecise-fuzzy information, on account of the following characteristics - 1) it can model the information that, values of some attributes are semantically closer than values of other attributes, and 2) it offers a mechanism to temper exaggerations in patient information. Although the algorithm requires precise training data, its utility for fuzzy training data is argued for. This is supported by the case study on infectious disease dataset, which indicates optimality of FNB over NB for the infectious disease domain. Further case studies on large datasets are required to establish utility of FNB.

Quantification of biophysical adaptation benefits from Climate-Smart Agriculture using a Bayesian Belief Network.

PubMed

de Nijs, Patrick J; Berry, Nicholas J; Wells, Geoff J; Reay, Dave S

2014-10-20

The need for smallholder farmers to adapt their practices to a changing climate is well recognised, particularly in Africa. The cost of adapting to climate change in Africa is estimated to be $20 to $30 billion per year, but the total amount pledged to finance adaptation falls significantly short of this requirement. The difficulty of assessing and monitoring when adaptation is achieved is one of the key barriers to the disbursement of performance-based adaptation finance. To demonstrate the potential of Bayesian Belief Networks for describing the impacts of specific activities on climate change resilience, we developed a simple model that incorporates climate projections, local environmental data, information from peer-reviewed literature and expert opinion to account for the adaptation benefits derived from Climate-Smart Agriculture activities in Malawi. This novel approach allows assessment of vulnerability to climate change under different land use activities and can be used to identify appropriate adaptation strategies and to quantify biophysical adaptation benefits from activities that are implemented. We suggest that multiple-indicator Bayesian Belief Network approaches can provide insights into adaptation planning for a wide range of applications and, if further explored, could be part of a set of important catalysts for the expansion of adaptation finance.

Quantification of biophysical adaptation benefits from Climate-Smart Agriculture using a Bayesian Belief Network

NASA Astrophysics Data System (ADS)

de Nijs, Patrick J.; Berry, Nicholas J.; Wells, Geoff J.; Reay, Dave S.

2014-10-01

The need for smallholder farmers to adapt their practices to a changing climate is well recognised, particularly in Africa. The cost of adapting to climate change in Africa is estimated to be $20 to $30 billion per year, but the total amount pledged to finance adaptation falls significantly short of this requirement. The difficulty of assessing and monitoring when adaptation is achieved is one of the key barriers to the disbursement of performance-based adaptation finance. To demonstrate the potential of Bayesian Belief Networks for describing the impacts of specific activities on climate change resilience, we developed a simple model that incorporates climate projections, local environmental data, information from peer-reviewed literature and expert opinion to account for the adaptation benefits derived from Climate-Smart Agriculture activities in Malawi. This novel approach allows assessment of vulnerability to climate change under different land use activities and can be used to identify appropriate adaptation strategies and to quantify biophysical adaptation benefits from activities that are implemented. We suggest that multiple-indicator Bayesian Belief Network approaches can provide insights into adaptation planning for a wide range of applications and, if further explored, could be part of a set of important catalysts for the expansion of adaptation finance.

Using Bayesian Inference Framework towards Identifying Gas Species and Concentration from High Temperature Resistive Sensor Array Data

DOE PAGES

Liu, Yixin; Zhou, Kai; Lei, Yu

2015-01-01

High temperature gas sensors have been highly demanded for combustion process optimization and toxic emissions control, which usually suffer from poor selectivity. In order to solve this selectivity issue and identify unknown reducing gas species (CO, CH 4 , and CH 8 ) and concentrations, a high temperature resistive sensor array data set was built in this study based on 5 reported sensors. As each sensor showed specific responses towards different types of reducing gas with certain concentrations, based on which calibration curves were fitted, providing benchmark sensor array response database, then Bayesian inference framework was utilized to process themore » sensor array data and build a sample selection program to simultaneously identify gas species and concentration, by formulating proper likelihood between input measured sensor array response pattern of an unknown gas and each sampled sensor array response pattern in benchmark database. This algorithm shows good robustness which can accurately identify gas species and predict gas concentration with a small error of less than 10% based on limited amount of experiment data. These features indicate that Bayesian probabilistic approach is a simple and efficient way to process sensor array data, which can significantly reduce the required computational overhead and training data.« less

Performance of Optimally Merged Multisatellite Precipitation Products Using the Dynamic Bayesian Model Averaging Scheme Over the Tibetan Plateau

NASA Astrophysics Data System (ADS)

Ma, Yingzhao; Hong, Yang; Chen, Yang; Yang, Yuan; Tang, Guoqiang; Yao, Yunjun; Long, Di; Li, Changmin; Han, Zhongying; Liu, Ronghua

2018-01-01

Accurate estimation of precipitation from satellites at high spatiotemporal scales over the Tibetan Plateau (TP) remains a challenge. In this study, we proposed a general framework for blending multiple satellite precipitation data using the dynamic Bayesian model averaging (BMA) algorithm. The blended experiment was performed at a daily 0.25° grid scale for 2007-2012 among Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42RT and 3B42V7, Climate Prediction Center MORPHing technique (CMORPH), and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Climate Data Record (PERSIANN-CDR). First, the BMA weights were optimized using the expectation-maximization (EM) method for each member on each day at 200 calibrated sites and then interpolated to the entire plateau using the ordinary kriging (OK) approach. Thus, the merging data were produced by weighted sums of the individuals over the plateau. The dynamic BMA approach showed better performance with a smaller root-mean-square error (RMSE) of 6.77 mm/day, higher correlation coefficient of 0.592, and closer Euclid value of 0.833, compared to the individuals at 15 validated sites. Moreover, BMA has proven to be more robust in terms of seasonality, topography, and other parameters than traditional ensemble methods including simple model averaging (SMA) and one-outlier removed (OOR). Error analysis between BMA and the state-of-the-art IMERG in the summer of 2014 further proved that the performance of BMA was superior with respect to multisatellite precipitation data merging. This study demonstrates that BMA provides a new solution for blending multiple satellite data in regions with limited gauges.

Coping with Trial-to-Trial Variability of Event Related Signals: A Bayesian Inference Approach

NASA Technical Reports Server (NTRS)

Ding, Mingzhou; Chen, Youghong; Knuth, Kevin H.; Bressler, Steven L.; Schroeder, Charles E.

2005-01-01

In electro-neurophysiology, single-trial brain responses to a sensory stimulus or a motor act are commonly assumed to result from the linear superposition of a stereotypic event-related signal (e.g. the event-related potential or ERP) that is invariant across trials and some ongoing brain activity often referred to as noise. To extract the signal, one performs an ensemble average of the brain responses over many identical trials to attenuate the noise. To date, h s simple signal-plus-noise (SPN) model has been the dominant approach in cognitive neuroscience. Mounting empirical evidence has shown that the assumptions underlying this model may be overly simplistic. More realistic models have been proposed that account for the trial-to-trial variability of the event-related signal as well as the possibility of multiple differentially varying components within a given ERP waveform. The variable-signal-plus-noise (VSPN) model, which has been demonstrated to provide the foundation for separation and characterization of multiple differentially varying components, has the potential to provide a rich source of information for questions related to neural functions that complement the SPN model. Thus, being able to estimate the amplitude and latency of each ERP component on a trial-by-trial basis provides a critical link between the perceived benefits of the VSPN model and its many concrete applications. In this paper we describe a Bayesian approach to deal with this issue and the resulting strategy is referred to as the differentially Variable Component Analysis (dVCA). We compare the performance of dVCA on simulated data with Independent Component Analysis (ICA) and analyze neurobiological recordings from monkeys performing cognitive tasks.

Unveiling an ancient biological invasion: molecular analysis of an old European alien, the crested porcupine (Hystrix cristata).

PubMed

Trucchi, Emiliano; Sbordoni, Valerio

2009-05-18

Biological invasions can be considered one of the main threats to biodiversity, and the recognition of common ecological and evolutionary features among invaders can help developing a predictive framework to control further invasions. In particular, the analysis of successful invasive species and of their autochthonous source populations by means of genetic, phylogeographic and demographic tools can provide novel insights into the study of biological invasion patterns. Today, long-term dynamics of biological invasions are still poorly understood and need further investigations. Moreover, distribution and molecular data on native populations could contribute to the recognition of common evolutionary features of successful aliens. We analyzed 2,195 mitochondrial base pairs, including Cytochrome b, Control Region and rRNA 12S, in 161 Italian and 27 African specimens and assessed the ancient invasive origin of Italian crested porcupine (Hystrix cristata) populations from Tunisia. Molecular coalescent-based Bayesian analyses proposed the Roman Age as a putative timeframe of introduction and suggested a retention of genetic diversity during the early phases of colonization. The characterization of the native African genetic background revealed the existence of two differentiated clades: a Mediterranean group and a Sub-Saharan one. Both standard population genetic and advanced molecular demography tools (Bayesian Skyline Plot) did not evidence a clear genetic signature of the expected increase in population size after introduction. Along with the genetic diversity retention during the bottlenecked steps of introduction, this finding could be better described by hypothesizing a multi-invasion event. Evidences of the ancient anthropogenic invasive origin of the Italian Hystrix cristata populations were clearly shown and the native African genetic background was preliminary described. A more complex pattern than a simple demographic exponential growth from a single propagule seems to have characterized this long-term invasion.

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.

Quantum state estimation when qubits are lost: a no-data-left-behind approach

DOE PAGES

Williams, Brian P.; Lougovski, Pavel

2017-04-06

We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we report the first closed-form Bayesian mean and maximum likelihood estimates for the ideal single qubit. Due to computational constraints, we utilize numerical sampling to determine the Bayesian mean estimate for a photonic two-qubit experiment in which our novel analysis reduces burdens associated with experimental asymmetries and inefficiencies. This method can be applied to quantum states of any dimension and experimental complexity.

Potential of SNP markers for the characterization of Brazilian cassava germplasm.

PubMed

de Oliveira, Eder Jorge; Ferreira, Cláudia Fortes; da Silva Santos, Vanderlei; de Jesus, Onildo Nunes; Oliveira, Gilmara Alvarenga Fachardo; da Silva, Maiane Suzarte

2014-06-01

High-throughput markers, such as SNPs, along with different methodologies were used to evaluate the applicability of the Bayesian approach and the multivariate analysis in structuring the genetic diversity in cassavas. The objective of the present work was to evaluate the diversity and genetic structure of the largest cassava germplasm bank in Brazil. Complementary methodological approaches such as discriminant analysis of principal components (DAPC), Bayesian analysis and molecular analysis of variance (AMOVA) were used to understand the structure and diversity of 1,280 accessions genotyped using 402 single nucleotide polymorphism markers. The genetic diversity (0.327) and the average observed heterozygosity (0.322) were high considering the bi-allelic markers. In terms of population, the presence of a complex genetic structure was observed indicating the formation of 30 clusters by DAPC and 34 clusters by Bayesian analysis. Both methodologies presented difficulties and controversies in terms of the allocation of some accessions to specific clusters. However, the clusters suggested by the DAPC analysis seemed to be more consistent for presenting higher probability of allocation of the accessions within the clusters. Prior information related to breeding patterns and geographic origins of the accessions were not sufficient for providing clear differentiation between the clusters according to the AMOVA analysis. In contrast, the F ST was maximized when considering the clusters suggested by the Bayesian and DAPC analyses. The high frequency of germplasm exchange between producers and the subsequent alteration of the name of the same material may be one of the causes of the low association between genetic diversity and geographic origin. The results of this study may benefit cassava germplasm conservation programs, and contribute to the maximization of genetic gains in breeding programs.

Integrating ecosystems measurements from multiple eddy-covariance sites to a simple model of ecosystem process - Are there possibilities for a uniform model calibration?

