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.

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.

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…

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…

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.

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.

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

PubMed

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

2013-08-30

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

Bayesian 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.

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.

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

[Bayesian statistics in medicine -- part II: main applications and inference].

PubMed

Montomoli, C; Nichelatti, M

2008-01-01

Bayesian statistics is not only used when one is dealing with 2-way tables, but it can be used for inferential purposes. Using the basic concepts presented in the first part, this paper aims to give a simple overview of Bayesian methods by introducing its foundation (Bayes' theorem) and then applying this rule to a very simple practical example; whenever possible, the elementary processes at the basis of analysis are compared to those of frequentist (classical) statistical analysis. The Bayesian reasoning is naturally connected to medical activity, since it appears to be quite similar to a diagnostic process.

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

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.

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...

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…

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.

The Importance of Proving the Null

ERIC Educational Resources Information Center

Gallistel, C. R.

2009-01-01

Null hypotheses are simple, precise, and theoretically important. Conventional statistical analysis cannot support them; Bayesian analysis can. The challenge in a Bayesian analysis is to formulate a suitably vague alternative, because the vaguer the alternative is (the more it spreads out the unit mass of prior probability), the more the null is…

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…

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.

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...

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.

Bayesian Analysis of Longitudinal Data Using Growth Curve Models

ERIC Educational Resources Information Center

Zhang, Zhiyong; Hamagami, Fumiaki; Wang, Lijuan Lijuan; Nesselroade, John R.; Grimm, Kevin J.

2007-01-01

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data…

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.

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.

Application of Bayesian Approach in Cancer Clinical Trial

PubMed Central

Bhattacharjee, Atanu

2014-01-01

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

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.

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.

Bayesian Factor Analysis When Only a Sample Covariance Matrix Is Available

ERIC Educational Resources Information Center

Hayashi, Kentaro; Arav, Marina

2006-01-01

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

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.

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.

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.

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.

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).

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.

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.

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.

Enhancements of Bayesian Blocks; Application to Large Light Curve Databases

NASA Technical Reports Server (NTRS)

Scargle, Jeff

2015-01-01

Bayesian Blocks are optimal piecewise linear representations (step function fits) of light-curves. The simple algorithm implementing this idea, using dynamic programming, has been extended to include more data modes and fitness metrics, multivariate analysis, and data on the circle (Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations, Scargle, Norris, Jackson and Chiang 2013, ApJ, 764, 167), as well as new results on background subtraction and refinement of the procedure for precise timing of transient events in sparse data. Example demonstrations will include exploratory analysis of the Kepler light curve archive in a search for "star-tickling" signals from extraterrestrial civilizations. (The Cepheid Galactic Internet, Learned, Kudritzki, Pakvasa1, and Zee, 2008, arXiv: 0809.0339; Walkowicz et al., in progress).

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.

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

Model-based Bayesian inference for ROC data analysis

NASA Astrophysics Data System (ADS)

Lei, Tianhu; Bae, K. Ty

2013-03-01

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

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.

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.

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…

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2005-10-01

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

Bayesian 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%.

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

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.

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.

Applications of Bayesian Procrustes shape analysis to ensemble radar reflectivity nowcast verification

NASA Astrophysics Data System (ADS)

Fox, Neil I.; Micheas, Athanasios C.; Peng, Yuqiang

2016-07-01

This paper introduces the use of Bayesian full Procrustes shape analysis in object-oriented meteorological applications. In particular, the Procrustes methodology is used to generate mean forecast precipitation fields from a set of ensemble forecasts. This approach has advantages over other ensemble averaging techniques in that it can produce a forecast that retains the morphological features of the precipitation structures and present the range of forecast outcomes represented by the ensemble. The production of the ensemble mean avoids the problems of smoothing that result from simple pixel or cell averaging, while producing credible sets that retain information on ensemble spread. Also in this paper, the full Bayesian Procrustes scheme is used as an object verification tool for precipitation forecasts. This is an extension of a previously presented Procrustes shape analysis based verification approach into a full Bayesian format designed to handle the verification of precipitation forecasts that match objects from an ensemble of forecast fields to a single truth image. The methodology is tested on radar reflectivity nowcasts produced in the Warning Decision Support System - Integrated Information (WDSS-II) by varying parameters in the K-means cluster tracking scheme.

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.

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.

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

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…

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.

Metis: A Pure Metropolis Markov Chain Monte Carlo Bayesian Inference Library

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

Bates, Cameron Russell; Mckigney, Edward Allen

The use of Bayesian inference in data analysis has become the standard for large scienti c experiments [1, 2]. The Monte Carlo Codes Group(XCP-3) at Los Alamos has developed a simple set of algorithms currently implemented in C++ and Python to easily perform at-prior Markov Chain Monte Carlo Bayesian inference with pure Metropolis sampling. These implementations are designed to be user friendly and extensible for customization based on speci c application requirements. This document describes the algorithmic choices made and presents two use cases.

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.

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

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.

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.

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.

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.

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.

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…

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 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.

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.

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.

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.

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.

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.

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…

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.

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.

Understanding the Uncertainty of an Effectiveness-Cost Ratio in Educational Resource Allocation: A Bayesian Approach

ERIC Educational Resources Information Center

Pan, Yilin

2016-01-01

Given the necessity to bridge the gap between what happened and what is likely to happen, this paper aims to explore how to apply Bayesian inference to cost-effectiveness analysis so as to capture the uncertainty of a ratio-type efficiency measure. The first part of the paper summarizes the characteristics of the evaluation data that are commonly…

Bayesian hierarchical model for large-scale covariance matrix estimation.

PubMed

Zhu, Dongxiao; Hero, Alfred O

2007-12-01

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.

Bayesian spatial prediction of the site index in the study of the Missouri Ozark Forest Ecosystem Project

Treesearch

Xiaoqian Sun; Zhuoqiong He; John Kabrick

2008-01-01

This paper presents a Bayesian spatial method for analysing the site index data from the Missouri Ozark Forest Ecosystem Project (MOFEP). Based on ecological background and availability, we select three variables, the aspect class, the soil depth and the land type association as covariates for analysis. To allow great flexibility of the smoothness of the random field,...

Quantity of dates trumps quality of dates for dense Bayesian radiocarbon sediment chronologies - Gas ion source 14C dating instructed by simultaneous Bayesian accumulation rate modeling

NASA Astrophysics Data System (ADS)

Rosenheim, B. E.; Firesinger, D.; Roberts, M. L.; Burton, J. R.; Khan, N.; Moyer, R. P.

2016-12-01

Radiocarbon (14C) sediment core chronologies benefit from a high density of dates, even when precision of individual dates is sacrificed. This is demonstrated by a combined approach of rapid 14C analysis of CO2 gas generated from carbonates and organic material coupled with Bayesian statistical modeling. Analysis of 14C is facilitated by the gas ion source on the Continuous Flow Accelerator Mass Spectrometry (CFAMS) system at the Woods Hole Oceanographic Institution's National Ocean Sciences Accelerator Mass Spectrometry facility. This instrument is capable of producing a 14C determination of +/- 100 14C y precision every 4-5 minutes, with limited sample handling (dissolution of carbonates and/or combustion of organic carbon in evacuated containers). Rapid analysis allows over-preparation of samples to include replicates at each depth and/or comparison of different sample types at particular depths in a sediment or peat core. Analysis priority is given to depths that have the least chronologic precision as determined by Bayesian modeling of the chronology of calibrated ages. Use of such a statistical approach to determine the order in which samples are run ensures that the chronology constantly improves so long as material is available for the analysis of chronologic weak points. Ultimately, accuracy of the chronology is determined by the material that is actually being dated, and our combined approach allows testing of different constituents of the organic carbon pool and the carbonate minerals within a core. We will present preliminary results from a deep-sea sediment core abundant in deep-sea foraminifera as well as coastal wetland peat cores to demonstrate statistical improvements in sediment- and peat-core chronologies obtained by increasing the quantity and decreasing the quality of individual dates.

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

Gagné, Jonathan; Lafrenière, David; Doyon, René

We present Bayesian Analysis for Nearby Young AssociatioNs II (BANYAN II), a modified Bayesian analysis for assessing the membership of later-than-M5 objects to any of several Nearby Young Associations (NYAs). In addition to using kinematic information (from sky position and proper motion), this analysis exploits 2MASS-WISE color-magnitude diagrams in which old and young objects follow distinct sequences. As an improvement over our earlier work, the spatial and kinematic distributions for each association are now modeled as ellipsoids whose axes need not be aligned with the Galactic coordinate axes, and we use prior probabilities matching the expected populations of the NYAsmore » considered versus field stars. We present an extensive contamination analysis to characterize the performance of our new method. We find that Bayesian probabilities are generally representative of contamination rates, except when a parallax measurement is considered. In this case contamination rates become significantly smaller and hence Bayesian probabilities for NYA memberships are pessimistic. We apply this new algorithm to a sample of 158 objects from the literature that are either known to display spectroscopic signs of youth or have unusually red near-infrared colors for their spectral type. Based on our analysis, we identify 25 objects as new highly probable candidates to NYAs, including a new M7.5 bona fide member to Tucana-Horologium, making it the latest-type member. In addition, we reveal that a known L2γ dwarf is co-moving with a bright M5 dwarf, and we show for the first time that two of the currently known ultra red L dwarfs are strong candidates to the AB Doradus moving group. Several objects identified here as highly probable members to NYAs could be free-floating planetary-mass objects if their membership is confirmed.« less

Risk analysis of new oral anticoagulants for gastrointestinal bleeding and intracranial hemorrhage in atrial fibrillation patients: a systematic review and network meta-analysis.

PubMed

Xu, Wei-Wei; Hu, Shen-Jiang; Wu, Tao

2017-07-01

Antithrombotic therapy using new oral anticoagulants (NOACs) in patients with atrial fibrillation (AF) has been generally shown to have a favorable risk-benefit profile. Since there has been dispute about the risks of gastrointestinal bleeding (GIB) and intracranial hemorrhage (ICH), we sought to conduct a systematic review and network meta-analysis using Bayesian inference to analyze the risks of GIB and ICH in AF patients taking NOACs. We analyzed data from 20 randomized controlled trials of 91 671 AF patients receiving anticoagulants, antiplatelet drugs, or placebo. Bayesian network meta-analysis of two different evidence networks was performed using a binomial likelihood model, based on a network in which different agents (and doses) were treated as separate nodes. Odds ratios (ORs) and 95% confidence intervals (CIs) were modeled using Markov chain Monte Carlo methods. Indirect comparisons with the Bayesian model confirmed that aspirin+clopidogrel significantly increased the risk of GIB in AF patients compared to the placebo (OR 0.33, 95% CI 0.01-0.92). Warfarin was identified as greatly increasing the risk of ICH compared to edoxaban 30 mg (OR 3.42, 95% CI 1.22-7.24) and dabigatran 110 mg (OR 3.56, 95% CI 1.10-8.45). We further ranked the NOACs for the lowest risk of GIB (apixaban 5 mg) and ICH (apixaban 5 mg, dabigatran 110 mg, and edoxaban 30 mg). Bayesian network meta-analysis of treatment of non-valvular AF patients with anticoagulants suggested that NOACs do not increase risks of GIB and/or ICH, compared to each other.