NASA Astrophysics Data System (ADS)

Minunno, Francesco; Peltoniemi, Mikko; Launiainen, Samuli; Mäkelä, Annikki

2014-05-01

Biogeochemical models quantify the material and energy flux exchanges between biosphere, atmosphere and soil, however there is still considerable uncertainty underpinning model structure and parametrization. The increasing availability of data from of multiple sources provides useful information for model calibration and validation at different space and time scales. We calibrated a simplified ecosystem process model PRELES to data from multiple sites. In this work we had the following objective: to compare a multi-site calibration and site-specific calibrations, in order to test if PRELES is a model of general applicability, and to test how well one parameterization can predict ecosystem fluxes. Model calibration and evaluation were carried out by the means of the Bayesian method; Bayesian calibration (BC) and Bayesian model comparison (BMC) were used to quantify the uncertainty in model parameters and model structure. Evapotranspiration (ET) and gross primary production (GPP) measurements collected in 9 sites of Finland and Sweden were used in the study; half dataset was used for model calibrations and half for the comparative analyses. 10 BCs were performed; the model was independently calibrated for each of the nine sites (site-specific calibrations) and a multi-site calibration was achieved using the data from all the sites in one BC. Then 9 BMCs were carried out, one for each site, using output from the multi-site and the site-specific versions of PRELES. Similar estimates were obtained for the parameters at which model outputs are most sensitive. Not surprisingly, the joint posterior distribution achieved through the multi-site calibration was characterized by lower uncertainty, because more data were involved in the calibration process. No significant differences were encountered in the prediction of the multi-site and site-specific versions of PRELES, and after BMC, we concluded that the model can be reliably used at regional scale to simulate carbon and water fluxes of Boreal forests. Despite being a simple model, PRELES provided good estimates of GPP and ET; only for one site PRELES multi-site version underestimated water fluxes. Our study implies convergence of GPP and water processes in boreal zone to the extent that their plausible prediction is possible with a simple model using global parameterization.

A Simple Method for Estimating Informative Node Age Priors for the Fossil Calibration of Molecular Divergence Time Analyses

PubMed Central

Nowak, Michael D.; Smith, Andrew B.; Simpson, Carl; Zwickl, Derrick J.

2013-01-01

Molecular divergence time analyses often rely on the age of fossil lineages to calibrate node age estimates. Most divergence time analyses are now performed in a Bayesian framework, where fossil calibrations are incorporated as parametric prior probabilities on node ages. It is widely accepted that an ideal parameterization of such node age prior probabilities should be based on a comprehensive analysis of the fossil record of the clade of interest, but there is currently no generally applicable approach for calculating such informative priors. We provide here a simple and easily implemented method that employs fossil data to estimate the likely amount of missing history prior to the oldest fossil occurrence of a clade, which can be used to fit an informative parametric prior probability distribution on a node age. Specifically, our method uses the extant diversity and the stratigraphic distribution of fossil lineages confidently assigned to a clade to fit a branching model of lineage diversification. Conditioning this on a simple model of fossil preservation, we estimate the likely amount of missing history prior to the oldest fossil occurrence of a clade. The likelihood surface of missing history can then be translated into a parametric prior probability distribution on the age of the clade of interest. We show that the method performs well with simulated fossil distribution data, but that the likelihood surface of missing history can at times be too complex for the distribution-fitting algorithm employed by our software tool. An empirical example of the application of our method is performed to estimate echinoid node ages. A simulation-based sensitivity analysis using the echinoid data set shows that node age prior distributions estimated under poor preservation rates are significantly less informative than those estimated under high preservation rates. PMID:23755303

Some methodological issues in the longitudinal analysis of demographic data.

PubMed

Krishinan, P

1982-12-01

Most demographic data are macro (or aggregate) in nature. Some relevant methodological issues are presented here in a time series study using aggregate data. The micro-macro distinction is relative. Time enters into the micro and macro variables in different ways. A simple micro model of rural-urban migration is given. Method 1 is to assume homogeneity in behavior. Method 2 is a Bayesian estimation. A discusssion of the results follows. Time series models of aggregate data are given. The nature of the model--predictive or explanatory--must be decided on. Explanatory models in longitudinal studies have been developed. Ways to go to the micro level from the macro are discussed. The aggregation-disaggregation problem in demography is not similar to that in econometrics. To understand small populations, separate micro level data have to be collected and analyzed and appropriate models developed. Both types of models have their uses.

A Bayesian Interpretation of First-Order Phase Transitions

NASA Astrophysics Data System (ADS)

Davis, Sergio; Peralta, Joaquín; Navarrete, Yasmín; González, Diego; Gutiérrez, Gonzalo

2016-03-01

In this work we review the formalism used in describing the thermodynamics of first-order phase transitions from the point of view of maximum entropy inference. We present the concepts of transition temperature, latent heat and entropy difference between phases as emergent from the more fundamental concept of internal energy, after a statistical inference analysis. We explicitly demonstrate this point of view by making inferences on a simple game, resulting in the same formalism as in thermodynamical phase transitions. We show that analogous quantities will inevitably arise in any problem of inferring the result of a yes/no question, given two different states of knowledge and information in the form of expectation values. This exposition may help to clarify the role of these thermodynamical quantities in the context of different first-order phase transitions such as the case of magnetic Hamiltonians (e.g. the Potts model).

Competing risk models in reliability systems, a weibull distribution model with bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, Ismed; Satria Gondokaryono, Yudi

2016-02-01

In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range between the true value and the maximum likelihood estimated value lines.

Uncertainty Quantification of Hypothesis Testing for the Integrated Knowledge Engine

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

Cuellar, Leticia

2012-05-31

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

Missing value imputation: with application to handwriting data

NASA Astrophysics Data System (ADS)

Xu, Zhen; Srihari, Sargur N.

2015-01-01

Missing values make pattern analysis difficult, particularly with limited available data. In longitudinal research, missing values accumulate, thereby aggravating the problem. Here we consider how to deal with temporal data with missing values in handwriting analysis. In the task of studying development of individuality of handwriting, we encountered the fact that feature values are missing for several individuals at several time instances. Six algorithms, i.e., random imputation, mean imputation, most likely independent value imputation, and three methods based on Bayesian network (static Bayesian network, parameter EM, and structural EM), are compared with children's handwriting data. We evaluate the accuracy and robustness of the algorithms under different ratios of missing data and missing values, and useful conclusions are given. Specifically, static Bayesian network is used for our data which contain around 5% missing data to provide adequate accuracy and low computational cost.

Bayesian estimation of dynamic matching function for U-V analysis in Japan

NASA Astrophysics Data System (ADS)

Kyo, Koki; Noda, Hideo; Kitagawa, Genshiro

2012-05-01

In this paper we propose a Bayesian method for analyzing unemployment dynamics. We derive a Beveridge curve for unemployment and vacancy (U-V) analysis from a Bayesian model based on a labor market matching function. In our framework, the efficiency of matching and the elasticities of new hiring with respect to unemployment and vacancy are regarded as time varying parameters. To construct a flexible model and obtain reasonable estimates in an underdetermined estimation problem, we treat the time varying parameters as random variables and introduce smoothness priors. The model is then described in a state space representation, enabling the parameter estimation to be carried out using Kalman filter and fixed interval smoothing. In such a representation, dynamic features of the cyclic unemployment rate and the structural-frictional unemployment rate can be accurately captured.

Are Student Evaluations of Teaching Effectiveness Valid for Measuring Student Learning Outcomes in Business Related Classes? A Neural Network and Bayesian Analyses

ERIC Educational Resources Information Center

Galbraith, Craig S.; Merrill, Gregory B.; Kline, Doug M.

2012-01-01

In this study we investigate the underlying relational structure between student evaluations of teaching effectiveness (SETEs) and achievement of student learning outcomes in 116 business related courses. Utilizing traditional statistical techniques, a neural network analysis and a Bayesian data reduction and classification algorithm, we find…

Designing a Mobile Training System in Rural Areas with Bayesian Factor Models

ERIC Educational Resources Information Center

Omidi Najafabadi, Maryam; Mirdamadi, Seyed Mehdi; Payandeh Najafabadi, Amir Teimour

2014-01-01

The facts that the wireless technologies (1) are more convenient; and (2) need less skill than desktop computers, play a crucial role to decrease digital gap in rural areas. This study employed the Bayesian Confirmatory Factor Analysis (CFA) to design a mobile training system in rural areas of Iran. It categorized challenges, potential, and…

Assessing the Impact of Retreat Mechanisms in a Simple Antarctic Ice Sheet Model Using Bayesian Calibration.

PubMed

Ruckert, Kelsey L; Shaffer, Gary; Pollard, David; Guan, Yawen; Wong, Tony E; Forest, Chris E; Keller, Klaus

2017-01-01

The response of the Antarctic ice sheet (AIS) to changing climate forcings is an important driver of sea-level changes. Anthropogenic climate change may drive a sizeable AIS tipping point response with subsequent increases in coastal flooding risks. Many studies analyzing flood risks use simple models to project the future responses of AIS and its sea-level contributions. These analyses have provided important new insights, but they are often silent on the effects of potentially important processes such as Marine Ice Sheet Instability (MISI) or Marine Ice Cliff Instability (MICI). These approximations can be well justified and result in more parsimonious and transparent model structures. This raises the question of how this approximation impacts hindcasts and projections. Here, we calibrate a previously published and relatively simple AIS model, which neglects the effects of MICI and regional characteristics, using a combination of observational constraints and a Bayesian inversion method. Specifically, we approximate the effects of missing MICI by comparing our results to those from expert assessments with more realistic models and quantify the bias during the last interglacial when MICI may have been triggered. Our results suggest that the model can approximate the process of MISI and reproduce the projected median melt from some previous expert assessments in the year 2100. Yet, our mean hindcast is roughly 3/4 of the observed data during the last interglacial period and our mean projection is roughly 1/6 and 1/10 of the mean from a model accounting for MICI in the year 2100. These results suggest that missing MICI and/or regional characteristics can lead to a low-bias during warming period AIS melting and hence a potential low-bias in projected sea levels and flood risks.

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

PubMed Central

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

2003-01-01

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

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

NASA Astrophysics Data System (ADS)

Sadegh, Mojtaba; Ragno, Elisa; AghaKouchak, Amir

2017-06-01

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

Bayesian inference of interaction properties of noisy dynamical systems with time-varying coupling: capabilities and limitations

NASA Astrophysics Data System (ADS)

Wilting, Jens; Lehnertz, Klaus

2015-08-01

We investigate a recently published analysis framework based on Bayesian inference for the time-resolved characterization of interaction properties of noisy, coupled dynamical systems. It promises wide applicability and a better time resolution than well-established methods. At the example of representative model systems, we show that the analysis framework has the same weaknesses as previous methods, particularly when investigating interacting, structurally different non-linear oscillators. We also inspect the tracking of time-varying interaction properties and propose a further modification of the algorithm, which improves the reliability of obtained results. We exemplarily investigate the suitability of this algorithm to infer strength and direction of interactions between various regions of the human brain during an epileptic seizure. Within the limitations of the applicability of this analysis tool, we show that the modified algorithm indeed allows a better time resolution through Bayesian inference when compared to previous methods based on least square fits.

Bayesian Tracking within a Feedback Sensing Environment: Estimating Interacting, Spatially Constrained Complex Dynamical Systems from Multiple Sources of Controllable Devices

DTIC Science & Technology

2014-07-25

composition of simple temporal structures to a speaker diarization task with the goal of segmenting conference audio in the presence of an unknown number of...application domains including neuroimaging, diverse document selection, speaker diarization , stock modeling, and target tracking. We detail each of...recall performance than competing methods in a task of discovering articles preferred by the user • a gold-standard speaker diarization method, as

The ambient dose equivalent at flight altitudes: a fit to a large set of data using a Bayesian approach.