Analysis of statistical and standard algorithms for detecting muscle onset with surface electromyography.

PubMed

Tenan, Matthew S; Tweedell, Andrew J; Haynes, Courtney A

2017-01-01

The timing of muscle activity is a commonly applied analytic method to understand how the nervous system controls movement. This study systematically evaluates six classes of standard and statistical algorithms to determine muscle onset in both experimental surface electromyography (EMG) and simulated EMG with a known onset time. Eighteen participants had EMG collected from the biceps brachii and vastus lateralis while performing a biceps curl or knee extension, respectively. Three established methods and three statistical methods for EMG onset were evaluated. Linear envelope, Teager-Kaiser energy operator + linear envelope and sample entropy were the established methods evaluated while general time series mean/variance, sequential and batch processing of parametric and nonparametric tools, and Bayesian changepoint analysis were the statistical techniques used. Visual EMG onset (experimental data) and objective EMG onset (simulated data) were compared with algorithmic EMG onset via root mean square error and linear regression models for stepwise elimination of inferior algorithms. The top algorithms for both data types were analyzed for their mean agreement with the gold standard onset and evaluation of 95% confidence intervals. The top algorithms were all Bayesian changepoint analysis iterations where the parameter of the prior (p0) was zero. The best performing Bayesian algorithms were p0 = 0 and a posterior probability for onset determination at 60-90%. While existing algorithms performed reasonably, the Bayesian changepoint analysis methodology provides greater reliability and accuracy when determining the singular onset of EMG activity in a time series. Further research is needed to determine if this class of algorithms perform equally well when the time series has multiple bursts of muscle activity.

"A Bayesian sensitivity analysis to evaluate the impact of unmeasured confounding with external data: a real world comparative effectiveness study in osteoporosis".

PubMed

Zhang, Xiang; Faries, Douglas E; Boytsov, Natalie; Stamey, James D; Seaman, John W

2016-09-01

Observational studies are frequently used to assess the effectiveness of medical interventions in routine clinical practice. However, the use of observational data for comparative effectiveness is challenged by selection bias and the potential of unmeasured confounding. This is especially problematic for analyses using a health care administrative database, in which key clinical measures are often not available. This paper provides an approach to conducting a sensitivity analyses to investigate the impact of unmeasured confounding in observational studies. In a real world osteoporosis comparative effectiveness study, the bone mineral density (BMD) score, an important predictor of fracture risk and a factor in the selection of osteoporosis treatments, is unavailable in the data base and lack of baseline BMD could potentially lead to significant selection bias. We implemented Bayesian twin-regression models, which simultaneously model both the observed outcome and the unobserved unmeasured confounder, using information from external sources. A sensitivity analysis was also conducted to assess the robustness of our conclusions to changes in such external data. The use of Bayesian modeling in this study suggests that the lack of baseline BMD did have a strong impact on the analysis, reversing the direction of the estimated effect (odds ratio of fracture incidence at 24 months: 0.40 vs. 1.36, with/without adjusting for unmeasured baseline BMD). The Bayesian twin-regression models provide a flexible sensitivity analysis tool to quantitatively assess the impact of unmeasured confounding in observational studies. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Fuzzy Bayesian Network-Bow-Tie Analysis of Gas Leakage during Biomass Gasification

PubMed Central

Yan, Fang; Xu, Kaili; Yao, Xiwen; Li, Yang

2016-01-01

Biomass gasification technology has been rapidly developed recently. But fire and poisoning accidents caused by gas leakage restrict the development and promotion of biomass gasification. Therefore, probabilistic safety assessment (PSA) is necessary for biomass gasification system. Subsequently, Bayesian network-bow-tie (BN-bow-tie) analysis was proposed by mapping bow-tie analysis into Bayesian network (BN). Causes of gas leakage and the accidents triggered by gas leakage can be obtained by bow-tie analysis, and BN was used to confirm the critical nodes of accidents by introducing corresponding three importance measures. Meanwhile, certain occurrence probability of failure was needed in PSA. In view of the insufficient failure data of biomass gasification, the occurrence probability of failure which cannot be obtained from standard reliability data sources was confirmed by fuzzy methods based on expert judgment. An improved approach considered expert weighting to aggregate fuzzy numbers included triangular and trapezoidal numbers was proposed, and the occurrence probability of failure was obtained. Finally, safety measures were indicated based on the obtained critical nodes. The theoretical occurrence probabilities in one year of gas leakage and the accidents caused by it were reduced to 1/10.3 of the original values by these safety measures. PMID:27463975

DATMAN: A reliability data analysis program using Bayesian updating

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

Becker, M.; Feltus, M.A.

1996-12-31

Preventive maintenance (PM) techniques focus on the prevention of failures, in particular, system components that are important to plant functions. Reliability-centered maintenance (RCM) improves on the PM techniques by introducing a set of guidelines by which to evaluate the system functions. It also minimizes intrusive maintenance, labor, and equipment downtime without sacrificing system performance when its function is essential for plant safety. Both the PM and RCM approaches require that system reliability data be updated as more component failures and operation time are acquired. Systems reliability and the likelihood of component failures can be calculated by Bayesian statistical methods, whichmore » can update these data. The DATMAN computer code has been developed at Penn State to simplify the Bayesian analysis by performing tedious calculations needed for RCM reliability analysis. DATMAN reads data for updating, fits a distribution that best fits the data, and calculates component reliability. DATMAN provides a user-friendly interface menu that allows the user to choose from several common prior and posterior distributions, insert new failure data, and visually select the distribution that matches the data most accurately.« less

Bayesian dynamic mediation analysis.

PubMed

Huang, Jing; Yuan, Ying

2017-12-01

Most existing methods for mediation analysis assume that mediation is a stationary, time-invariant process, which overlooks the inherently dynamic nature of many human psychological processes and behavioral activities. In this article, we consider mediation as a dynamic process that continuously changes over time. We propose Bayesian multilevel time-varying coefficient models to describe and estimate such dynamic mediation effects. By taking the nonparametric penalized spline approach, the proposed method is flexible and able to accommodate any shape of the relationship between time and mediation effects. Simulation studies show that the proposed method works well and faithfully reflects the true nature of the mediation process. By modeling mediation effect nonparametrically as a continuous function of time, our method provides a valuable tool to help researchers obtain a more complete understanding of the dynamic nature of the mediation process underlying psychological and behavioral phenomena. We also briefly discuss an alternative approach of using dynamic autoregressive mediation model to estimate the dynamic mediation effect. The computer code is provided to implement the proposed Bayesian dynamic mediation analysis. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Physics of ultrasonic wave propagation in bone and heart characterized using Bayesian parameter estimation

NASA Astrophysics Data System (ADS)

Anderson, Christian Carl

This Dissertation explores the physics underlying the propagation of ultrasonic waves in bone and in heart tissue through the use of Bayesian probability theory. Quantitative ultrasound is a noninvasive modality used for clinical detection, characterization, and evaluation of bone quality and cardiovascular disease. Approaches that extend the state of knowledge of the physics underpinning the interaction of ultrasound with inherently inhomogeneous and isotropic tissue have the potential to enhance its clinical utility. Simulations of fast and slow compressional wave propagation in cancellous bone were carried out to demonstrate the plausibility of a proposed explanation for the widely reported anomalous negative dispersion in cancellous bone. The results showed that negative dispersion could arise from analysis that proceeded under the assumption that the data consist of only a single ultrasonic wave, when in fact two overlapping and interfering waves are present. The confounding effect of overlapping fast and slow waves was addressed by applying Bayesian parameter estimation to simulated data, to experimental data acquired on bone-mimicking phantoms, and to data acquired in vitro on cancellous bone. The Bayesian approach successfully estimated the properties of the individual fast and slow waves even when they strongly overlapped in the acquired data. The Bayesian parameter estimation technique was further applied to an investigation of the anisotropy of ultrasonic properties in cancellous bone. The degree to which fast and slow waves overlap is partially determined by the angle of insonation of ultrasound relative to the predominant direction of trabecular orientation. In the past, studies of anisotropy have been limited by interference between fast and slow waves over a portion of the range of insonation angles. Bayesian analysis estimated attenuation, velocity, and amplitude parameters over the entire range of insonation angles, allowing a more complete characterization of anisotropy. A novel piecewise linear model for the cyclic variation of ultrasonic backscatter from myocardium was proposed. Models of cyclic variation for 100 type 2 diabetes patients and 43 normal control subjects were constructed using Bayesian parameter estimation. Parameters determined from the model, specifically rise time and slew rate, were found to be more reliable in differentiating between subject groups than the previously employed magnitude parameter.

On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood.

PubMed

Karabatsos, George

2018-06-01

This article introduces a Bayesian method for testing the axioms of additive conjoint measurement. The method is based on an importance sampling algorithm that performs likelihood-free, approximate Bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem. This new method improves upon previous methods because it provides an omnibus test of the entire hierarchy of cancellation axioms, beyond double cancellation. It does so while accounting for the posterior uncertainty that is inherent in the empirical orderings that are implied by these axioms, together. The new method is illustrated through a test of the cancellation axioms on a classic survey data set, and through the analysis of simulated data.

Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis

PubMed Central

Fancher, Chris M.; Han, Zhen; Levin, Igor; Page, Katharine; Reich, Brian J.; Smith, Ralph C.; Wilson, Alyson G.; Jones, Jacob L.

2016-01-01

A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method. PMID:27550221

Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes.

PubMed

Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D

2016-10-01

This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. © The Author 2016. Published by Oxford University Press.

Cross-view gait recognition using joint Bayesian

NASA Astrophysics Data System (ADS)

Li, Chao; Sun, Shouqian; Chen, Xiaoyu; Min, Xin

2017-07-01

Human gait, as a soft biometric, helps to recognize people by walking. To further improve the recognition performance under cross-view condition, we propose Joint Bayesian to model the view variance. We evaluated our prosed method with the largest population (OULP) dataset which makes our result reliable in a statically way. As a result, we confirmed our proposed method significantly outperformed state-of-the-art approaches for both identification and verification tasks. Finally, sensitivity analysis on the number of training subjects was conducted, we find Joint Bayesian could achieve competitive results even with a small subset of training subjects (100 subjects). For further comparison, experimental results, learning models, and test codes are available.

Bayesian model selection techniques as decision support for shaping a statistical analysis plan of a clinical trial: An example from a vertigo phase III study with longitudinal count data as primary endpoint

PubMed Central

2012-01-01

Background A statistical analysis plan (SAP) is a critical link between how a clinical trial is conducted and the clinical study report. To secure objective study results, regulatory bodies expect that the SAP will meet requirements in pre-specifying inferential analyses and other important statistical techniques. To write a good SAP for model-based sensitivity and ancillary analyses involves non-trivial decisions on and justification of many aspects of the chosen setting. In particular, trials with longitudinal count data as primary endpoints pose challenges for model choice and model validation. In the random effects setting, frequentist strategies for model assessment and model diagnosis are complex and not easily implemented and have several limitations. Therefore, it is of interest to explore Bayesian alternatives which provide the needed decision support to finalize a SAP. Methods We focus on generalized linear mixed models (GLMMs) for the analysis of longitudinal count data. A series of distributions with over- and under-dispersion is considered. Additionally, the structure of the variance components is modified. We perform a simulation study to investigate the discriminatory power of Bayesian tools for model criticism in different scenarios derived from the model setting. We apply the findings to the data from an open clinical trial on vertigo attacks. These data are seen as pilot data for an ongoing phase III trial. To fit GLMMs we use a novel Bayesian computational approach based on integrated nested Laplace approximations (INLAs). The INLA methodology enables the direct computation of leave-one-out predictive distributions. These distributions are crucial for Bayesian model assessment. We evaluate competing GLMMs for longitudinal count data according to the deviance information criterion (DIC) or probability integral transform (PIT), and by using proper scoring rules (e.g. the logarithmic score). Results The instruments under study provide excellent tools for preparing decisions within the SAP in a transparent way when structuring the primary analysis, sensitivity or ancillary analyses, and specific analyses for secondary endpoints. The mean logarithmic score and DIC discriminate well between different model scenarios. It becomes obvious that the naive choice of a conventional random effects Poisson model is often inappropriate for real-life count data. The findings are used to specify an appropriate mixed model employed in the sensitivity analyses of an ongoing phase III trial. Conclusions The proposed Bayesian methods are not only appealing for inference but notably provide a sophisticated insight into different aspects of model performance, such as forecast verification or calibration checks, and can be applied within the model selection process. The mean of the logarithmic score is a robust tool for model ranking and is not sensitive to sample size. Therefore, these Bayesian model selection techniques offer helpful decision support for shaping sensitivity and ancillary analyses in a statistical analysis plan of a clinical trial with longitudinal count data as the primary endpoint. PMID:22962944

Bayesian model selection techniques as decision support for shaping a statistical analysis plan of a clinical trial: an example from a vertigo phase III study with longitudinal count data as primary endpoint.

PubMed

Adrion, Christine; Mansmann, Ulrich

2012-09-10

A statistical analysis plan (SAP) is a critical link between how a clinical trial is conducted and the clinical study report. To secure objective study results, regulatory bodies expect that the SAP will meet requirements in pre-specifying inferential analyses and other important statistical techniques. To write a good SAP for model-based sensitivity and ancillary analyses involves non-trivial decisions on and justification of many aspects of the chosen setting. In particular, trials with longitudinal count data as primary endpoints pose challenges for model choice and model validation. In the random effects setting, frequentist strategies for model assessment and model diagnosis are complex and not easily implemented and have several limitations. Therefore, it is of interest to explore Bayesian alternatives which provide the needed decision support to finalize a SAP. We focus on generalized linear mixed models (GLMMs) for the analysis of longitudinal count data. A series of distributions with over- and under-dispersion is considered. Additionally, the structure of the variance components is modified. We perform a simulation study to investigate the discriminatory power of Bayesian tools for model criticism in different scenarios derived from the model setting. We apply the findings to the data from an open clinical trial on vertigo attacks. These data are seen as pilot data for an ongoing phase III trial. To fit GLMMs we use a novel Bayesian computational approach based on integrated nested Laplace approximations (INLAs). The INLA methodology enables the direct computation of leave-one-out predictive distributions. These distributions are crucial for Bayesian model assessment. We evaluate competing GLMMs for longitudinal count data according to the deviance information criterion (DIC) or probability integral transform (PIT), and by using proper scoring rules (e.g. the logarithmic score). The instruments under study provide excellent tools for preparing decisions within the SAP in a transparent way when structuring the primary analysis, sensitivity or ancillary analyses, and specific analyses for secondary endpoints. The mean logarithmic score and DIC discriminate well between different model scenarios. It becomes obvious that the naive choice of a conventional random effects Poisson model is often inappropriate for real-life count data. The findings are used to specify an appropriate mixed model employed in the sensitivity analyses of an ongoing phase III trial. The proposed Bayesian methods are not only appealing for inference but notably provide a sophisticated insight into different aspects of model performance, such as forecast verification or calibration checks, and can be applied within the model selection process. The mean of the logarithmic score is a robust tool for model ranking and is not sensitive to sample size. Therefore, these Bayesian model selection techniques offer helpful decision support for shaping sensitivity and ancillary analyses in a statistical analysis plan of a clinical trial with longitudinal count data as the primary endpoint.

[Bayesian approach for the cost-effectiveness evaluation of healthcare technologies].

PubMed

Berchialla, Paola; Gregori, Dario; Brunello, Franco; Veltri, Andrea; Petrinco, Michele; Pagano, Eva

2009-01-01

The development of Bayesian statistical methods for the assessment of the cost-effectiveness of health care technologies is reviewed. Although many studies adopt a frequentist approach, several authors have advocated the use of Bayesian methods in health economics. Emphasis has been placed on the advantages of the Bayesian approach, which include: (i) the ability to make more intuitive and meaningful inferences; (ii) the ability to tackle complex problems, such as allowing for the inclusion of patients who generate no cost, thanks to the availability of powerful computational algorithms; (iii) the importance of a full use of quantitative and structural prior information to produce realistic inferences. Much literature comparing the cost-effectiveness of two treatments is based on the incremental cost-effectiveness ratio. However, new methods are arising with the purpose of decision making. These methods are based on a net benefits approach. In the present context, the cost-effectiveness acceptability curves have been pointed out to be intrinsically Bayesian in their formulation. They plot the probability of a positive net benefit against the threshold cost of a unit increase in efficacy.A case study is presented in order to illustrate the Bayesian statistics in the cost-effectiveness analysis. Emphasis is placed on the cost-effectiveness acceptability curves. Advantages and disadvantages of the method described in this paper have been compared to frequentist methods and discussed.

Convergence analysis of surrogate-based methods for Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Yan, Liang; Zhang, Yuan-Xiang

2017-12-01

The major challenges in the Bayesian inverse problems arise from the need for repeated evaluations of the forward model, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. Many attempts at accelerating Bayesian inference have relied on surrogates for the forward model, typically constructed through repeated forward simulations that are performed in an offline phase. Although such approaches can be quite effective at reducing computation cost, there has been little analysis of the approximation on posterior inference. In this work, we prove error bounds on the Kullback-Leibler (KL) distance between the true posterior distribution and the approximation based on surrogate models. Our rigorous error analysis show that if the forward model approximation converges at certain rate in the prior-weighted L 2 norm, then the posterior distribution generated by the approximation converges to the true posterior at least two times faster in the KL sense. The error bound on the Hellinger distance is also provided. To provide concrete examples focusing on the use of the surrogate model based methods, we present an efficient technique for constructing stochastic surrogate models to accelerate the Bayesian inference approach. The Christoffel least squares algorithms, based on generalized polynomial chaos, are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. The numerical strategy and the predicted convergence rates are then demonstrated on the nonlinear inverse problems, involving the inference of parameters appearing in partial differential equations.

A novel Bayesian approach to acoustic emission data analysis.

PubMed

Agletdinov, E; Pomponi, E; Merson, D; Vinogradov, A

2016-12-01

Acoustic emission (AE) technique is a popular tool for materials characterization and non-destructive testing. Originating from the stochastic motion of defects in solids, AE is a random process by nature. The challenging problem arises whenever an attempt is made to identify specific points corresponding to the changes in the trends in the fluctuating AE time series. A general Bayesian framework is proposed for the analysis of AE time series, aiming at automated finding the breakpoints signaling a crossover in the dynamics of underlying AE sources. Copyright © 2016 Elsevier B.V. All rights reserved.

Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background

NASA Astrophysics Data System (ADS)

McEwen, J. D.; Feeney, S. M.; Peiris, H. V.; Wiaux, Y.; Ringeval, C.; Bouchet, F. R.

2017-12-01

Cosmic strings are a well-motivated extension to the standard cosmological model and could induce a subdominant component in the anisotropies of the cosmic microwave background (CMB), in addition to the standard inflationary component. The detection of strings, while observationally challenging, would provide a direct probe of physics at very high-energy scales. We develop a framework for cosmic string inference from observations of the CMB made over the celestial sphere, performing a Bayesian analysis in wavelet space where the string-induced CMB component has distinct statistical properties to the standard inflationary component. Our wavelet-Bayesian framework provides a principled approach to compute the posterior distribution of the string tension Gμ and the Bayesian evidence ratio comparing the string model to the standard inflationary model. Furthermore, we present a technique to recover an estimate of any string-induced CMB map embedded in observational data. Using Planck-like simulations, we demonstrate the application of our framework and evaluate its performance. The method is sensitive to Gμ ∼ 5 × 10-7 for Nambu-Goto string simulations that include an integrated Sachs-Wolfe contribution only and do not include any recombination effects, before any parameters of the analysis are optimized. The sensitivity of the method compares favourably with other techniques applied to the same simulations.

Statistical comparison of a hybrid approach with approximate and exact inference models for Fusion 2+

NASA Astrophysics Data System (ADS)

Lee, K. David; Wiesenfeld, Eric; Gelfand, Andrew

2007-04-01

One of the greatest challenges in modern combat is maintaining a high level of timely Situational Awareness (SA). In many situations, computational complexity and accuracy considerations make the development and deployment of real-time, high-level inference tools very difficult. An innovative hybrid framework that combines Bayesian inference, in the form of Bayesian Networks, and Possibility Theory, in the form of Fuzzy Logic systems, has recently been introduced to provide a rigorous framework for high-level inference. In previous research, the theoretical basis and benefits of the hybrid approach have been developed. However, lacking is a concrete experimental comparison of the hybrid framework with traditional fusion methods, to demonstrate and quantify this benefit. The goal of this research, therefore, is to provide a statistical analysis on the comparison of the accuracy and performance of hybrid network theory, with pure Bayesian and Fuzzy systems and an inexact Bayesian system approximated using Particle Filtering. To accomplish this task, domain specific models will be developed under these different theoretical approaches and then evaluated, via Monte Carlo Simulation, in comparison to situational ground truth to measure accuracy and fidelity. Following this, a rigorous statistical analysis of the performance results will be performed, to quantify the benefit of hybrid inference to other fusion tools.

Bayesian Analysis for Risk Assessment of Selected Medical Events in Support of the Integrated Medical Model Effort

NASA Technical Reports Server (NTRS)

Gilkey, Kelly M.; Myers, Jerry G.; McRae, Michael P.; Griffin, Elise A.; Kallrui, Aditya S.