PubMed

Wissmann, F; Reginatto, M; Möller, T

2010-09-01

The problem of finding a simple, generally applicable description of worldwide measured ambient dose equivalent rates at aviation altitudes between 8 and 12 km is difficult to solve due to the large variety of functional forms and parametrisations that are possible. We present an approach that uses Bayesian statistics and Monte Carlo methods to fit mathematical models to a large set of data and to compare the different models. About 2500 data points measured in the periods 1997-1999 and 2003-2006 were used. Since the data cover wide ranges of barometric altitude, vertical cut-off rigidity and phases in the solar cycle 23, we developed functions which depend on these three variables. Whereas the dependence on the vertical cut-off rigidity is described by an exponential, the dependences on barometric altitude and solar activity may be approximated by linear functions in the ranges under consideration. Therefore, a simple Taylor expansion was used to define different models and to investigate the relevance of the different expansion coefficients. With the method presented here, it is possible to obtain probability distributions for each expansion coefficient and thus to extract reliable uncertainties even for the dose rate evaluated. The resulting function agrees well with new measurements made at fixed geographic positions and during long haul flights covering a wide range of latitudes.

A simple parametric model observer for quality assurance in computer tomography

NASA Astrophysics Data System (ADS)

Anton, M.; Khanin, A.; Kretz, T.; Reginatto, M.; Elster, C.

2018-04-01

Model observers are mathematical classifiers that are used for the quality assessment of imaging systems such as computer tomography. The quality of the imaging system is quantified by means of the performance of a selected model observer. For binary classification tasks, the performance of the model observer is defined by the area under its ROC curve (AUC). Typically, the AUC is estimated by applying the model observer to a large set of training and test data. However, the recording of these large data sets is not always practical for routine quality assurance. In this paper we propose as an alternative a parametric model observer that is based on a simple phantom, and we provide a Bayesian estimation of its AUC. It is shown that a limited number of repeatedly recorded images (10–15) is already sufficient to obtain results suitable for the quality assessment of an imaging system. A MATLAB® function is provided for the calculation of the results. The performance of the proposed model observer is compared to that of the established channelized Hotelling observer and the nonprewhitening matched filter for simulated images as well as for images obtained from a low-contrast phantom on an x-ray tomography scanner. The results suggest that the proposed parametric model observer, along with its Bayesian treatment, can provide an efficient, practical alternative for the quality assessment of CT imaging systems.

Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis-Hastings Markov Chain Monte Carlo algorithm

NASA Astrophysics Data System (ADS)

Wang, Hongrui; Wang, Cheng; Wang, Ying; Gao, Xiong; Yu, Chen

2017-06-01

This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLE confidence interval and thus more precise estimation by using the related information from regional gage stations. The Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.

Bayesian estimates of the incidence of rare cancers in Europe.

PubMed

Botta, Laura; Capocaccia, Riccardo; Trama, Annalisa; Herrmann, Christian; Salmerón, Diego; De Angelis, Roberta; Mallone, Sandra; Bidoli, Ettore; Marcos-Gragera, Rafael; Dudek-Godeau, Dorota; Gatta, Gemma; Cleries, Ramon

2018-04-21

The RARECAREnet project has updated the estimates of the burden of the 198 rare cancers in each European country. Suspecting that scant data could affect the reliability of statistical analysis, we employed a Bayesian approach to estimate the incidence of these cancers. We analyzed about 2,000,000 rare cancers diagnosed in 2000-2007 provided by 83 population-based cancer registries from 27 European countries. We considered European incidence rates (IRs), calculated over all the data available in RARECAREnet, as a valid a priori to merge with country-specific observed data. Therefore we provided (1) Bayesian estimates of IRs and the yearly numbers of cases of rare cancers in each country; (2) the expected time (T) in years needed to observe one new case; and (3) practical criteria to decide when to use the Bayesian approach. Bayesian and classical estimates did not differ much; substantial differences (>10%) ranged from 77 rare cancers in Iceland to 14 in England. The smaller the population the larger the number of rare cancers needing a Bayesian approach. Bayesian estimates were useful for cancers with fewer than 150 observed cases in a country during the study period; this occurred mostly when the population of the country is small. For the first time the Bayesian estimates of IRs and the yearly expected numbers of cases for each rare cancer in each individual European country were calculated. Moreover, the indicator T is useful to convey incidence estimates for exceptionally rare cancers and in small countries; it far exceeds the professional lifespan of a medical doctor. Copyright © 2018 Elsevier Ltd. All rights reserved.

Joint analysis of input and parametric uncertainties in watershed water quality modeling: A formal Bayesian approach

NASA Astrophysics Data System (ADS)

Han, Feng; Zheng, Yi

2018-06-01

Significant Input uncertainty is a major source of error in watershed water quality (WWQ) modeling. It remains challenging to address the input uncertainty in a rigorous Bayesian framework. This study develops the Bayesian Analysis of Input and Parametric Uncertainties (BAIPU), an approach for the joint analysis of input and parametric uncertainties through a tight coupling of Markov Chain Monte Carlo (MCMC) analysis and Bayesian Model Averaging (BMA). The formal likelihood function for this approach is derived considering a lag-1 autocorrelated, heteroscedastic, and Skew Exponential Power (SEP) distributed error model. A series of numerical experiments were performed based on a synthetic nitrate pollution case and on a real study case in the Newport Bay Watershed, California. The Soil and Water Assessment Tool (SWAT) and Differential Evolution Adaptive Metropolis (DREAM(ZS)) were used as the representative WWQ model and MCMC algorithm, respectively. The major findings include the following: (1) the BAIPU can be implemented and used to appropriately identify the uncertain parameters and characterize the predictive uncertainty; (2) the compensation effect between the input and parametric uncertainties can seriously mislead the modeling based management decisions, if the input uncertainty is not explicitly accounted for; (3) the BAIPU accounts for the interaction between the input and parametric uncertainties and therefore provides more accurate calibration and uncertainty results than a sequential analysis of the uncertainties; and (4) the BAIPU quantifies the credibility of different input assumptions on a statistical basis and can be implemented as an effective inverse modeling approach to the joint inference of parameters and inputs.

Social deprivation and population density are not associated with small area risk of amyotrophic lateral sclerosis.

PubMed

Rooney, James P K; Tobin, Katy; Crampsie, Arlene; Vajda, Alice; Heverin, Mark; McLaughlin, Russell; Staines, Anthony; Hardiman, Orla

2015-10-01

Evidence of an association between areal ALS risk and population density has been previously reported. We aim to examine ALS spatial incidence in Ireland using small areas, to compare this analysis with our previous analysis of larger areas and to examine the associations between population density, social deprivation and ALS incidence. Residential area social deprivation has not been previously investigated as a risk factor for ALS. Using the Irish ALS register, we included all cases of ALS diagnosed in Ireland from 1995-2013. 2006 census data was used to calculate age and sex standardised expected cases per small area. Social deprivation was assessed using the pobalHP deprivation index. Bayesian smoothing was used to calculate small area relative risk for ALS, whilst cluster analysis was performed using SaTScan. The effects of population density and social deprivation were tested in two ways: (1) as covariates in the Bayesian spatial model; (2) via post-Bayesian regression. 1701 cases were included. Bayesian smoothed maps of relative risk at small area resolution matched closely to our previous analysis at a larger area resolution. Cluster analysis identified two areas of significant low risk. These areas did not correlate with population density or social deprivation indices. Two areas showing low frequency of ALS have been identified in the Republic of Ireland. These areas do not correlate with population density or residential area social deprivation, indicating that other reasons, such as genetic admixture may account for the observed findings. Copyright © 2015 Elsevier Inc. All rights reserved.

Bayesian state space models for dynamic genetic network construction across multiple tissues.

PubMed

Liang, Yulan; Kelemen, Arpad

2016-08-01

Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.

On the uncertainty in single molecule fluorescent lifetime and energy emission measurements

NASA Technical Reports Server (NTRS)

Brown, Emery N.; Zhang, Zhenhua; Mccollom, Alex D.

1995-01-01

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least square methods agree and are optimal when the number of detected photons is large however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67% of those can be noise and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous poisson processes, we derive the exact joint arrival time probably density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. the ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background nose and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

On the Uncertainty in Single Molecule Fluorescent Lifetime and Energy Emission Measurements

NASA Technical Reports Server (NTRS)

Brown, Emery N.; Zhang, Zhenhua; McCollom, Alex D.

1996-01-01

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least squares methods agree and are optimal when the number of detected photons is large, however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67 percent of those can be noise, and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous Poisson processes, we derive the exact joint arrival time probability density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. The ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background noise and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

Bayesian Analysis of Biogeography when the Number of Areas is Large

PubMed Central

Landis, Michael J.; Matzke, Nicholas J.; Moore, Brian R.; Huelsenbeck, John P.

2013-01-01

Historical biogeography is increasingly studied from an explicitly statistical perspective, using stochastic models to describe the evolution of species range as a continuous-time Markov process of dispersal between and extinction within a set of discrete geographic areas. The main constraint of these methods is the computational limit on the number of areas that can be specified. We propose a Bayesian approach for inferring biogeographic history that extends the application of biogeographic models to the analysis of more realistic problems that involve a large number of areas. Our solution is based on a “data-augmentation” approach, in which we first populate the tree with a history of biogeographic events that is consistent with the observed species ranges at the tips of the tree. We then calculate the likelihood of a given history by adopting a mechanistic interpretation of the instantaneous-rate matrix, which specifies both the exponential waiting times between biogeographic events and the relative probabilities of each biogeographic change. We develop this approach in a Bayesian framework, marginalizing over all possible biogeographic histories using Markov chain Monte Carlo (MCMC). Besides dramatically increasing the number of areas that can be accommodated in a biogeographic analysis, our method allows the parameters of a given biogeographic model to be estimated and different biogeographic models to be objectively compared. Our approach is implemented in the program, BayArea. [ancestral area analysis; Bayesian biogeographic inference; data augmentation; historical biogeography; Markov chain Monte Carlo.] PMID:23736102

A Defence of the AR4’s Bayesian Approach to Quantifying Uncertainty

NASA Astrophysics Data System (ADS)

Vezer, M. A.

2009-12-01

The field of climate change research is a kimberlite pipe filled with philosophic diamonds waiting to be mined and analyzed by philosophers. Within the scientific literature on climate change, there is much philosophical dialogue regarding the methods and implications of climate studies. To this date, however, discourse regarding the philosophy of climate science has been confined predominately to scientific - rather than philosophical - investigations. In this paper, I hope to bring one such issue to the surface for explicit philosophical analysis: The purpose of this paper is to address a philosophical debate pertaining to the expressions of uncertainty in the International Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), which, as will be noted, has received significant attention in scientific journals and books, as well as sporadic glances from the popular press. My thesis is that the AR4’s Bayesian method of uncertainty analysis and uncertainty expression is justifiable on pragmatic grounds: it overcomes problems associated with vagueness, thereby facilitating communication between scientists and policy makers such that the latter can formulate decision analyses in response to the views of the former. Further, I argue that the most pronounced criticisms against the AR4’s Bayesian approach, which are outlined below, are misguided. §1 Introduction Central to AR4 is a list of terms related to uncertainty that in colloquial conversations would be considered vague. The IPCC attempts to reduce the vagueness of its expressions of uncertainty by calibrating uncertainty terms with numerical probability values derived from a subjective Bayesian methodology. This style of analysis and expression has stimulated some controversy, as critics reject as inappropriate and even misleading the association of uncertainty terms with Bayesian probabilities. [...] The format of the paper is as follows. The investigation begins (§2) with an explanation of background considerations relevant to the IPCC and its use of uncertainty expressions. It then (§3) outlines some general philosophical worries regarding vague expressions and (§4) relates those worries to the AR4 and its method of dealing with them, which is a subjective Bayesian probability analysis. The next phase of the paper (§5) examines the notions of ‘objective’ and ‘subjective’ probability interpretations and compares the IPCC’s subjective Bayesian strategy with a frequentist approach. It then (§6) addresses objections to that methodology, and concludes (§7) that those objections are wrongheaded.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Spiritual and ceremonial plants in North America: an assessment of Moerman's ethnobotanical database comparing Residual, Binomial, Bayesian and Imprecise Dirichlet Model (IDM) analysis.