2012-01-01

The Exploration Medical Capability project is creating a catalog of risk assessments using the Integrated Medical Model (IMM). The IMM is a software-based system intended to assist mission planners in preparing for spaceflight missions by helping them to make informed decisions about medical preparations and supplies needed for combating and treating various medical events using Probabilistic Risk Assessment. The objective is to use statistical analyses to inform the IMM decision tool with estimated probabilities of medical events occurring during an exploration mission. Because data regarding astronaut health are limited, Bayesian statistical analysis is used. Bayesian inference combines prior knowledge, such as data from the general U.S. population, the U.S. Submarine Force, or the analog astronaut population located at the NASA Johnson Space Center, with observed data for the medical condition of interest. The posterior results reflect the best evidence for specific medical events occurring in flight. Bayes theorem provides a formal mechanism for combining available observed data with data from similar studies to support the quantification process. The IMM team performed Bayesian updates on the following medical events: angina, appendicitis, atrial fibrillation, atrial flutter, dental abscess, dental caries, dental periodontal disease, gallstone disease, herpes zoster, renal stones, seizure, and stroke.

BaTMAn: Bayesian Technique for Multi-image Analysis

NASA Astrophysics Data System (ADS)

Casado, J.; Ascasibar, Y.; García-Benito, R.; Guidi, G.; Choudhury, O. S.; Bellocchi, E.; Sánchez, S. F.; Díaz, A. I.

2016-12-01

Bayesian Technique for Multi-image Analysis (BaTMAn) characterizes any astronomical dataset containing spatial information and performs a tessellation based on the measurements and errors provided as input. The algorithm iteratively merges spatial elements as long as they are statistically consistent with carrying the same information (i.e. identical signal within the errors). The output segmentations successfully adapt to the underlying spatial structure, regardless of its morphology and/or the statistical properties of the noise. BaTMAn identifies (and keeps) all the statistically-significant information contained in the input multi-image (e.g. an IFS datacube). The main aim of the algorithm is to characterize spatially-resolved data prior to their analysis.

A comparison of two worlds: How does Bayes hold up to the status quo for the analysis of clinical trials?

PubMed

Pressman, Alice R; Avins, Andrew L; Hubbard, Alan; Satariano, William A

2011-07-01

There is a paucity of literature comparing Bayesian analytic techniques with traditional approaches for analyzing clinical trials using real trial data. We compared Bayesian and frequentist group sequential methods using data from two published clinical trials. We chose two widely accepted frequentist rules, O'Brien-Fleming and Lan-DeMets, and conjugate Bayesian priors. Using the nonparametric bootstrap, we estimated a sampling distribution of stopping times for each method. Because current practice dictates the preservation of an experiment-wise false positive rate (Type I error), we approximated these error rates for our Bayesian and frequentist analyses with the posterior probability of detecting an effect in a simulated null sample. Thus for the data-generated distribution represented by these trials, we were able to compare the relative performance of these techniques. No final outcomes differed from those of the original trials. However, the timing of trial termination differed substantially by method and varied by trial. For one trial, group sequential designs of either type dictated early stopping of the study. In the other, stopping times were dependent upon the choice of spending function and prior distribution. Results indicate that trialists ought to consider Bayesian methods in addition to traditional approaches for analysis of clinical trials. Though findings from this small sample did not demonstrate either method to consistently outperform the other, they did suggest the need to replicate these comparisons using data from varied clinical trials in order to determine the conditions under which the different methods would be most efficient. Copyright © 2011 Elsevier Inc. All rights reserved.

A comparison of two worlds: How does Bayes hold up to the status quo for the analysis of clinical trials?

PubMed Central

Pressman, Alice R.; Avins, Andrew L.; Hubbard, Alan; Satariano, William A.

2014-01-01

Background There is a paucity of literature comparing Bayesian analytic techniques with traditional approaches for analyzing clinical trials using real trial data. Methods We compared Bayesian and frequentist group sequential methods using data from two published clinical trials. We chose two widely accepted frequentist rules, O'Brien–Fleming and Lan–DeMets, and conjugate Bayesian priors. Using the nonparametric bootstrap, we estimated a sampling distribution of stopping times for each method. Because current practice dictates the preservation of an experiment-wise false positive rate (Type I error), we approximated these error rates for our Bayesian and frequentist analyses with the posterior probability of detecting an effect in a simulated null sample. Thus for the data-generated distribution represented by these trials, we were able to compare the relative performance of these techniques. Results No final outcomes differed from those of the original trials. However, the timing of trial termination differed substantially by method and varied by trial. For one trial, group sequential designs of either type dictated early stopping of the study. In the other, stopping times were dependent upon the choice of spending function and prior distribution. Conclusions Results indicate that trialists ought to consider Bayesian methods in addition to traditional approaches for analysis of clinical trials. Though findings from this small sample did not demonstrate either method to consistently outperform the other, they did suggest the need to replicate these comparisons using data from varied clinical trials in order to determine the conditions under which the different methods would be most efficient. PMID:21453792

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

PubMed

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

2009-01-01

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

Testing adaptive toolbox models: a Bayesian hierarchical approach.

PubMed

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

2013-01-01

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

Bayesian networks in neuroscience: a survey.

PubMed

Bielza, Concha; Larrañaga, Pedro

2014-01-01

Bayesian networks are a type of probabilistic graphical models lie at the intersection between statistics and machine learning. They have been shown to be powerful tools to encode dependence relationships among the variables of a domain under uncertainty. Thanks to their generality, Bayesian networks can accommodate continuous and discrete variables, as well as temporal processes. In this paper we review Bayesian networks and how they can be learned automatically from data by means of structure learning algorithms. Also, we examine how a user can take advantage of these networks for reasoning by exact or approximate inference algorithms that propagate the given evidence through the graphical structure. Despite their applicability in many fields, they have been little used in neuroscience, where they have focused on specific problems, like functional connectivity analysis from neuroimaging data. Here we survey key research in neuroscience where Bayesian networks have been used with different aims: discover associations between variables, perform probabilistic reasoning over the model, and classify new observations with and without supervision. The networks are learned from data of any kind-morphological, electrophysiological, -omics and neuroimaging-, thereby broadening the scope-molecular, cellular, structural, functional, cognitive and medical- of the brain aspects to be studied.

Rediscovery of Good-Turing estimators via Bayesian nonparametrics.

PubMed

Favaro, Stefano; Nipoti, Bernardo; Teh, Yee Whye

2016-03-01

The problem of estimating discovery probabilities originated in the context of statistical ecology, and in recent years it has become popular due to its frequent appearance in challenging applications arising in genetics, bioinformatics, linguistics, designs of experiments, machine learning, etc. A full range of statistical approaches, parametric and nonparametric as well as frequentist and Bayesian, has been proposed for estimating discovery probabilities. In this article, we investigate the relationships between the celebrated Good-Turing approach, which is a frequentist nonparametric approach developed in the 1940s, and a Bayesian nonparametric approach recently introduced in the literature. Specifically, under the assumption of a two parameter Poisson-Dirichlet prior, we show that Bayesian nonparametric estimators of discovery probabilities are asymptotically equivalent, for a large sample size, to suitably smoothed Good-Turing estimators. As a by-product of this result, we introduce and investigate a methodology for deriving exact and asymptotic credible intervals to be associated with the Bayesian nonparametric estimators of discovery probabilities. The proposed methodology is illustrated through a comprehensive simulation study and the analysis of Expressed Sequence Tags data generated by sequencing a benchmark complementary DNA library. © 2015, The International Biometric Society.

Bayesian networks in neuroscience: a survey

PubMed Central

Bielza, Concha; Larrañaga, Pedro

2014-01-01

Bayesian networks are a type of probabilistic graphical models lie at the intersection between statistics and machine learning. They have been shown to be powerful tools to encode dependence relationships among the variables of a domain under uncertainty. Thanks to their generality, Bayesian networks can accommodate continuous and discrete variables, as well as temporal processes. In this paper we review Bayesian networks and how they can be learned automatically from data by means of structure learning algorithms. Also, we examine how a user can take advantage of these networks for reasoning by exact or approximate inference algorithms that propagate the given evidence through the graphical structure. Despite their applicability in many fields, they have been little used in neuroscience, where they have focused on specific problems, like functional connectivity analysis from neuroimaging data. Here we survey key research in neuroscience where Bayesian networks have been used with different aims: discover associations between variables, perform probabilistic reasoning over the model, and classify new observations with and without supervision. The networks are learned from data of any kind–morphological, electrophysiological, -omics and neuroimaging–, thereby broadening the scope–molecular, cellular, structural, functional, cognitive and medical– of the brain aspects to be studied. PMID:25360109

MapReduce Based Parallel Bayesian Network for Manufacturing Quality Control

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

A Bayesian sequential design with adaptive randomization for 2-sided hypothesis test.

PubMed

Yu, Qingzhao; Zhu, Lin; Zhu, Han

2017-11-01

Bayesian sequential and adaptive randomization designs are gaining popularity in clinical trials thanks to their potentials to reduce the number of required participants and save resources. We propose a Bayesian sequential design with adaptive randomization rates so as to more efficiently attribute newly recruited patients to different treatment arms. In this paper, we consider 2-arm clinical trials. Patients are allocated to the 2 arms with a randomization rate to achieve minimum variance for the test statistic. Algorithms are presented to calculate the optimal randomization rate, critical values, and power for the proposed design. Sensitivity analysis is implemented to check the influence on design by changing the prior distributions. Simulation studies are applied to compare the proposed method and traditional methods in terms of power and actual sample sizes. Simulations show that, when total sample size is fixed, the proposed design can obtain greater power and/or cost smaller actual sample size than the traditional Bayesian sequential design. Finally, we apply the proposed method to a real data set and compare the results with the Bayesian sequential design without adaptive randomization in terms of sample sizes. The proposed method can further reduce required sample size. Copyright © 2017 John Wiley & Sons, Ltd.

Analysis of the Bayesian Cramér-Rao lower bound in astrometry. Studying the impact of prior information in the location of an object

NASA Astrophysics Data System (ADS)

Echeverria, Alex; Silva, Jorge F.; Mendez, Rene A.; Orchard, Marcos

2016-10-01

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims: We analyze bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (I.e., the position is a random variable) from observations that are statistically dependent on the position. Methods: We characterize the Bayesian Cramér-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background. Results: We quantify and analyze the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions: The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.

Which is best for osteoporotic vertebral compression fractures: balloon kyphoplasty, percutaneous vertebroplasty or non-surgical treatment? A study protocol for a Bayesian network meta-analysis

PubMed Central

Kan, Shun-Li; Yuan, Zhi-Fang; Chen, Ling-Xiao; Sun, Jing-Cheng; Ning, Guang-Zhi; Feng, Shi-Qing

2017-01-01

Introduction Osteoporotic vertebral compression fractures (OVCFs) commonly cause both acute and chronic back pain, substantial spinal deformity, functional disability and decreased quality of life and increase the risk of future vertebral fractures and mortality. Percutaneous vertebroplasty (PVP), balloon kyphoplasty (BK) and non-surgical treatment (NST) are mostly used for the treatment of OVCFs. However, which treatment is preferred is unknown. The purpose of this study is to comprehensively review the literature and ascertain the relative efficacy and safety of BK, PVP and NST for patients with OVCFs using a Bayesian network meta-analysis. Methods and analysis We will comprehensively search PubMed, EMBASE and the Cochrane Central Register of Controlled Trials, to include randomided controlled trials that compare BK, PVP or NST for treating OVCFs. The risk of bias for individual studies will be assessed according to the Cochrane Handbook. Bayesian network meta-analysis will be performed to compare the efficacy and safety of BK, PVP and NST. The quality of evidence will be evaluated by GRADE. Ethics and dissemination Ethical approval and patient consent are not required since this study is a meta-analysis based on published studies. The results of this network meta-analysis will be submitted to a peer-reviewed journal for publication. PROSPERO registration number CRD42016039452; Pre-results. PMID:28093431

A Bayesian account of quantum histories

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

Marlow, Thomas

2006-05-15

We investigate whether quantum history theories can be consistent with Bayesian reasoning and whether such an analysis helps clarify the interpretation of such theories. First, we summarise and extend recent work categorising two different approaches to formalising multi-time measurements in quantum theory. The standard approach consists of describing an ordered series of measurements in terms of history propositions with non-additive 'probabilities.' The non-standard approach consists of defining multi-time measurements to consist of sets of exclusive and exhaustive history propositions and recovering the single-time exclusivity of results when discussing single-time history propositions. We analyse whether such history propositions can be consistentmore » with Bayes' rule. We show that certain class of histories are given a natural Bayesian interpretation, namely, the linearly positive histories originally introduced by Goldstein and Page. Thus, we argue that this gives a certain amount of interpretational clarity to the non-standard approach. We also attempt a justification of our analysis using Cox's axioms of probability theory.« less

Online Dectection and Modeling of Safety Boundaries for Aerospace Application Using Bayesian Statistics

NASA Technical Reports Server (NTRS)

He, Yuning

2015-01-01

The behavior of complex aerospace systems is governed by numerous parameters. For safety analysis it is important to understand how the system behaves with respect to these parameter values. In particular, understanding the boundaries between safe and unsafe regions is of major importance. In this paper, we describe a hierarchical Bayesian statistical modeling approach for the online detection and characterization of such boundaries. Our method for classification with active learning uses a particle filter-based model and a boundary-aware metric for best performance. From a library of candidate shapes incorporated with domain expert knowledge, the location and parameters of the boundaries are estimated using advanced Bayesian modeling techniques. The results of our boundary analysis are then provided in a form understandable by the domain expert. We illustrate our approach using a simulation model of a NASA neuro-adaptive flight control system, as well as a system for the detection of separation violations in the terminal airspace.

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

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

PubMed Central

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

2016-01-01

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

Experimentally Derived δ13C and δ15N Discrimination Factors for Gray Wolves and the Impact of Prior Information in Bayesian Mixing Models

PubMed Central

Bucci, Melanie E.; Callahan, Peggy; Koprowski, John L.; Polfus, Jean L.; Krausman, Paul R.

2015-01-01

Stable isotope analysis of diet has become a common tool in conservation research. However, the multiple sources of uncertainty inherent in this analysis framework involve consequences that have not been thoroughly addressed. Uncertainty arises from the choice of trophic discrimination factors, and for Bayesian stable isotope mixing models (SIMMs), the specification of prior information; the combined effect of these aspects has not been explicitly tested. We used a captive feeding study of gray wolves (Canis lupus) to determine the first experimentally-derived trophic discrimination factors of C and N for this large carnivore of broad conservation interest. Using the estimated diet in our controlled system and data from a published study on wild wolves and their prey in Montana, USA, we then investigated the simultaneous effect of discrimination factors and prior information on diet reconstruction with Bayesian SIMMs. Discrimination factors for gray wolves and their prey were 1.97‰ for δ13C and 3.04‰ for δ15N. Specifying wolf discrimination factors, as opposed to the commonly used red fox (Vulpes vulpes) factors, made little practical difference to estimates of wolf diet, but prior information had a strong effect on bias, precision, and accuracy of posterior estimates. Without specifying prior information in our Bayesian SIMM, it was not possible to produce SIMM posteriors statistically similar to the estimated diet in our controlled study or the diet of wild wolves. Our study demonstrates the critical effect of prior information on estimates of animal diets using Bayesian SIMMs, and suggests species-specific trophic discrimination factors are of secondary importance. When using stable isotope analysis to inform conservation decisions researchers should understand the limits of their data. It may be difficult to obtain useful information from SIMMs if informative priors are omitted and species-specific discrimination factors are unavailable. PMID:25803664

Experimentally derived δ¹³C and δ¹⁵N discrimination factors for gray wolves and the impact of prior information in Bayesian mixing models.

PubMed

Derbridge, Jonathan J; Merkle, Jerod A; Bucci, Melanie E; Callahan, Peggy; Koprowski, John L; Polfus, Jean L; Krausman, Paul R

2015-01-01

Stable isotope analysis of diet has become a common tool in conservation research. However, the multiple sources of uncertainty inherent in this analysis framework involve consequences that have not been thoroughly addressed. Uncertainty arises from the choice of trophic discrimination factors, and for Bayesian stable isotope mixing models (SIMMs), the specification of prior information; the combined effect of these aspects has not been explicitly tested. We used a captive feeding study of gray wolves (Canis lupus) to determine the first experimentally-derived trophic discrimination factors of C and N for this large carnivore of broad conservation interest. Using the estimated diet in our controlled system and data from a published study on wild wolves and their prey in Montana, USA, we then investigated the simultaneous effect of discrimination factors and prior information on diet reconstruction with Bayesian SIMMs. Discrimination factors for gray wolves and their prey were 1.97‰ for δ13C and 3.04‰ for δ15N. Specifying wolf discrimination factors, as opposed to the commonly used red fox (Vulpes vulpes) factors, made little practical difference to estimates of wolf diet, but prior information had a strong effect on bias, precision, and accuracy of posterior estimates. Without specifying prior information in our Bayesian SIMM, it was not possible to produce SIMM posteriors statistically similar to the estimated diet in our controlled study or the diet of wild wolves. Our study demonstrates the critical effect of prior information on estimates of animal diets using Bayesian SIMMs, and suggests species-specific trophic discrimination factors are of secondary importance. When using stable isotope analysis to inform conservation decisions researchers should understand the limits of their data. It may be difficult to obtain useful information from SIMMs if informative priors are omitted and species-specific discrimination factors are unavailable.

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

PubMed

Beach, Jeremy; Burstyn, Igor; Cherry, Nicola

2012-07-01

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

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2014-01-01

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

Sparse Bayesian Learning for Identifying Imaging Biomarkers in AD Prediction

PubMed Central

Shen, Li; Qi, Yuan; Kim, Sungeun; Nho, Kwangsik; Wan, Jing; Risacher, Shannon L.; Saykin, Andrew J.

2010-01-01

We apply sparse Bayesian learning methods, automatic relevance determination (ARD) and predictive ARD (PARD), to Alzheimer’s disease (AD) classification to make accurate prediction and identify critical imaging markers relevant to AD at the same time. ARD is one of the most successful Bayesian feature selection methods. PARD is a powerful Bayesian feature selection method, and provides sparse models that is easy to interpret. PARD selects the model with the best estimate of the predictive performance instead of choosing the one with the largest marginal model likelihood. Comparative study with support vector machine (SVM) shows that ARD/PARD in general outperform SVM in terms of prediction accuracy. Additional comparison with surface-based general linear model (GLM) analysis shows that regions with strongest signals are identified by both GLM and ARD/PARD. While GLM P-map returns significant regions all over the cortex, ARD/PARD provide a small number of relevant and meaningful imaging markers with predictive power, including both cortical and subcortical measures. PMID:20879451

A conceptual model for site-level ecology of the giant gartersnake (Thamnophis gigas) in the Sacramento Valley, California

USGS Publications Warehouse

Halstead, Brian J.; Wylie, Glenn D.; Casazza, Michael L.; Hansen, Eric C.; Scherer, Rick D.; Patterson, Laura C.

2015-08-14

Bayesian networks further provide a clear visual display of the model that facilitates understanding among various stakeholders (Marcot and others, 2001; Uusitalo , 2007). Empirical data and expert judgment can be combined, as continuous or categorical variables, to update knowledge about the system (Marcot and others, 2001; Uusitalo , 2007). Importantly, Bayesian network models allow inference from causes to consequences, but also from consequences to causes, so that data can inform the states of nodes (values of different random variables) in either direction (Marcot and others, 2001; Uusitalo , 2007). Because they can incorporate both decision nodes that represent management actions and utility nodes that quantify the costs and benefits of outcomes, Bayesian networks are ideally suited to risk analysis and adaptive management (Nyberg and others, 2006; Howes and others, 2010). Thus, Bayesian network models are useful in situations where empirical data are not available, such as questions concerning the responses of giant gartersnakes to management.

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

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

2016-08-01

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

Improved Accuracy Using Recursive Bayesian Estimation Based Language Model Fusion in ERP-Based BCI Typing Systems

PubMed Central

Orhan, U.; Erdogmus, D.; Roark, B.; Oken, B.; Purwar, S.; Hild, K. E.; Fowler, A.; Fried-Oken, M.

2013-01-01

RSVP Keyboard™ is an electroencephalography (EEG) based brain computer interface (BCI) typing system, designed as an assistive technology for the communication needs of people with locked-in syndrome (LIS). It relies on rapid serial visual presentation (RSVP) and does not require precise eye gaze control. Existing BCI typing systems which uses event related potentials (ERP) in EEG suffer from low accuracy due to low signal-to-noise ratio. Henceforth, RSVP Keyboard™ utilizes a context based decision making via incorporating a language model, to improve the accuracy of letter decisions. To further improve the contributions of the language model, we propose recursive Bayesian estimation, which relies on non-committing string decisions, and conduct an offline analysis, which compares it with the existing naïve Bayesian fusion approach. The results indicate the superiority of the recursive Bayesian fusion and in the next generation of RSVP Keyboard™ we plan to incorporate this new approach. PMID:23366432

Bayesian analysis of caustic-crossing microlensing events

NASA Astrophysics Data System (ADS)

Cassan, A.; Horne, K.; Kains, N.; Tsapras, Y.; Browne, P.