PubMed

Turi, Christina E; Murch, Susan J

2013-07-09

Ethnobotanical research and the study of plants used for rituals, ceremonies and to connect with the spirit world have led to the discovery of many novel psychoactive compounds such as nicotine, caffeine, and cocaine. In North America, spiritual and ceremonial uses of plants are well documented and can be accessed online via the University of Michigan's Native American Ethnobotany Database. The objective of the study was to compare Residual, Bayesian, Binomial and Imprecise Dirichlet Model (IDM) analyses of ritual, ceremonial and spiritual plants in Moerman's ethnobotanical database and to identify genera that may be good candidates for the discovery of novel psychoactive compounds. The database was queried with the following format "Family Name AND Ceremonial OR Spiritual" for 263 North American botanical families. Spiritual and ceremonial flora consisted of 86 families with 517 species belonging to 292 genera. Spiritual taxa were then grouped further into ceremonial medicines and items categories. Residual, Bayesian, Binomial and IDM analysis were performed to identify over and under-utilized families. The 4 statistical approaches were in good agreement when identifying under-utilized families but large families (>393 species) were underemphasized by Binomial, Bayesian and IDM approaches for over-utilization. Residual, Binomial, and IDM analysis identified similar families as over-utilized in the medium (92-392 species) and small (<92 species) classes. The families Apiaceae, Asteraceae, Ericacea, Pinaceae and Salicaceae were identified as significantly over-utilized as ceremonial medicines in medium and large sized families. Analysis of genera within the Apiaceae and Asteraceae suggest that the genus Ligusticum and Artemisia are good candidates for facilitating the discovery of novel psychoactive compounds. The 4 statistical approaches were not consistent in the selection of over-utilization of flora. Residual analysis revealed overall trends that were supported by Binomial analysis when separated into small, medium and large families. The Bayesian, Binomial and IDM approaches identified different genera as potentially important. Species belonging to the genus Artemisia and Ligusticum were most consistently identified and may be valuable in future studies of the ethnopharmacology. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Integrated software health management for aerospace guidance, navigation, and control systems: A probabilistic reasoning approach

NASA Astrophysics Data System (ADS)

Mbaya, Timmy

Embedded Aerospace Systems have to perform safety and mission critical operations in a real-time environment where timing and functional correctness are extremely important. Guidance, Navigation, and Control (GN&C) systems substantially rely on complex software interfacing with hardware in real-time; any faults in software or hardware, or their interaction could result in fatal consequences. Integrated Software Health Management (ISWHM) provides an approach for detection and diagnosis of software failures while the software is in operation. The ISWHM approach is based on probabilistic modeling of software and hardware sensors using a Bayesian network. To meet memory and timing constraints of real-time embedded execution, the Bayesian network is compiled into an Arithmetic Circuit, which is used for on-line monitoring. This type of system monitoring, using an ISWHM, provides automated reasoning capabilities that compute diagnoses in a timely manner when failures occur. This reasoning capability enables time-critical mitigating decisions and relieves the human agent from the time-consuming and arduous task of foraging through a multitude of isolated---and often contradictory---diagnosis data. For the purpose of demonstrating the relevance of ISWHM, modeling and reasoning is performed on a simple simulated aerospace system running on a real-time operating system emulator, the OSEK/Trampoline platform. Models for a small satellite and an F-16 fighter jet GN&C (Guidance, Navigation, and Control) system have been implemented. Analysis of the ISWHM is then performed by injecting faults and analyzing the ISWHM's diagnoses.

Historical connectivity, contemporary isolation and local adaptation in a widespread but discontinuously distributed species endemic to Taiwan, Rhododendron oldhamii (Ericaceae)

PubMed Central

Hsieh, Y-C; Chung, J-D; Wang, C-N; Chang, C-T; Chen, C-Y; Hwang, S-Y

2013-01-01

Elucidation of the evolutionary processes that constrain or facilitate adaptive divergence is a central goal in evolutionary biology, especially in non-model organisms. We tested whether changes in dynamics of gene flow (historical vs contemporary) caused population isolation and examined local adaptation in response to environmental selective forces in fragmented Rhododendron oldhamii populations. Variation in 26 expressed sequence tag-simple sequence repeat loci from 18 populations in Taiwan was investigated by examining patterns of genetic diversity, inbreeding, geographic structure, recent bottlenecks, and historical and contemporary gene flow. Selection associated with environmental variables was also examined. Bayesian clustering analysis revealed four regional population groups of north, central, south and southeast with significant genetic differentiation. Historical bottlenecks beginning 9168–13,092 years ago and ending 1584–3504 years ago were revealed by estimates using approximate Bayesian computation for all four regional samples analyzed. Recent migration within and across geographic regions was limited. However, major dispersal sources were found within geographic regions. Altitudinal clines of allelic frequencies of environmentally associated positively selected outliers were found, indicating adaptive divergence. Our results point to a transition from historical population connectivity toward contemporary population isolation and divergence on a regional scale. Spatial and temporal dispersal differences may have resulted in regional population divergence and local adaptation associated with environmental variables, which may have played roles as selective forces at a regional scale. PMID:23591517

Estimation of submarine mass failure probability from a sequence of deposits with age dates

USGS Publications Warehouse

Geist, Eric L.; Chaytor, Jason D.; Parsons, Thomas E.; ten Brink, Uri S.

2013-01-01

The empirical probability of submarine mass failure is quantified from a sequence of dated mass-transport deposits. Several different techniques are described to estimate the parameters for a suite of candidate probability models. The techniques, previously developed for analyzing paleoseismic data, include maximum likelihood and Type II (Bayesian) maximum likelihood methods derived from renewal process theory and Monte Carlo methods. The estimated mean return time from these methods, unlike estimates from a simple arithmetic mean of the center age dates and standard likelihood methods, includes the effects of age-dating uncertainty and of open time intervals before the first and after the last event. The likelihood techniques are evaluated using Akaike’s Information Criterion (AIC) and Akaike’s Bayesian Information Criterion (ABIC) to select the optimal model. The techniques are applied to mass transport deposits recorded in two Integrated Ocean Drilling Program (IODP) drill sites located in the Ursa Basin, northern Gulf of Mexico. Dates of the deposits were constrained by regional bio- and magnetostratigraphy from a previous study. Results of the analysis indicate that submarine mass failures in this location occur primarily according to a Poisson process in which failures are independent and return times follow an exponential distribution. However, some of the model results suggest that submarine mass failures may occur quasiperiodically at one of the sites (U1324). The suite of techniques described in this study provides quantitative probability estimates of submarine mass failure occurrence, for any number of deposits and age uncertainty distributions.

Bayesian wavelet PCA methodology for turbomachinery damage diagnosis under uncertainty

NASA Astrophysics Data System (ADS)

Xu, Shengli; Jiang, Xiaomo; Huang, Jinzhi; Yang, Shuhua; Wang, Xiaofang

2016-12-01

Centrifugal compressor often suffers various defects such as impeller cracking, resulting in forced outage of the total plant. Damage diagnostics and condition monitoring of such a turbomachinery system has become an increasingly important and powerful tool to prevent potential failure in components and reduce unplanned forced outage and further maintenance costs, while improving reliability, availability and maintainability of a turbomachinery system. This paper presents a probabilistic signal processing methodology for damage diagnostics using multiple time history data collected from different locations of a turbomachine, considering data uncertainty and multivariate correlation. The proposed methodology is based on the integration of three advanced state-of-the-art data mining techniques: discrete wavelet packet transform, Bayesian hypothesis testing, and probabilistic principal component analysis. The multiresolution wavelet analysis approach is employed to decompose a time series signal into different levels of wavelet coefficients. These coefficients represent multiple time-frequency resolutions of a signal. Bayesian hypothesis testing is then applied to each level of wavelet coefficient to remove possible imperfections. The ratio of posterior odds Bayesian approach provides a direct means to assess whether there is imperfection in the decomposed coefficients, thus avoiding over-denoising. Power spectral density estimated by the Welch method is utilized to evaluate the effectiveness of Bayesian wavelet cleansing method. Furthermore, the probabilistic principal component analysis approach is developed to reduce dimensionality of multiple time series and to address multivariate correlation and data uncertainty for damage diagnostics. The proposed methodology and generalized framework is demonstrated with a set of sensor data collected from a real-world centrifugal compressor with impeller cracks, through both time series and contour analyses of vibration signal and principal components.

Substantial advantage of a combined Bayesian and genotyping approach in testosterone doping tests.

PubMed

Schulze, Jenny Jakobsson; Lundmark, Jonas; Garle, Mats; Ekström, Lena; Sottas, Pierre-Edouard; Rane, Anders

2009-03-01

Testosterone abuse is conventionally assessed by the urinary testosterone/epitestosterone (T/E) ratio, levels above 4.0 being considered suspicious. A deletion polymorphism in the gene coding for UGT2B17 is strongly associated with reduced testosterone glucuronide (TG) levels in urine. Many of the individuals devoid of the gene would not reach a T/E ratio of 4.0 after testosterone intake. Future test programs will most likely shift from population based- to individual-based T/E cut-off ratios using Bayesian inference. A longitudinal analysis is dependent on an individual's true negative baseline T/E ratio. The aim was to investigate whether it is possible to increase the sensitivity and specificity of the T/E test by addition of UGT2B17 genotype information in a Bayesian framework. A single intramuscular dose of 500mg testosterone enanthate was given to 55 healthy male volunteers with either two, one or no allele (ins/ins, ins/del or del/del) of the UGT2B17 gene. Urinary excretion of TG and the T/E ratio was measured during 15 days. The Bayesian analysis was conducted to calculate the individual T/E cut-off ratio. When adding the genotype information, the program returned lower individual cut-off ratios in all del/del subjects increasing the sensitivity of the test considerably. It will be difficult, if not impossible, to discriminate between a true negative baseline T/E value and a false negative one without knowledge of the UGT2B17 genotype. UGT2B17 genotype information is crucial, both to decide which initial cut-off ratio to use for an individual, and for increasing the sensitivity of the Bayesian analysis.

Capturing changes in flood risk with Bayesian approaches for flood damage assessment

NASA Astrophysics Data System (ADS)

Vogel, Kristin; Schröter, Kai; Kreibich, Heidi; Thieken, Annegret; Müller, Meike; Sieg, Tobias; Laudan, Jonas; Kienzler, Sarah; Weise, Laura; Merz, Bruno; Scherbaum, Frank

2016-04-01

Flood risk is a function of hazard as well as of exposure and vulnerability. All three components are under change over space and time and have to be considered for reliable damage estimations and risk analyses, since this is the basis for an efficient, adaptable risk management. Hitherto, models for estimating flood damage are comparatively simple and cannot sufficiently account for changing conditions. The Bayesian network approach allows for a multivariate modeling of complex systems without relying on expert knowledge about physical constraints. In a Bayesian network each model component is considered to be a random variable. The way of interactions between those variables can be learned from observations or be defined by expert knowledge. Even a combination of both is possible. Moreover, the probabilistic framework captures uncertainties related to the prediction and provides a probability distribution for the damage instead of a point estimate. The graphical representation of Bayesian networks helps to study the change of probabilities for changing circumstances and may thus simplify the communication between scientists and public authorities. In the framework of the DFG-Research Training Group "NatRiskChange" we aim to develop Bayesian networks for flood damage and vulnerability assessments of residential buildings and companies under changing conditions. A Bayesian network learned from data, collected over the last 15 years in flooded regions in the Elbe and Danube catchments (Germany), reveals the impact of many variables like building characteristics, precaution and warning situation on flood damage to residential buildings. While the handling of incomplete and hybrid (discrete mixed with continuous) data are the most challenging issues in the study on residential buildings, a similar study, that focuses on the vulnerability of small to medium sized companies, bears new challenges. Relying on a much smaller data set for the determination of the model parameters, overly complex models should be avoided. A so called Markov Blanket approach aims at the identification of the most relevant factors and constructs a Bayesian network based on those findings. With our approach we want to exploit a major advantage of Bayesian networks which is their ability to consider dependencies not only pairwise, but to capture the joint effects and interactions of driving forces. Hence, the flood damage network does not only show the impact of precaution on the building damage separately, but also reveals the mutual effects of precaution and the quality of warning for a variety of flood settings. Thus, it allows for a consideration of changing conditions and different courses of action and forms a novel and valuable tool for decision support. This study is funded by the Deutsche Forschungsgemeinschaft (DFG) within the research training program GRK 2043/1 "NatRiskChange - Natural hazards and risks in a changing world" at the University of Potsdam.

Comparing energy sources for surgical ablation of atrial fibrillation: a Bayesian network meta-analysis of randomized, controlled trials.

PubMed

Phan, Kevin; Xie, Ashleigh; Kumar, Narendra; Wong, Sophia; Medi, Caroline; La Meir, Mark; Yan, Tristan D

2015-08-01

Simplified maze procedures involving radiofrequency, cryoenergy and microwave energy sources have been increasingly utilized for surgical treatment of atrial fibrillation as an alternative to the traditional cut-and-sew approach. In the absence of direct comparisons, a Bayesian network meta-analysis is another alternative to assess the relative effect of different treatments, using indirect evidence. A Bayesian meta-analysis of indirect evidence was performed using 16 published randomized trials identified from 6 databases. Rank probability analysis was used to rank each intervention in terms of their probability of having the best outcome. Sinus rhythm prevalence beyond the 12-month follow-up was similar between the cut-and-sew, microwave and radiofrequency approaches, which were all ranked better than cryoablation (respectively, 39, 36, and 25 vs 1%). The cut-and-sew maze was ranked worst in terms of mortality outcomes compared with microwave, radiofrequency and cryoenergy (2 vs 19, 34, and 24%, respectively). The cut-and-sew maze procedure was associated with significantly lower stroke rates compared with microwave ablation [odds ratio <0.01; 95% confidence interval 0.00, 0.82], and ranked the best in terms of pacemaker requirements compared with microwave, radiofrequency and cryoenergy (81 vs 14, and 1, <0.01% respectively). Bayesian rank probability analysis shows that the cut-and-sew approach is associated with the best outcomes in terms of sinus rhythm prevalence and stroke outcomes, and remains the gold standard approach for AF treatment. Given the limitations of indirect comparison analysis, these results should be viewed with caution and not over-interpreted. © The Author 2014. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery. All rights reserved.

Spatiotemporal Phylogenetic Analysis and Molecular Characterisation of Infectious Bursal Disease Viruses Based on the VP2 Hyper-Variable Region

PubMed Central

Dolz, Roser; Valle, Rosa; Perera, Carmen L.; Bertran, Kateri; Frías, Maria T.; Majó, Natàlia; Ganges, Llilianne; Pérez, Lester J.

2013-01-01

Background Infectious bursal disease is a highly contagious and acute viral disease caused by the infectious bursal disease virus (IBDV); it affects all major poultry producing areas of the world. The current study was designed to rigorously measure the global phylogeographic dynamics of IBDV strains to gain insight into viral population expansion as well as the emergence, spread and pattern of the geographical structure of very virulent IBDV (vvIBDV) strains. Methodology/Principal Findings Sequences of the hyper-variable region of the VP2 (HVR-VP2) gene from IBDV strains isolated from diverse geographic locations were obtained from the GenBank database; Cuban sequences were obtained in the current work. All sequences were analysed by Bayesian phylogeographic analysis, implemented in the Bayesian Evolutionary Analysis Sampling Trees (BEAST), Bayesian Tip-association Significance testing (BaTS) and Spatial Phylogenetic Reconstruction of Evolutionary Dynamics (SPREAD) software packages. Selection pressure on the HVR-VP2 was also assessed. The phylogeographic association-trait analysis showed that viruses sampled from individual countries tend to cluster together, suggesting a geographic pattern for IBDV strains. Spatial analysis from this study revealed that strains carrying sequences that were linked to increased virulence of IBDV appeared in Iran in 1981 and spread to Western Europe (Belgium) in 1987, Africa (Egypt) around 1990, East Asia (China and Japan) in 1993, the Caribbean Region (Cuba) by 1995 and South America (Brazil) around 2000. Selection pressure analysis showed that several codons in the HVR-VP2 region were under purifying selection. Conclusions/Significance To our knowledge, this work is the first study applying the Bayesian phylogeographic reconstruction approach to analyse the emergence and spread of vvIBDV strains worldwide. PMID:23805195

Spatiotemporal Phylogenetic Analysis and Molecular Characterisation of Infectious Bursal Disease Viruses Based on the VP2 Hyper-Variable Region.

PubMed

Alfonso-Morales, Abdulahi; Martínez-Pérez, Orlando; Dolz, Roser; Valle, Rosa; Perera, Carmen L; Bertran, Kateri; Frías, Maria T; Majó, Natàlia; Ganges, Llilianne; Pérez, Lester J

2013-01-01

Infectious bursal disease is a highly contagious and acute viral disease caused by the infectious bursal disease virus (IBDV); it affects all major poultry producing areas of the world. The current study was designed to rigorously measure the global phylogeographic dynamics of IBDV strains to gain insight into viral population expansion as well as the emergence, spread and pattern of the geographical structure of very virulent IBDV (vvIBDV) strains. Sequences of the hyper-variable region of the VP2 (HVR-VP2) gene from IBDV strains isolated from diverse geographic locations were obtained from the GenBank database; Cuban sequences were obtained in the current work. All sequences were analysed by Bayesian phylogeographic analysis, implemented in the Bayesian Evolutionary Analysis Sampling Trees (BEAST), Bayesian Tip-association Significance testing (BaTS) and Spatial Phylogenetic Reconstruction of Evolutionary Dynamics (SPREAD) software packages. Selection pressure on the HVR-VP2 was also assessed. The phylogeographic association-trait analysis showed that viruses sampled from individual countries tend to cluster together, suggesting a geographic pattern for IBDV strains. Spatial analysis from this study revealed that strains carrying sequences that were linked to increased virulence of IBDV appeared in Iran in 1981 and spread to Western Europe (Belgium) in 1987, Africa (Egypt) around 1990, East Asia (China and Japan) in 1993, the Caribbean Region (Cuba) by 1995 and South America (Brazil) around 2000. Selection pressure analysis showed that several codons in the HVR-VP2 region were under purifying selection. To our knowledge, this work is the first study applying the Bayesian phylogeographic reconstruction approach to analyse the emergence and spread of vvIBDV strains worldwide.

Parameterization of aquatic ecosystem functioning and its natural variation: Hierarchical Bayesian modelling of plankton food web dynamics

NASA Astrophysics Data System (ADS)

Norros, Veera; Laine, Marko; Lignell, Risto; Thingstad, Frede

2017-10-01

Methods for extracting empirically and theoretically sound parameter values are urgently needed in aquatic ecosystem modelling to describe key flows and their variation in the system. Here, we compare three Bayesian formulations for mechanistic model parameterization that differ in their assumptions about the variation in parameter values between various datasets: 1) global analysis - no variation, 2) separate analysis - independent variation and 3) hierarchical analysis - variation arising from a shared distribution defined by hyperparameters. We tested these methods, using computer-generated and empirical data, coupled with simplified and reasonably realistic plankton food web models, respectively. While all methods were adequate, the simulated example demonstrated that a well-designed hierarchical analysis can result in the most accurate and precise parameter estimates and predictions, due to its ability to combine information across datasets. However, our results also highlighted sensitivity to hyperparameter prior distributions as an important caveat of hierarchical analysis. In the more complex empirical example, hierarchical analysis was able to combine precise identification of parameter values with reasonably good predictive performance, although the ranking of the methods was less straightforward. We conclude that hierarchical Bayesian analysis is a promising tool for identifying key ecosystem-functioning parameters and their variation from empirical datasets.

Iterative Assessment of Statistically-Oriented and Standard Algorithms for Determining Muscle Onset with Intramuscular Electromyography.

PubMed

Tenan, Matthew S; Tweedell, Andrew J; Haynes, Courtney A

2017-12-01

The onset of muscle activity, as measured by electromyography (EMG), is a commonly applied metric in biomechanics. Intramuscular EMG is often used to examine deep musculature and there are currently no studies examining the effectiveness of algorithms for intramuscular EMG onset. The present study examines standard surface EMG onset algorithms (linear envelope, Teager-Kaiser Energy Operator, and sample entropy) and novel algorithms (time series mean-variance analysis, sequential/batch processing with parametric and nonparametric methods, and Bayesian changepoint analysis). Thirteen male and 5 female subjects had intramuscular EMG collected during isolated biceps brachii and vastus lateralis contractions, resulting in 103 trials. EMG onset was visually determined twice by 3 blinded reviewers. Since the reliability of visual onset was high (ICC (1,1) : 0.92), the mean of the 6 visual assessments was contrasted with the algorithmic approaches. Poorly performing algorithms were stepwise eliminated via (1) root mean square error analysis, (2) algorithm failure to identify onset/premature onset, (3) linear regression analysis, and (4) Bland-Altman plots. The top performing algorithms were all based on Bayesian changepoint analysis of rectified EMG and were statistically indistinguishable from visual analysis. Bayesian changepoint analysis has the potential to produce more reliable, accurate, and objective intramuscular EMG onset results than standard methodologies.

Bayesian Statistical Analysis of Historical and Late Holocene Rates of Sea-Level Change

NASA Astrophysics Data System (ADS)

Cahill, Niamh; Parnell, Andrew; Kemp, Andrew; Horton, Benjamin

2014-05-01

A fundamental concern associated with climate change is the rate at which sea levels are rising. Studies of past sea level (particularly beyond the instrumental data range) allow modern sea-level rise to be placed in a more complete context. Considering this, we perform a Bayesian statistical analysis on historical and late Holocene rates of sea-level change. The data that form the input to the statistical model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. The aims are to estimate rates of sea-level rise, to determine when modern rates of sea-level rise began and to observe how these rates have been changing over time. Many of the current methods for doing this use simple linear regression to estimate rates. This is often inappropriate as it is too rigid and it can ignore uncertainties that arise as part of the data collection exercise. This can lead to over confidence in the sea-level trends being characterized. The proposed Bayesian model places a Gaussian process prior on the rate process (i.e. the process that determines how rates of sea-level are changing over time). The likelihood of the observed data is the integral of this process. When dealing with proxy reconstructions, this is set in an errors-in-variables framework so as to take account of age uncertainty. It is also necessary, in this case, for the model to account for glacio-isostatic adjustment, which introduces a covariance between individual age and sea-level observations. This method provides a flexible fit and it allows for the direct estimation of the rate process with full consideration of all sources of uncertainty. Analysis of tide-gauge datasets and proxy reconstructions in this way means that changing rates of sea level can be estimated more comprehensively and accurately than previously possible. The model captures the continuous and dynamic evolution of sea-level change and results show that not only are modern sea levels rising but that the rates of rise are continuously increasing. Analysis of the a global tide-gauge record (Church and White, 2011) indicated that the rate of sea-level rise increased continuously since 1880AD and is currently 2.57mm/yr (95% credible interval of 1.71 to 4.35mm/yr). Application of the model a proxy reconstruction from North Carolina (Kemp et al., 2011) indicated that the mean rate of rise in this locality since the middle of the 19th century (current rate of 2.66 mm/yr with a 95% credible interval of 1.29 to 4.59mm/yr) is in agreement with results from the tide gauge analysis and is unprecedented in at least the last 2000 years.

Quantitative trait nucleotide analysis using Bayesian model selection.