2010-06-01

Aims: Caustic-crossing binary-lens microlensing events are important anomalous events because they are capable of detecting an extrasolar planet companion orbiting the lens star. Fast and robust modelling methods are thus of prime interest in helping to decide whether a planet is detected by an event. Cassan introduced a new set of parameters to model binary-lens events, which are closely related to properties of the light curve. In this work, we explain how Bayesian priors can be added to this framework, and investigate on interesting options. Methods: We develop a mathematical formulation that allows us to compute analytically the priors on the new parameters, given some previous knowledge about other physical quantities. We explicitly compute the priors for a number of interesting cases, and show how this can be implemented in a fully Bayesian, Markov chain Monte Carlo algorithm. Results: Using Bayesian priors can accelerate microlens fitting codes by reducing the time spent considering physically implausible models, and helps us to discriminate between alternative models based on the physical plausibility of their parameters.

Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions.

PubMed

Vernon, Ian; Liu, Junli; Goldstein, Michael; Rowe, James; Topping, Jen; Lindsey, Keith

2018-01-02

Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embeded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty. The approach is demonstrated via application to a model of hormonal crosstalk in Arabidopsis root development, which has 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches between model output and observed trend data. The multiple insights into the model's structure that this analysis provides are discussed. The methodology is applied to a second related model, and the biological consequences of the resulting comparison, including the evaluation of gene functions, are described. Bayesian uncertainty analysis for complex models using both emulators and history matching is shown to be a powerful technique that can greatly aid the study of a large class of systems biology models. It both provides insight into model behaviour and identifies the sets of rate parameters of interest.

Analysis of statistical and standard algorithms for detecting muscle onset with surface electromyography

PubMed Central

Tweedell, Andrew J.; Haynes, Courtney A.

2017-01-01

The timing of muscle activity is a commonly applied analytic method to understand how the nervous system controls movement. This study systematically evaluates six classes of standard and statistical algorithms to determine muscle onset in both experimental surface electromyography (EMG) and simulated EMG with a known onset time. Eighteen participants had EMG collected from the biceps brachii and vastus lateralis while performing a biceps curl or knee extension, respectively. Three established methods and three statistical methods for EMG onset were evaluated. Linear envelope, Teager-Kaiser energy operator + linear envelope and sample entropy were the established methods evaluated while general time series mean/variance, sequential and batch processing of parametric and nonparametric tools, and Bayesian changepoint analysis were the statistical techniques used. Visual EMG onset (experimental data) and objective EMG onset (simulated data) were compared with algorithmic EMG onset via root mean square error and linear regression models for stepwise elimination of inferior algorithms. The top algorithms for both data types were analyzed for their mean agreement with the gold standard onset and evaluation of 95% confidence intervals. The top algorithms were all Bayesian changepoint analysis iterations where the parameter of the prior (p0) was zero. The best performing Bayesian algorithms were p0 = 0 and a posterior probability for onset determination at 60–90%. While existing algorithms performed reasonably, the Bayesian changepoint analysis methodology provides greater reliability and accuracy when determining the singular onset of EMG activity in a time series. Further research is needed to determine if this class of algorithms perform equally well when the time series has multiple bursts of muscle activity. PMID:28489897

A Bayesian goodness of fit test and semiparametric generalization of logistic regression with measurement data.

PubMed

Schörgendorfer, Angela; Branscum, Adam J; Hanson, Timothy E

2013-06-01

Logistic regression is a popular tool for risk analysis in medical and population health science. With continuous response data, it is common to create a dichotomous outcome for logistic regression analysis by specifying a threshold for positivity. Fitting a linear regression to the nondichotomized response variable assuming a logistic sampling model for the data has been empirically shown to yield more efficient estimates of odds ratios than ordinary logistic regression of the dichotomized endpoint. We illustrate that risk inference is not robust to departures from the parametric logistic distribution. Moreover, the model assumption of proportional odds is generally not satisfied when the condition of a logistic distribution for the data is violated, leading to biased inference from a parametric logistic analysis. We develop novel Bayesian semiparametric methodology for testing goodness of fit of parametric logistic regression with continuous measurement data. The testing procedures hold for any cutoff threshold and our approach simultaneously provides the ability to perform semiparametric risk estimation. Bayes factors are calculated using the Savage-Dickey ratio for testing the null hypothesis of logistic regression versus a semiparametric generalization. We propose a fully Bayesian and a computationally efficient empirical Bayesian approach to testing, and we present methods for semiparametric estimation of risks, relative risks, and odds ratios when parametric logistic regression fails. Theoretical results establish the consistency of the empirical Bayes test. Results from simulated data show that the proposed approach provides accurate inference irrespective of whether parametric assumptions hold or not. Evaluation of risk factors for obesity shows that different inferences are derived from an analysis of a real data set when deviations from a logistic distribution are permissible in a flexible semiparametric framework. © 2013, The International Biometric Society.

Bayesian paradox in homeland security and homeland defense

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Forrester, Thomas; Wang, Wenjian

2011-06-01

In this paper we discuss a rather surprising result of Bayesian inference analysis: performance of a broad variety of sensors depends not only on a sensor system itself, but also on CONOPS parameters in such a way that even an excellent sensor system can perform poorly if absolute probabilities of a threat (target) are lower than a false alarm probability. This result, which we call Bayesian paradox, holds not only for binary sensors as discussed in the lead author's previous papers, but also for a more general class of multi-target sensors, discussed also in this paper. Examples include: ATR (automatic target recognition), luggage X-ray inspection for explosives, medical diagnostics, car engine diagnostics, judicial decisions, and many other issues.

A Bayesian modification to the Jelinski-Moranda software reliability growth model

NASA Technical Reports Server (NTRS)

Littlewood, B.; Sofer, A.

1983-01-01

The Jelinski-Moranda (JM) model for software reliability was examined. It is suggested that a major reason for the poor results given by this model is the poor performance of the maximum likelihood method (ML) of parameter estimation. A reparameterization and Bayesian analysis, involving a slight modelling change, are proposed. It is shown that this new Bayesian-Jelinski-Moranda model (BJM) is mathematically quite tractable, and several metrics of interest to practitioners are obtained. The BJM and JM models are compared by using several sets of real software failure data collected and in all cases the BJM model gives superior reliability predictions. A change in the assumption which underlay both models to present the debugging process more accurately is discussed.

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

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

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

2016-07-01

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

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

A Bayesian alternative for multi-objective ecohydrological model specification

NASA Astrophysics Data System (ADS)

Tang, Yating; Marshall, Lucy; Sharma, Ashish; Ajami, Hoori

2018-01-01

Recent studies have identified the importance of vegetation processes in terrestrial hydrologic systems. Process-based ecohydrological models combine hydrological, physical, biochemical and ecological processes of the catchments, and as such are generally more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov chain Monte Carlo (MCMC) techniques. The Bayesian approach offers an appealing alternative to traditional multi-objective hydrologic model calibrations by defining proper prior distributions that can be considered analogous to the ad-hoc weighting often prescribed in multi-objective calibration. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological modeling framework based on a traditional Pareto-based model calibration technique. In our study, a Pareto-based multi-objective optimization and a formal Bayesian framework are implemented in a conceptual ecohydrological model that combines a hydrological model (HYMOD) and a modified Bucket Grassland Model (BGM). Simulations focused on one objective (streamflow/LAI) and multiple objectives (streamflow and LAI) with different emphasis defined via the prior distribution of the model error parameters. Results show more reliable outputs for both predicted streamflow and LAI using Bayesian multi-objective calibration with specified prior distributions for error parameters based on results from the Pareto front in the ecohydrological modeling. The methodology implemented here provides insight into the usefulness of multiobjective Bayesian calibration for ecohydrologic systems and the importance of appropriate prior distributions in such approaches.

The Importance of Proving the Null

PubMed Central

Gallistel, C. R.

2010-01-01

Null hypotheses are simple, precise, and theoretically important. Conventional statistical analysis cannot support them; Bayesian analysis can. The challenge in a Bayesian analysis is to formulate a suitably vague alternative, because the vaguer the alternative is (the more it spreads out the unit mass of prior probability), the more the null is favored. A general solution is a sensitivity analysis: Compute the odds for or against the null as a function of the limit(s) on the vagueness of the alternative. If the odds on the null approach 1 from above as the hypothesized maximum size of the possible effect approaches 0, then the data favor the null over any vaguer alternative to it. The simple computations and the intuitive graphic representation of the analysis are illustrated by the analysis of diverse examples from the current literature. They pose 3 common experimental questions: (a) Are 2 means the same? (b) Is performance at chance? (c) Are factors additive? PMID:19348549

A Flexible Hierarchical Bayesian Modeling Technique for Risk Analysis of Major Accidents.

PubMed

Yu, Hongyang; Khan, Faisal; Veitch, Brian

2017-09-01

Safety analysis of rare events with potentially catastrophic consequences is challenged by data scarcity and uncertainty. Traditional causation-based approaches, such as fault tree and event tree (used to model rare event), suffer from a number of weaknesses. These include the static structure of the event causation, lack of event occurrence data, and need for reliable prior information. In this study, a new hierarchical Bayesian modeling based technique is proposed to overcome these drawbacks. The proposed technique can be used as a flexible technique for risk analysis of major accidents. It enables both forward and backward analysis in quantitative reasoning and the treatment of interdependence among the model parameters. Source-to-source variability in data sources is also taken into account through a robust probabilistic safety analysis. The applicability of the proposed technique has been demonstrated through a case study in marine and offshore industry. © 2017 Society for Risk Analysis.

Integrated Data Analysis for Fusion: A Bayesian Tutorial for Fusion Diagnosticians

NASA Astrophysics Data System (ADS)

Dinklage, Andreas; Dreier, Heiko; Fischer, Rainer; Gori, Silvio; Preuss, Roland; Toussaint, Udo von

2008-03-01

Integrated Data Analysis (IDA) offers a unified way of combining information relevant to fusion experiments. Thereby, IDA meets with typical issues arising in fusion data analysis. In IDA, all information is consistently formulated as probability density functions quantifying uncertainties in the analysis within the Bayesian probability theory. For a single diagnostic, IDA allows the identification of faulty measurements and improvements in the setup. For a set of diagnostics, IDA gives joint error distributions allowing the comparison and integration of different diagnostics results. Validation of physics models can be performed by model comparison techniques. Typical data analysis applications benefit from IDA capabilities of nonlinear error propagation, the inclusion of systematic effects and the comparison of different physics models. Applications range from outlier detection, background discrimination, model assessment and design of diagnostics. In order to cope with next step fusion device requirements, appropriate techniques are explored for fast analysis applications.

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

PubMed

Shen, Y; Cooper, G F

2010-01-01

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

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

PubMed Central

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

2017-01-01

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

Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series.

PubMed

Bruce, Scott A; Hall, Martica H; Buysse, Daniel J; Krafty, Robert T

2018-03-01

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely ignored due to a lack of methods that can assess the changing nature of the relationship through time. This article introduces a method for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates, which we refer to as conditional adaptive Bayesian spectrum analysis (CABS). The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. CABS is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The proposed methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse. © 2017, The International Biometric Society.