PubMed

Blangero, John; Goring, Harald H H; Kent, Jack W; Williams, Jeff T; Peterson, Charles P; Almasy, Laura; Dyer, Thomas D

2005-10-01

Although much attention has been given to statistical genetic methods for the initial localization and fine mapping of quantitative trait loci (QTLs), little methodological work has been done to date on the problem of statistically identifying the most likely functional polymorphisms using sequence data. In this paper we provide a general statistical genetic framework, called Bayesian quantitative trait nucleotide (BQTN) analysis, for assessing the likely functional status of genetic variants. The approach requires the initial enumeration of all genetic variants in a set of resequenced individuals. These polymorphisms are then typed in a large number of individuals (potentially in families), and marker variation is related to quantitative phenotypic variation using Bayesian model selection and averaging. For each sequence variant a posterior probability of effect is obtained and can be used to prioritize additional molecular functional experiments. An example of this quantitative nucleotide analysis is provided using the GAW12 simulated data. The results show that the BQTN method may be useful for choosing the most likely functional variants within a gene (or set of genes). We also include instructions on how to use our computer program, SOLAR, for association analysis and BQTN analysis.

Framework for network modularization and Bayesian network analysis to investigate the perturbed metabolic network

PubMed Central

2011-01-01

Background Genome-scale metabolic network models have contributed to elucidating biological phenomena, and predicting gene targets to engineer for biotechnological applications. With their increasing importance, their precise network characterization has also been crucial for better understanding of the cellular physiology. Results We herein introduce a framework for network modularization and Bayesian network analysis (FMB) to investigate organism’s metabolism under perturbation. FMB reveals direction of influences among metabolic modules, in which reactions with similar or positively correlated flux variation patterns are clustered, in response to specific perturbation using metabolic flux data. With metabolic flux data calculated by constraints-based flux analysis under both control and perturbation conditions, FMB, in essence, reveals the effects of specific perturbations on the biological system through network modularization and Bayesian network analysis at metabolic modular level. As a demonstration, this framework was applied to the genetically perturbed Escherichia coli metabolism, which is a lpdA gene knockout mutant, using its genome-scale metabolic network model. Conclusions After all, it provides alternative scenarios of metabolic flux distributions in response to the perturbation, which are complementary to the data obtained from conventionally available genome-wide high-throughput techniques or metabolic flux analysis. PMID:22784571

Framework for network modularization and Bayesian network analysis to investigate the perturbed metabolic network.

PubMed

Kim, Hyun Uk; Kim, Tae Yong; Lee, Sang Yup

2011-01-01

Genome-scale metabolic network models have contributed to elucidating biological phenomena, and predicting gene targets to engineer for biotechnological applications. With their increasing importance, their precise network characterization has also been crucial for better understanding of the cellular physiology. We herein introduce a framework for network modularization and Bayesian network analysis (FMB) to investigate organism's metabolism under perturbation. FMB reveals direction of influences among metabolic modules, in which reactions with similar or positively correlated flux variation patterns are clustered, in response to specific perturbation using metabolic flux data. With metabolic flux data calculated by constraints-based flux analysis under both control and perturbation conditions, FMB, in essence, reveals the effects of specific perturbations on the biological system through network modularization and Bayesian network analysis at metabolic modular level. As a demonstration, this framework was applied to the genetically perturbed Escherichia coli metabolism, which is a lpdA gene knockout mutant, using its genome-scale metabolic network model. After all, it provides alternative scenarios of metabolic flux distributions in response to the perturbation, which are complementary to the data obtained from conventionally available genome-wide high-throughput techniques or metabolic flux analysis.

Combined target factor analysis and Bayesian soft-classification of interference-contaminated samples: forensic fire debris analysis.

PubMed

Williams, Mary R; Sigman, Michael E; Lewis, Jennifer; Pitan, Kelly McHugh

2012-10-10

A bayesian soft classification method combined with target factor analysis (TFA) is described and tested for the analysis of fire debris data. The method relies on analysis of the average mass spectrum across the chromatographic profile (i.e., the total ion spectrum, TIS) from multiple samples taken from a single fire scene. A library of TIS from reference ignitable liquids with assigned ASTM classification is used as the target factors in TFA. The class-conditional distributions of correlations between the target and predicted factors for each ASTM class are represented by kernel functions and analyzed by bayesian decision theory. The soft classification approach assists in assessing the probability that ignitable liquid residue from a specific ASTM E1618 class, is present in a set of samples from a single fire scene, even in the presence of unspecified background contributions from pyrolysis products. The method is demonstrated with sample data sets and then tested on laboratory-scale burn data and large-scale field test burns. The overall performance achieved in laboratory and field test of the method is approximately 80% correct classification of fire debris samples. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Bayesian structural equation modeling: a more flexible representation of substantive theory.

PubMed

Muthén, Bengt; Asparouhov, Tihomir

2012-09-01

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from Holzinger and Swineford's (1939) classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988.

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

ERIC Educational Resources Information Center

Tsutakawa, Robert K.; Lin, Hsin Ying

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

A total-evidence approach to dating with fossils, applied to the early radiation of the hymenoptera.

PubMed

Ronquist, Fredrik; Klopfstein, Seraina; Vilhelmsen, Lars; Schulmeister, Susanne; Murray, Debra L; Rasnitsyn, Alexandr P

2012-12-01

Phylogenies are usually dated by calibrating interior nodes against the fossil record. This relies on indirect methods that, in the worst case, misrepresent the fossil information. Here, we contrast such node dating with an approach that includes fossils along with the extant taxa in a Bayesian total-evidence analysis. As a test case, we focus on the early radiation of the Hymenoptera, mostly documented by poorly preserved impression fossils that are difficult to place phylogenetically. Specifically, we compare node dating using nine calibration points derived from the fossil record with total-evidence dating based on 343 morphological characters scored for 45 fossil (4--20 complete) and 68 extant taxa. In both cases we use molecular data from seven markers (∼5 kb) for the extant taxa. Because it is difficult to model speciation, extinction, sampling, and fossil preservation realistically, we develop a simple uniform prior for clock trees with fossils, and we use relaxed clock models to accommodate rate variation across the tree. Despite considerable uncertainty in the placement of most fossils, we find that they contribute significantly to the estimation of divergence times in the total-evidence analysis. In particular, the posterior distributions on divergence times are less sensitive to prior assumptions and tend to be more precise than in node dating. The total-evidence analysis also shows that four of the seven Hymenoptera calibration points used in node dating are likely to be based on erroneous or doubtful assumptions about the fossil placement. With respect to the early radiation of Hymenoptera, our results suggest that the crown group dates back to the Carboniferous, ∼309 Ma (95% interval: 291--347 Ma), and diversified into major extant lineages much earlier than previously thought, well before the Triassic. [Bayesian inference; fossil dating; morphological evolution; relaxed clock; statistical phylogenetics.].

A Total-Evidence Approach to Dating with Fossils, Applied to the Early Radiation of the Hymenoptera

PubMed Central

Ronquist, Fredrik; Klopfstein, Seraina; Vilhelmsen, Lars; Schulmeister, Susanne; Murray, Debra L.; Rasnitsyn, Alexandr P.

2012-01-01

Abstract Phylogenies are usually dated by calibrating interior nodes against the fossil record. This relies on indirect methods that, in the worst case, misrepresent the fossil information. Here, we contrast such node dating with an approach that includes fossils along with the extant taxa in a Bayesian total-evidence analysis. As a test case, we focus on the early radiation of the Hymenoptera, mostly documented by poorly preserved impression fossils that are difficult to place phylogenetically. Specifically, we compare node dating using nine calibration points derived from the fossil record with total-evidence dating based on 343 morphological characters scored for 45 fossil (4--20 complete) and 68 extant taxa. In both cases we use molecular data from seven markers (∼5 kb) for the extant taxa. Because it is difficult to model speciation, extinction, sampling, and fossil preservation realistically, we develop a simple uniform prior for clock trees with fossils, and we use relaxed clock models to accommodate rate variation across the tree. Despite considerable uncertainty in the placement of most fossils, we find that they contribute significantly to the estimation of divergence times in the total-evidence analysis. In particular, the posterior distributions on divergence times are less sensitive to prior assumptions and tend to be more precise than in node dating. The total-evidence analysis also shows that four of the seven Hymenoptera calibration points used in node dating are likely to be based on erroneous or doubtful assumptions about the fossil placement. With respect to the early radiation of Hymenoptera, our results suggest that the crown group dates back to the Carboniferous, ∼309 Ma (95% interval: 291--347 Ma), and diversified into major extant lineages much earlier than previously thought, well before the Triassic. [Bayesian inference; fossil dating; morphological evolution; relaxed clock; statistical phylogenetics.] PMID:22723471

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies

PubMed Central

2010-01-01

Background Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Results Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Conclusions Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data. PMID:21062443

A Bayesian Meta-Analysis on Prevalence of Hepatitis B Virus Infection among Chinese Volunteer Blood Donors

PubMed Central

Liu, Guang-ying; Zheng, Yang; Deng, Yan; Gao, Yan-yan; Wang, Lie

2013-01-01

Background Although transfusion-transmitted infection of hepatitis B virus (HBV) threatens the blood safety of China, the nationwide circumstance of HBV infection among blood donors is still unclear. Objectives To comprehensively estimate the prevalence of HBsAg positive and HBV occult infection (OBI) among Chinese volunteer blood donors through bayesian meta-analysis. Methods We performed an electronic search in Pub-Med, Web of Knowledge, Medline, Wanfang Data and CNKI, complemented by a hand search of relevant reference lists. Two authors independently extracted data from the eligible studies. Then two bayesian random-effect meta-analyses were performed, followed by bayesian meta-regressions. Results 5957412 and 571227 donors were identified in HBsAg group and OBI group, respectively. The pooled prevalence of HBsAg group and OBI group among donors is 1.085% (95% credible interval [CI] 0.859%∼1.398%) and 0.094% (95% CI 0.0578%∼0.1655%). For HBsAg group, subgroup analysis shows the more developed area has a lower prevalence than the less developed area; meta-regression indicates there is a significant decreasing trend in HBsAg positive prevalence with sampling year (beta = −0.1202, 95% −0.2081∼−0.0312). Conclusion Blood safety against HBV infection in China is suffering serious threats and the government should take effective measures to improve this situation. PMID:24236110

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

DOE PAGES

Alderman, Phillip D.; Stanfill, Bryan

2016-10-06

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

Multiscale hidden Markov models for photon-limited imaging

NASA Astrophysics Data System (ADS)

Nowak, Robert D.

1999-06-01

Photon-limited image analysis is often hindered by low signal-to-noise ratios. A novel Bayesian multiscale modeling and analysis method is developed in this paper to assist in these challenging situations. In addition to providing a very natural and useful framework for modeling an d processing images, Bayesian multiscale analysis is often much less computationally demanding compared to classical Markov random field models. This paper focuses on a probabilistic graph model called the multiscale hidden Markov model (MHMM), which captures the key inter-scale dependencies present in natural image intensities. The MHMM framework presented here is specifically designed for photon-limited imagin applications involving Poisson statistics, and applications to image intensity analysis are examined.

Numerical study on the sequential Bayesian approach for radioactive materials detection

NASA Astrophysics Data System (ADS)

Qingpei, Xiang; Dongfeng, Tian; Jianyu, Zhu; Fanhua, Hao; Ge, Ding; Jun, Zeng

2013-01-01

A new detection method, based on the sequential Bayesian approach proposed by Candy et al., offers new horizons for the research of radioactive detection. Compared with the commonly adopted detection methods incorporated with statistical theory, the sequential Bayesian approach offers the advantages of shorter verification time during the analysis of spectra that contain low total counts, especially in complex radionuclide components. In this paper, a simulation experiment platform implanted with the methodology of sequential Bayesian approach was developed. Events sequences of γ-rays associating with the true parameters of a LaBr3(Ce) detector were obtained based on an events sequence generator using Monte Carlo sampling theory to study the performance of the sequential Bayesian approach. The numerical experimental results are in accordance with those of Candy. Moreover, the relationship between the detection model and the event generator, respectively represented by the expected detection rate (Am) and the tested detection rate (Gm) parameters, is investigated. To achieve an optimal performance for this processor, the interval of the tested detection rate as a function of the expected detection rate is also presented.

Bayesian Inference for Time Trends in Parameter Values using Weighted Evidence Sets

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

D. L. Kelly; A. Malkhasyan

2010-09-01

There is a nearly ubiquitous assumption in PSA that parameter values are at least piecewise-constant in time. As a result, Bayesian inference tends to incorporate many years of plant operation, over which there have been significant changes in plant operational and maintenance practices, plant management, etc. These changes can cause significant changes in parameter values over time; however, failure to perform Bayesian inference in the proper time-dependent framework can mask these changes. Failure to question the assumption of constant parameter values, and failure to perform Bayesian inference in the proper time-dependent framework were noted as important issues in NUREG/CR-6813, performedmore » for the U. S. Nuclear Regulatory Commission’s Advisory Committee on Reactor Safeguards in 2003. That report noted that “in-dustry lacks tools to perform time-trend analysis with Bayesian updating.” This paper describes an applica-tion of time-dependent Bayesian inference methods developed for the European Commission Ageing PSA Network. These methods utilize open-source software, implementing Markov chain Monte Carlo sampling. The paper also illustrates an approach to incorporating multiple sources of data via applicability weighting factors that address differences in key influences, such as vendor, component boundaries, conditions of the operating environment, etc.« less

Bayesian Inference for Time Trends in Parameter Values: Case Study for the Ageing PSA Network of the European Commission

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

Dana L. Kelly; Albert Malkhasyan

2010-06-01

There is a nearly ubiquitous assumption in PSA that parameter values are at least piecewise-constant in time. As a result, Bayesian inference tends to incorporate many years of plant operation, over which there have been significant changes in plant operational and maintenance practices, plant management, etc. These changes can cause significant changes in parameter values over time; however, failure to perform Bayesian inference in the proper time-dependent framework can mask these changes. Failure to question the assumption of constant parameter values, and failure to perform Bayesian inference in the proper time-dependent framework were noted as important issues in NUREG/CR-6813, performedmore » for the U. S. Nuclear Regulatory Commission’s Advisory Committee on Reactor Safeguards in 2003. That report noted that “industry lacks tools to perform time-trend analysis with Bayesian updating.” This paper describes an application of time-dependent Bayesian inference methods developed for the European Commission Ageing PSA Network. These methods utilize open-source software, implementing Markov chain Monte Carlo sampling. The paper also illustrates the development of a generic prior distribution, which incorporates multiple sources of generic data via weighting factors that address differences in key influences, such as vendor, component boundaries, conditions of the operating environment, etc.« less

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

Introduction of Bayesian network in risk analysis of maritime accidents in Bangladesh

NASA Astrophysics Data System (ADS)

Rahman, Sohanur

2017-12-01

Due to the unique geographic location, complex navigation environment and intense vessel traffic, a considerable number of maritime accidents occurred in Bangladesh which caused serious loss of life, property and environmental contamination. Based on the historical data of maritime accidents from 1981 to 2015, which has been collected from Department of Shipping (DOS) and Bangladesh Inland Water Transport Authority (BIWTA), this paper conducted a risk analysis of maritime accidents by applying Bayesian network. In order to conduct this study, a Bayesian network model has been developed to find out the relation among parameters and the probability of them which affect accidents based on the accident investigation report of Bangladesh. Furthermore, number of accidents in different categories has also been investigated in this paper. Finally, some viable recommendations have been proposed in order to ensure greater safety of inland vessels in Bangladesh.

Confirmatory Factor Analysis Alternative: Free, Accessible CBID Software.

PubMed

Bott, Marjorie; Karanevich, Alex G; Garrard, Lili; Price, Larry R; Mudaranthakam, Dinesh Pal; Gajewski, Byron

2018-02-01

New software that performs Classical and Bayesian Instrument Development (CBID) is reported that seamlessly integrates expert (content validity) and participant data (construct validity) to produce entire reliability estimates with smaller sample requirements. The free CBID software can be accessed through a website and used by clinical investigators in new instrument development. Demonstrations are presented of the three approaches using the CBID software: (a) traditional confirmatory factor analysis (CFA), (b) Bayesian CFA using flat uninformative prior, and (c) Bayesian CFA using content expert data (informative prior). Outcomes of usability testing demonstrate the need to make the user-friendly, free CBID software available to interdisciplinary researchers. CBID has the potential to be a new and expeditious method for instrument development, adding to our current measurement toolbox. This allows for the development of new instruments for measuring determinants of health in smaller diverse populations or populations of rare diseases.

Assessing noninferiority in a three-arm trial using the Bayesian approach.

PubMed

Ghosh, Pulak; Nathoo, Farouk; Gönen, Mithat; Tiwari, Ram C

2011-07-10

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm trial consists of a placebo, a reference and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with comparing this reference to an experimental treatment. In this paper, we consider the analysis of non-inferiority trials using Bayesian methods which incorporate both parametric as well as semi-parametric models. The resulting testing approach is both flexible and robust. The benefit of the proposed Bayesian methods is assessed via simulation, based on a study examining home-based blood pressure interventions. Copyright © 2011 John Wiley & Sons, Ltd.

Applying Bayesian belief networks in rapid response situations

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

Gibson, William L; Deborah, Leishman, A.; Van Eeckhout, Edward

2008-01-01

The authors have developed an enhanced Bayesian analysis tool called the Integrated Knowledge Engine (IKE) for monitoring and surveillance. The enhancements are suited for Rapid Response Situations where decisions must be made based on uncertain and incomplete evidence from many diverse and heterogeneous sources. The enhancements extend the probabilistic results of the traditional Bayesian analysis by (1) better quantifying uncertainty arising from model parameter uncertainty and uncertain evidence, (2) optimizing the collection of evidence to reach conclusions more quickly, and (3) allowing the analyst to determine the influence of the remaining evidence that cannot be obtained in the time allowed.more » These extended features give the analyst and decision maker a better comprehension of the adequacy of the acquired evidence and hence the quality of the hurried decisions. They also describe two example systems where the above features are highlighted.« less

Bayesian tomography and integrated data analysis in fusion diagnostics

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

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

2016-11-15

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

A statistical model investigating the prevalence of tuberculosis in New York City using counting processes with two change-points

PubMed Central

ACHCAR, J. A.; MARTINEZ, E. Z.; RUFFINO-NETTO, A.; PAULINO, C. D.; SOARES, P.

2008-01-01

SUMMARY We considered a Bayesian analysis for the prevalence of tuberculosis cases in New York City from 1970 to 2000. This counting dataset presented two change-points during this period. We modelled this counting dataset considering non-homogeneous Poisson processes in the presence of the two-change points. A Bayesian analysis for the data is considered using Markov chain Monte Carlo methods. Simulated Gibbs samples for the parameters of interest were obtained using WinBugs software. PMID:18346287

Crystalline nucleation in undercooled liquids: a Bayesian data-analysis approach for a nonhomogeneous Poisson process.

PubMed

Filipponi, A; Di Cicco, A; Principi, E

2012-12-01

A Bayesian data-analysis approach to data sets of maximum undercooling temperatures recorded in repeated melting-cooling cycles of high-purity samples is proposed. The crystallization phenomenon is described in terms of a nonhomogeneous Poisson process driven by a temperature-dependent sample nucleation rate J(T). The method was extensively tested by computer simulations and applied to real data for undercooled liquid Ge. It proved to be particularly useful in the case of scarce data sets where the usage of binned data would degrade the available experimental information.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Fragment virtual screening based on Bayesian categorization for discovering novel VEGFR-2 scaffolds.

PubMed

Zhang, Yanmin; Jiao, Yu; Xiong, Xiao; Liu, Haichun; Ran, Ting; Xu, Jinxing; Lu, Shuai; Xu, Anyang; Pan, Jing; Qiao, Xin; Shi, Zhihao; Lu, Tao; Chen, Yadong

2015-11-01

The discovery of novel scaffolds against a specific target has long been one of the most significant but challengeable goals in discovering lead compounds. A scaffold that binds in important regions of the active pocket is more favorable as a starting point because scaffolds generally possess greater optimization possibilities. However, due to the lack of sufficient chemical space diversity of the databases and the ineffectiveness of the screening methods, it still remains a great challenge to discover novel active scaffolds. Since the strengths and weaknesses of both fragment-based drug design and traditional virtual screening (VS), we proposed a fragment VS concept based on Bayesian categorization for the discovery of novel scaffolds. This work investigated the proposal through an application on VEGFR-2 target. Firstly, scaffold and structural diversity of chemical space for 10 compound databases were explicitly evaluated. Simultaneously, a robust Bayesian classification model was constructed for screening not only compound databases but also their corresponding fragment databases. Although analysis of the scaffold diversity demonstrated a very unevenly distribution of scaffolds over molecules, results showed that our Bayesian model behaved better in screening fragments than molecules. Through a literature retrospective research, several generated fragments with relatively high Bayesian scores indeed exhibit VEGFR-2 biological activity, which strongly proved the effectiveness of fragment VS based on Bayesian categorization models. This investigation of Bayesian-based fragment VS can further emphasize the necessity for enrichment of compound databases employed in lead discovery by amplifying the diversity of databases with novel structures.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Bayesian depth estimation from monocular natural images.

PubMed

Su, Che-Chun; Cormack, Lawrence K; Bovik, Alan C

2017-05-01

Estimating an accurate and naturalistic dense depth map from a single monocular photographic image is a difficult problem. Nevertheless, human observers have little difficulty understanding the depth structure implied by photographs. Two-dimensional (2D) images of the real-world environment contain significant statistical information regarding the three-dimensional (3D) structure of the world that the vision system likely exploits to compute perceived depth, monocularly as well as binocularly. Toward understanding how this might be accomplished, we propose a Bayesian model of monocular depth computation that recovers detailed 3D scene structures by extracting reliable, robust, depth-sensitive statistical features from single natural images. These features are derived using well-accepted univariate natural scene statistics (NSS) models and recent bivariate/correlation NSS models that describe the relationships between 2D photographic images and their associated depth maps. This is accomplished by building a dictionary of canonical local depth patterns from which NSS features are extracted as prior information. The dictionary is used to create a multivariate Gaussian mixture (MGM) likelihood model that associates local image features with depth patterns. A simple Bayesian predictor is then used to form spatial depth estimates. The depth results produced by the model, despite its simplicity, correlate well with ground-truth depths measured by a current-generation terrestrial light detection and ranging (LIDAR) scanner. Such a strong form of statistical depth information could be used by the visual system when creating overall estimated depth maps incorporating stereopsis, accommodation, and other conditions. Indeed, even in isolation, the Bayesian predictor delivers depth estimates that are competitive with state-of-the-art "computer vision" methods that utilize highly engineered image features and sophisticated machine learning algorithms.

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

NASA Astrophysics Data System (ADS)

Gunning, James; Glinsky, Michael E.