Computational statistics using the Bayesian Inference Engine

NASA Astrophysics Data System (ADS)

Weinberg, Martin D.

2013-09-01

This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimized software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organize and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasizes hybrid tempered Markov chain Monte Carlo schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE implements a full persistence or serialization system that stores the full byte-level image of the running inference and previously characterized posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU General Public License.

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

PubMed

Lefèvre, Thomas; Lepresle, Aude; Chariot, Patrick

2015-09-01

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

Bayesian imperfect information analysis for clinical recurrent data

PubMed Central

Chang, Chih-Kuang; Chang, Chi-Chang

2015-01-01

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

Deep Learning with Hierarchical Convolutional Factor Analysis

PubMed Central

Chen, Bo; Polatkan, Gungor; Sapiro, Guillermo; Blei, David; Dunson, David; Carin, Lawrence

2013-01-01

Unsupervised multi-layered (“deep”) models are considered for general data, with a particular focus on imagery. The model is represented using a hierarchical convolutional factor-analysis construction, with sparse factor loadings and scores. The computation of layer-dependent model parameters is implemented within a Bayesian setting, employing a Gibbs sampler and variational Bayesian (VB) analysis, that explicitly exploit the convolutional nature of the expansion. In order to address large-scale and streaming data, an online version of VB is also developed. The number of basis functions or dictionary elements at each layer is inferred from the data, based on a beta-Bernoulli implementation of the Indian buffet process. Example results are presented for several image-processing applications, with comparisons to related models in the literature. PMID:23787342

Bayesian estimation of self-similarity exponent

NASA Astrophysics Data System (ADS)

Makarava, Natallia; Benmehdi, Sabah; Holschneider, Matthias

2011-08-01

In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.

Bayesian analysis of physiologically based toxicokinetic and toxicodynamic models.

PubMed

Hack, C Eric

2006-04-17

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

Extraordinary Claims Require Extraordinary Evidence: The Case of Non-Local Perception, a Classical and Bayesian Review of Evidences

PubMed Central

Tressoldi, Patrizio E.

2011-01-01

Starting from the famous phrase “extraordinary claims require extraordinary evidence,” we will present the evidence supporting the concept that human visual perception may have non-local properties, in other words, that it may operate beyond the space and time constraints of sensory organs, in order to discuss which criteria can be used to define evidence as extraordinary. This evidence has been obtained from seven databases which are related to six different protocols used to test the reality and the functioning of non-local perception, analyzed using both a frequentist and a new Bayesian meta-analysis statistical procedure. According to a frequentist meta-analysis, the null hypothesis can be rejected for all six protocols even if the effect sizes range from 0.007 to 0.28. According to Bayesian meta-analysis, the Bayes factors provides strong evidence to support the alternative hypothesis (H1) over the null hypothesis (H0), but only for three out of the six protocols. We will discuss whether quantitative psychology can contribute to defining the criteria for the acceptance of new scientific ideas in order to avoid the inconclusive controversies between supporters and opponents. PMID:21713069

SOMBI: Bayesian identification of parameter relations in unstructured cosmological data

NASA Astrophysics Data System (ADS)

Frank, Philipp; Jasche, Jens; Enßlin, Torsten A.

2016-11-01

This work describes the implementation and application of a correlation determination method based on self organizing maps and Bayesian inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters in unstructured cosmological or astrophysical surveys by automatically identifying data clusters in high-dimensional datasets via the self organizing map neural network algorithm. Parameter relations are then revealed by means of a Bayesian inference within respective identified data clusters. Specifically such relations are assumed to be parametrized as a polynomial of unknown order. The Bayesian approach results in a posterior probability distribution function for respective polynomial coefficients. To decide which polynomial order suffices to describe correlation structures in data, we include a method for model selection, the Bayesian information criterion, to the analysis. The performance of the SOMBI algorithm is tested with mock data. As illustration we also provide applications of our method to cosmological data. In particular, we present results of a correlation analysis between galaxy and active galactic nucleus (AGN) properties provided by the SDSS catalog with the cosmic large-scale-structure (LSS). The results indicate that the combined galaxy and LSS dataset indeed is clustered into several sub-samples of data with different average properties (for example different stellar masses or web-type classifications). The majority of data clusters appear to have a similar correlation structure between galaxy properties and the LSS. In particular we revealed a positive and linear dependency between the stellar mass, the absolute magnitude and the color of a galaxy with the corresponding cosmic density field. A remaining subset of data shows inverted correlations, which might be an artifact of non-linear redshift distortions.

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.

Evidence cross-validation and Bayesian inference of MAST plasma equilibria

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

Nessi, G. T. von; Hole, M. J.; Svensson, J.

2012-01-15

In this paper, current profiles for plasma discharges on the mega-ampere spherical tokamak are directly calculated from pickup coil, flux loop, and motional-Stark effect observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart's law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the joint-European tokamak [Svensson and Werner,Plasma Phys. Controlledmore » Fusion 50(8), 085002 (2008)]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes' formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable a good agreement between Bayesian inference of the last-closed flux-surface with other corroborating data, such as that from force balance considerations using EFIT++[Appel et al., ''A unified approach to equilibrium reconstruction'' Proceedings of the 33rd EPS Conference on Plasma Physics (Rome, Italy, 2006)]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry as well as directly predicting the Shafranov shift of the plasma core.« less

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.

Bayesian Analysis of Silica Exposure and Lung Cancer Using Human and Animal Studies.

PubMed

Bartell, Scott M; Hamra, Ghassan Badri; Steenland, Kyle

2017-03-01

Bayesian methods can be used to incorporate external information into epidemiologic exposure-response analyses of silica and lung cancer. We used data from a pooled mortality analysis of silica and lung cancer (n = 65,980), using untransformed and log-transformed cumulative exposure. Animal data came from chronic silica inhalation studies using rats. We conducted Bayesian analyses with informative priors based on the animal data and different cross-species extrapolation factors. We also conducted analyses with exposure measurement error corrections in the absence of a gold standard, assuming Berkson-type error that increased with increasing exposure. The pooled animal data exposure-response coefficient was markedly higher (log exposure) or lower (untransformed exposure) than the coefficient for the pooled human data. With 10-fold uncertainty, the animal prior had little effect on results for pooled analyses and only modest effects in some individual studies. One-fold uncertainty produced markedly different results for both pooled and individual studies. Measurement error correction had little effect in pooled analyses using log exposure. Using untransformed exposure, measurement error correction caused a 5% decrease in the exposure-response coefficient for the pooled analysis and marked changes in some individual studies. The animal prior had more impact for smaller human studies and for one-fold versus three- or 10-fold uncertainty. Adjustment for Berkson error using Bayesian methods had little effect on the exposure-response coefficient when exposure was log transformed or when the sample size was large. See video abstract at, http://links.lww.com/EDE/B160.

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

Limitations of cytochrome oxidase I for the barcoding of Neritidae (Mollusca: Gastropoda) as revealed by Bayesian analysis.

PubMed

Chee, S Y

2015-05-25

The mitochondrial DNA (mtDNA) cytochrome oxidase I (COI) gene has been universally and successfully utilized as a barcoding gene, mainly because it can be amplified easily, applied across a wide range of taxa, and results can be obtained cheaply and quickly. However, in rare cases, the gene can fail to distinguish between species, particularly when exposed to highly sensitive methods of data analysis, such as the Bayesian method, or when taxa have undergone introgressive hybridization, over-splitting, or incomplete lineage sorting. Such cases require the use of alternative markers, and nuclear DNA markers are commonly used. In this study, a dendrogram produced by Bayesian analysis of an mtDNA COI dataset was compared with that of a nuclear DNA ATPS-α dataset, in order to evaluate the efficiency of COI in barcoding Malaysian nerites (Neritidae). In the COI dendrogram, most of the species were in individual clusters, except for two species: Nerita chamaeleon and N. histrio. These two species were placed in the same subcluster, whereas in the ATPS-α dendrogram they were in their own subclusters. Analysis of the ATPS-α gene also placed the two genera of nerites (Nerita and Neritina) in separate clusters, whereas COI gene analysis placed both genera in the same cluster. Therefore, in the case of the Neritidae, the ATPS-α gene is a better barcoding gene than the COI gene.

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.

A Bayesian sequential design using alpha spending function to control type I error.

PubMed

Zhu, Han; Yu, Qingzhao

2017-10-01

We propose in this article a Bayesian sequential design using alpha spending functions to control the overall type I error in phase III clinical trials. We provide algorithms to calculate critical values, power, and sample sizes for the proposed design. Sensitivity analysis is implemented to check the effects from different prior distributions, and conservative priors are recommended. We compare the power and actual sample sizes of the proposed Bayesian sequential design with different alpha spending functions through simulations. We also compare the power of the proposed method with frequentist sequential design using the same alpha spending function. Simulations show that, at the same sample size, the proposed method provides larger power than the corresponding frequentist sequential design. It also has larger power than traditional Bayesian sequential design which sets equal critical values for all interim analyses. When compared with other alpha spending functions, O'Brien-Fleming alpha spending function has the largest power and is the most conservative in terms that at the same sample size, the null hypothesis is the least likely to be rejected at early stage of clinical trials. And finally, we show that adding a step of stop for futility in the Bayesian sequential design can reduce the overall type I error and reduce the actual sample sizes.

Information Theoretic Studies and Assessment of Space Object Identification

DTIC Science & Technology

2014-03-24

localization are contained in Ref. [5]. 1.7.1 A Bayesian MPE Based Analysis of 2D Point-Source-Pair Superresolution In a second recently submitted paper [6], a...related problem of the optical superresolution (OSR) of a pair of equal-brightness point sources separated spatially by a distance (or angle) smaller...1403.4897 [physics.optics] (19 March 2014). 6. S. Prasad, “Asymptotics of Bayesian error probability and 2D pair superresolution ,” submitted to Opt. Express

A Bayesian Analysis of the Flood Frequency Hydrology Concept

DTIC Science & Technology

2016-02-01

located in northern Austria . It not only underscores attributes of the method as applied to the Kamp at Zwettl but also discusses ways in which the...hydrology concept originally performed by Viglione et al. (2013) for the 622 km2 Kamp at Zwettl river basin located in northern Austria . Eight primary...parts of the example originally profiled by Viglione et al. (2013) for the 622 km2 Kamp at Zwettl river basin located in northern Austria . A Bayesian

Conventional, Bayesian, and Modified Prony's methods for characterizing fast and slow waves in equine cancellous bone

PubMed Central

Groopman, Amber M.; Katz, Jonathan I.; Holland, Mark R.; Fujita, Fuminori; Matsukawa, Mami; Mizuno, Katsunori; Wear, Keith A.; Miller, James G.