2006-06-01

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

Remote Sensing Image Classification Applied to the First National Geographical Information Census of China

NASA Astrophysics Data System (ADS)

Yu, Xin; Wen, Zongyong; Zhu, Zhaorong; Xia, Qiang; Shun, Lan

2016-06-01

Image classification will still be a long way in the future, although it has gone almost half a century. In fact, researchers have gained many fruits in the image classification domain, but there is still a long distance between theory and practice. However, some new methods in the artificial intelligence domain will be absorbed into the image classification domain and draw on the strength of each to offset the weakness of the other, which will open up a new prospect. Usually, networks play the role of a high-level language, as is seen in Artificial Intelligence and statistics, because networks are used to build complex model from simple components. These years, Bayesian Networks, one of probabilistic networks, are a powerful data mining technique for handling uncertainty in complex domains. In this paper, we apply Tree Augmented Naive Bayesian Networks (TAN) to texture classification of High-resolution remote sensing images and put up a new method to construct the network topology structure in terms of training accuracy based on the training samples. Since 2013, China government has started the first national geographical information census project, which mainly interprets geographical information based on high-resolution remote sensing images. Therefore, this paper tries to apply Bayesian network to remote sensing image classification, in order to improve image interpretation in the first national geographical information census project. In the experiment, we choose some remote sensing images in Beijing. Experimental results demonstrate TAN outperform than Naive Bayesian Classifier (NBC) and Maximum Likelihood Classification Method (MLC) in the overall classification accuracy. In addition, the proposed method can reduce the workload of field workers and improve the work efficiency. Although it is time consuming, it will be an attractive and effective method for assisting office operation of image interpretation.

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.

Exploratory study on a statistical method to analyse time resolved data obtained during nanomaterial exposure measurements

NASA Astrophysics Data System (ADS)

Clerc, F.; Njiki-Menga, G.-H.; Witschger, O.

2013-04-01

Most of the measurement strategies that are suggested at the international level to assess workplace exposure to nanomaterials rely on devices measuring, in real time, airborne particles concentrations (according different metrics). Since none of the instruments to measure aerosols can distinguish a particle of interest to the background aerosol, the statistical analysis of time resolved data requires special attention. So far, very few approaches have been used for statistical analysis in the literature. This ranges from simple qualitative analysis of graphs to the implementation of more complex statistical models. To date, there is still no consensus on a particular approach and the current period is always looking for an appropriate and robust method. In this context, this exploratory study investigates a statistical method to analyse time resolved data based on a Bayesian probabilistic approach. To investigate and illustrate the use of the this statistical method, particle number concentration data from a workplace study that investigated the potential for exposure via inhalation from cleanout operations by sandpapering of a reactor producing nanocomposite thin films have been used. In this workplace study, the background issue has been addressed through the near-field and far-field approaches and several size integrated and time resolved devices have been used. The analysis of the results presented here focuses only on data obtained with two handheld condensation particle counters. While one was measuring at the source of the released particles, the other one was measuring in parallel far-field. The Bayesian probabilistic approach allows a probabilistic modelling of data series, and the observed task is modelled in the form of probability distributions. The probability distributions issuing from time resolved data obtained at the source can be compared with the probability distributions issuing from the time resolved data obtained far-field, leading in a quantitative estimation of the airborne particles released at the source when the task is performed. Beyond obtained results, this exploratory study indicates that the analysis of the results requires specific experience in statistics.

Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis–Hastings Markov Chain Monte Carlo algorithm

DOE PAGES

Wang, Hongrui; Wang, Cheng; Wang, Ying; ...

2017-04-05

This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLEmore » confidence interval and thus more precise estimation by using the related information from regional gage stations. As a result, the Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.« less

Learning Bayesian Networks from Correlated Data

NASA Astrophysics Data System (ADS)

Bae, Harold; Monti, Stefano; Montano, Monty; Steinberg, Martin H.; Perls, Thomas T.; Sebastiani, Paola

2016-05-01

Bayesian networks are probabilistic models that represent complex distributions in a modular way and have become very popular in many fields. There are many methods to build Bayesian networks from a random sample of independent and identically distributed observations. However, many observational studies are designed using some form of clustered sampling that introduces correlations between observations within the same cluster and ignoring this correlation typically inflates the rate of false positive associations. We describe a novel parameterization of Bayesian networks that uses random effects to model the correlation within sample units and can be used for structure and parameter learning from correlated data without inflating the Type I error rate. We compare different learning metrics using simulations and illustrate the method in two real examples: an analysis of genetic and non-genetic factors associated with human longevity from a family-based study, and an example of risk factors for complications of sickle cell anemia from a longitudinal study with repeated measures.

A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks

PubMed Central

Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan

2015-01-01

Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest. PMID:25491372

Asteroid orbital error analysis: Theory and application

NASA Technical Reports Server (NTRS)

Muinonen, K.; Bowell, Edward

1992-01-01

We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).

Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model.

PubMed

Sampid, Marius Galabe; Hasim, Haslifah M; Dai, Hongsheng

2018-01-01

In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student's-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis.

Spectral Analysis of B Stars: An Application of Bayesian Statistics

NASA Astrophysics Data System (ADS)

Mugnes, J.-M.; Robert, C.

2012-12-01

To better understand the processes involved in stellar physics, it is necessary to obtain accurate stellar parameters (effective temperature, surface gravity, abundances…). Spectral analysis is a powerful tool for investigating stars, but it is also vital to reduce uncertainties at a decent computational cost. Here we present a spectral analysis method based on a combination of Bayesian statistics and grids of synthetic spectra obtained with TLUSTY. This method simultaneously constrains the stellar parameters by using all the lines accessible in observed spectra and thus greatly reduces uncertainties and improves the overall spectrum fitting. Preliminary results are shown using spectra from the Observatoire du Mont-Mégantic.

Suggestions for presenting the results of data analyses

USGS Publications Warehouse

Anderson, David R.; Link, William A.; Johnson, Douglas H.; Burnham, Kenneth P.

2001-01-01

We give suggestions for the presentation of research results from frequentist, information-theoretic, and Bayesian analysis paradigms, followed by several general suggestions. The information-theoretic and Bayesian methods offer alternative approaches to data analysis and inference compared to traditionally used methods. Guidance is lacking on the presentation of results under these alternative procedures and on nontesting aspects of classical frequentists methods of statistical analysis. Null hypothesis testing has come under intense criticism. We recommend less reporting of the results of statistical tests of null hypotheses in cases where the null is surely false anyway, or where the null hypothesis is of little interest to science or management.

Rigorous Approach in Investigation of Seismic Structure and Source Characteristicsin Northeast Asia: Hierarchical and Trans-dimensional Bayesian Inversion

NASA Astrophysics Data System (ADS)

Mustac, M.; Kim, S.; Tkalcic, H.; Rhie, J.; Chen, Y.; Ford, S. R.; Sebastian, N.

2015-12-01

Conventional approaches to inverse problems suffer from non-linearity and non-uniqueness in estimations of seismic structures and source properties. Estimated results and associated uncertainties are often biased by applied regularizations and additional constraints, which are commonly introduced to solve such problems. Bayesian methods, however, provide statistically meaningful estimations of models and their uncertainties constrained by data information. In addition, hierarchical and trans-dimensional (trans-D) techniques are inherently implemented in the Bayesian framework to account for involved error statistics and model parameterizations, and, in turn, allow more rigorous estimations of the same. Here, we apply Bayesian methods throughout the entire inference process to estimate seismic structures and source properties in Northeast Asia including east China, the Korean peninsula, and the Japanese islands. Ambient noise analysis is first performed to obtain a base three-dimensional (3-D) heterogeneity model using continuous broadband waveforms from more than 300 stations. As for the tomography of surface wave group and phase velocities in the 5-70 s band, we adopt a hierarchical and trans-D Bayesian inversion method using Voronoi partition. The 3-D heterogeneity model is further improved by joint inversions of teleseismic receiver functions and dispersion data using a newly developed high-efficiency Bayesian technique. The obtained model is subsequently used to prepare 3-D structural Green's functions for the source characterization. A hierarchical Bayesian method for point source inversion using regional complete waveform data is applied to selected events from the region. The seismic structure and source characteristics with rigorously estimated uncertainties from the novel Bayesian methods provide enhanced monitoring and discrimination of seismic events in northeast Asia.

Computational models of the Posner simple and choice reaction time tasks

PubMed Central

Feher da Silva, Carolina; Baldo, Marcus V. C.

2015-01-01

The landmark experiments by Posner in the late 1970s have shown that reaction time (RT) is faster when the stimulus appears in an expected location, as indicated by a cue; since then, the so-called Posner task has been considered a “gold standard” test of spatial attention. It is thus fundamental to understand the neural mechanisms involved in performing it. To this end, we have developed a Bayesian detection system and small integrate-and-fire neural networks, which modeled sensory and motor circuits, respectively, and optimized them to perform the Posner task under different cue type proportions and noise levels. In doing so, main findings of experimental research on RT were replicated: the relative frequency effect, suboptimal RTs and significant error rates due to noise and invalid cues, slower RT for choice RT tasks than for simple RT tasks, fastest RTs for valid cues and slowest RTs for invalid cues. Analysis of the optimized systems revealed that the employed mechanisms were consistent with related findings in neurophysiology. Our models predict that (1) the results of a Posner task may be affected by the relative frequency of valid and neutral trials, (2) in simple RT tasks, input from multiple locations are added together to compose a stronger signal, and (3) the cue affects motor circuits more strongly in choice RT tasks than in simple RT tasks. In discussing the computational demands of the Posner task, attention has often been described as a filter that protects the nervous system, whose capacity is limited, from information overload. Our models, however, reveal that the main problems that must be overcome to perform the Posner task effectively are distinguishing signal from external noise and selecting the appropriate response in the presence of internal noise. PMID:26190997

Joint Bayesian Component Separation and CMB Power Spectrum Estimation

NASA Technical Reports Server (NTRS)

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

2008-01-01

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

Advances in the microrheology of complex fluids

NASA Astrophysics Data System (ADS)

Waigh, Thomas Andrew

2016-07-01

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

Admixture analysis in relation to pedigree studies of introgression in a minority British cattle breed: the Lincoln Red.

PubMed

Bray, T C; Hall, S J G; Bruford, M W

2014-02-01

Investigation of historic population processes using molecular data has been facilitated by the use of approximate Bayesian computation (ABC), which enables the consideration of multiple alternative demographic scenarios. The Lincoln Red cattle breed provides a relatively simple example of two well-documented admixture events. Using molecular data for this breed, we found that structure did not resolve very low (<5% levels) of introgression, possibly due to sampling limitations. We evaluated the performance of two ABC approaches (2BAD and DIYABC) against those of two earlier methodologies, ADMIX and LEADMIX, by comparing their interpretations with the conclusions drawn from herdbook analysis. The ABC methods gave credible values for the proportions of the Lincoln Red genotype that are attributable to Aberdeen Angus and Limousin, although estimates of effective population size and event timing were not realistic. We suggest ABC methods are a valuable supplement to pedigree-based studies but that the accuracy of admixture determination is likely to diminish with increasing complexity of the admixture scenario. © 2013 Blackwell Verlag GmbH.

In defence of model-based inference in phylogeography

PubMed Central

Beaumont, Mark A.; Nielsen, Rasmus; Robert, Christian; Hey, Jody; Gaggiotti, Oscar; Knowles, Lacey; Estoup, Arnaud; Panchal, Mahesh; Corander, Jukka; Hickerson, Mike; Sisson, Scott A.; Fagundes, Nelson; Chikhi, Lounès; Beerli, Peter; Vitalis, Renaud; Cornuet, Jean-Marie; Huelsenbeck, John; Foll, Matthieu; Yang, Ziheng; Rousset, Francois; Balding, David; Excoffier, Laurent

2017-01-01

Recent papers have promoted the view that model-based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested Clade Phylogeographic Analysis (NCPA) offers the best approach in statistical phylogeography. In order to remove the confusion and misconceptions introduced by these papers, we justify and explain the reasoning behind model-based inference. We argue that ABC is a statistically valid approach, alongside other computational statistical techniques that have been successfully used to infer parameters and compare models in population genetics. We also examine the NCPA method and highlight numerous deficiencies, either when used with single or multiple loci. We further show that the ages of clades are carelessly used to infer ages of demographic events, that these ages are estimated under a simple model of panmixia and population stationarity but are then used under different and unspecified models to test hypotheses, a usage the invalidates these testing procedures. We conclude by encouraging researchers to study and use model-based inference in population genetics. PMID:29284924