2015-01-01

Conventional, Bayesian, and the modified least-squares Prony's plus curve-fitting (MLSP + CF) methods were applied to data acquired using 1 MHz center frequency, broadband transducers on a single equine cancellous bone specimen that was systematically shortened from 11.8 mm down to 0.5 mm for a total of 24 sample thicknesses. Due to overlapping fast and slow waves, conventional analysis methods were restricted to data from sample thicknesses ranging from 11.8 mm to 6.0 mm. In contrast, Bayesian and MLSP + CF methods successfully separated fast and slow waves and provided reliable estimates of the ultrasonic properties of fast and slow waves for sample thicknesses ranging from 11.8 mm down to 3.5 mm. Comparisons of the three methods were carried out for phase velocity at the center frequency and the slope of the attenuation coefficient for the fast and slow waves. Good agreement among the three methods was also observed for average signal loss at the center frequency. The Bayesian and MLSP + CF approaches were able to separate the fast and slow waves and provide good estimates of the fast and slow wave properties even when the two wave modes overlapped in both time and frequency domains making conventional analysis methods unreliable. PMID:26328678

Bayesian networks and statistical analysis application to analyze the diagnostic test accuracy

NASA Astrophysics Data System (ADS)

Orzechowski, P.; Makal, Jaroslaw; Onisko, A.

2005-02-01

The computer aided BPH diagnosis system based on Bayesian network is described in the paper. First result are compared to a given statistical method. Different statistical methods are used successfully in medicine for years. However, the undoubted advantages of probabilistic methods make them useful in application in newly created systems which are frequent in medicine, but do not have full and competent knowledge. The article presents advantages of the computer aided BPH diagnosis system in clinical practice for urologists.

A Bayesian approach to the statistical analysis of device preference studies.

PubMed

Fu, Haoda; Qu, Yongming; Zhu, Baojin; Huster, William

2012-01-01

Drug delivery devices are required to have excellent technical specifications to deliver drugs accurately, and in addition, the devices should provide a satisfactory experience to patients because this can have a direct effect on drug compliance. To compare patients' experience with two devices, cross-over studies with patient-reported outcomes (PRO) as response variables are often used. Because of the strength of cross-over designs, each subject can directly compare the two devices by using the PRO variables, and variables indicating preference (preferring A, preferring B, or no preference) can be easily derived. Traditionally, methods based on frequentist statistics can be used to analyze such preference data, but there are some limitations for the frequentist methods. Recently, Bayesian methods are considered an acceptable method by the US Food and Drug Administration to design and analyze device studies. In this paper, we propose a Bayesian statistical method to analyze the data from preference trials. We demonstrate that the new Bayesian estimator enjoys some optimal properties versus the frequentist estimator. Copyright © 2012 John Wiley & Sons, Ltd.

Bayesian Multi-Trait Analysis Reveals a Useful Tool to Increase Oil Concentration and to Decrease Toxicity in Jatropha curcas L.

PubMed Central

Silva Junqueira, Vinícius; de Azevedo Peixoto, Leonardo; Galvêas Laviola, Bruno; Lopes Bhering, Leonardo; Mendonça, Simone; Agostini Costa, Tania da Silveira; Antoniassi, Rosemar

2016-01-01

The biggest challenge for jatropha breeding is to identify superior genotypes that present high seed yield and seed oil content with reduced toxicity levels. Therefore, the objective of this study was to estimate genetic parameters for three important traits (weight of 100 seed, oil seed content, and phorbol ester concentration), and to select superior genotypes to be used as progenitors in jatropha breeding. Additionally, the genotypic values and the genetic parameters estimated under the Bayesian multi-trait approach were used to evaluate different selection indices scenarios of 179 half-sib families. Three different scenarios and economic weights were considered. It was possible to simultaneously reduce toxicity and increase seed oil content and weight of 100 seed by using index selection based on genotypic value estimated by the Bayesian multi-trait approach. Indeed, we identified two families that present these characteristics by evaluating genetic diversity using the Ward clustering method, which suggested nine homogenous clusters. Future researches must integrate the Bayesian multi-trait methods with realized relationship matrix, aiming to build accurate selection indices models. PMID:27281340

Bayesian analysis of the flutter margin method in aeroelasticity

DOE PAGES

Khalil, Mohammad; Poirel, Dominique; Sarkar, Abhijit

2016-08-27

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

Adaptability and phenotypic stability of common bean genotypes through Bayesian inference.

PubMed

Corrêa, A M; Teodoro, P E; Gonçalves, M C; Barroso, L M A; Nascimento, M; Santos, A; Torres, F E

2016-04-27

This study used Bayesian inference to investigate the genotype x environment interaction in common bean grown in Mato Grosso do Sul State, and it also evaluated the efficiency of using informative and minimally informative a priori distributions. Six trials were conducted in randomized blocks, and the grain yield of 13 common bean genotypes was assessed. To represent the minimally informative a priori distributions, a probability distribution with high variance was used, and a meta-analysis concept was adopted to represent the informative a priori distributions. Bayes factors were used to conduct comparisons between the a priori distributions. The Bayesian inference was effective for the selection of upright common bean genotypes with high adaptability and phenotypic stability using the Eberhart and Russell method. Bayes factors indicated that the use of informative a priori distributions provided more accurate results than minimally informative a priori distributions. According to Bayesian inference, the EMGOPA-201, BAMBUÍ, CNF 4999, CNF 4129 A 54, and CNFv 8025 genotypes had specific adaptability to favorable environments, while the IAPAR 14 and IAC CARIOCA ETE genotypes had specific adaptability to unfavorable environments.

Bayesian molecular dating: opening up the black box.

PubMed

Bromham, Lindell; Duchêne, Sebastián; Hua, Xia; Ritchie, Andrew M; Duchêne, David A; Ho, Simon Y W

2018-05-01

Molecular dating analyses allow evolutionary timescales to be estimated from genetic data, offering an unprecedented capacity for investigating the evolutionary past of all species. These methods require us to make assumptions about the relationship between genetic change and evolutionary time, often referred to as a 'molecular clock'. Although initially regarded with scepticism, molecular dating has now been adopted in many areas of biology. This broad uptake has been due partly to the development of Bayesian methods that allow complex aspects of molecular evolution, such as variation in rates of change across lineages, to be taken into account. But in order to do this, Bayesian dating methods rely on a range of assumptions about the evolutionary process, which vary in their degree of biological realism and empirical support. These assumptions can have substantial impacts on the estimates produced by molecular dating analyses. The aim of this review is to open the 'black box' of Bayesian molecular dating and have a look at the machinery inside. We explain the components of these dating methods, the important decisions that researchers must make in their analyses, and the factors that need to be considered when interpreting results. We illustrate the effects that the choices of different models and priors can have on the outcome of the analysis, and suggest ways to explore these impacts. We describe some major research directions that may improve the reliability of Bayesian dating. The goal of our review is to help researchers to make informed choices when using Bayesian phylogenetic methods to estimate evolutionary rates and timescales. © 2017 Cambridge Philosophical Society.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics.

PubMed

Wu, Xiao-Lin; Sun, Chuanyu; Beissinger, Timothy M; Rosa, Guilherme Jm; Weigel, Kent A; Gatti, Natalia de Leon; Gianola, Daniel

2012-09-25

Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.

Bayesian Mass Estimates of the Milky Way: Including Measurement Uncertainties with Hierarchical Bayes

NASA Astrophysics Data System (ADS)

Eadie, Gwendolyn M.; Springford, Aaron; Harris, William E.

2017-02-01

We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie et al. and Eadie and Harris and builds upon the preliminary reports by Eadie et al. The method uses a distribution function f({ E },L) to model the Galaxy and kinematic data from satellite objects, such as globular clusters (GCs), to trace the Galaxy’s gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie and Harris and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within 125 kpc of 4.8× {10}11{M}⊙ with a 95% Bayesian credible region of (4.0{--}5.8)× {10}11{M}⊙ . Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

PubMed Central

2012-01-01

Background Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Results Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Conclusions Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs. PMID:23009363

Multi-Objective data analysis using Bayesian Inference for MagLIF experiments

NASA Astrophysics Data System (ADS)

Knapp, Patrick; Glinksy, Michael; Evans, Matthew; Gom, Matth; Han, Stephanie; Harding, Eric; Slutz, Steve; Hahn, Kelly; Harvey-Thompson, Adam; Geissel, Matthias; Ampleford, David; Jennings, Christopher; Schmit, Paul; Smith, Ian; Schwarz, Jens; Peterson, Kyle; Jones, Brent; Rochau, Gregory; Sinars, Daniel

2017-10-01

The MagLIF concept has recently demonstrated Gbar pressures and confinement of charged fusion products at stagnation. We present a new analysis methodology that allows for integration of multiple diagnostics including nuclear, x-ray imaging, and x-ray power to determine the temperature, pressure, liner areal density, and mix fraction. A simplified hot-spot model is used with a Bayesian inference network to determine the most probable model parameters that describe the observations while simultaneously revealing the principal uncertainties in the analysis. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.

Rational hypocrisy: a Bayesian analysis based on informal argumentation and slippery slopes.

PubMed

Rai, Tage S; Holyoak, Keith J

2014-01-01

Moral hypocrisy is typically viewed as an ethical accusation: Someone is applying different moral standards to essentially identical cases, dishonestly claiming that one action is acceptable while otherwise equivalent actions are not. We suggest that in some instances the apparent logical inconsistency stems from different evaluations of a weak argument, rather than dishonesty per se. Extending Corner, Hahn, and Oaksford's (2006) analysis of slippery slope arguments, we develop a Bayesian framework in which accusations of hypocrisy depend on inferences of shared category membership between proposed actions and previous standards, based on prior probabilities that inform the strength of competing hypotheses. Across three experiments, we demonstrate that inferences of hypocrisy increase as perceptions of the likelihood of shared category membership between precedent cases and current cases increase, that these inferences follow established principles of category induction, and that the presence of self-serving motives increases inferences of hypocrisy independent of changes in the actions themselves. Taken together, these results demonstrate that Bayesian analyses of weak arguments may have implications for assessing moral reasoning. © 2014 Cognitive Science Society, Inc.

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.

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis: A Comparison of Maximum Likelihood and Bayesian Estimations.

PubMed

Can, Seda; van de Schoot, Rens; Hox, Joop

2015-06-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions.

Bayesian Estimation of Thermonuclear Reaction Rates for Deuterium+Deuterium Reactions

NASA Astrophysics Data System (ADS)

Gómez Iñesta, Á.; Iliadis, C.; Coc, A.

2017-11-01

The study of d+d reactions is of major interest since their reaction rates affect the predicted abundances of D, 3He, and 7Li. In particular, recent measurements of primordial D/H ratios call for reduced uncertainties in the theoretical abundances predicted by Big Bang nucleosynthesis (BBN). Different authors have studied reactions involved in BBN by incorporating new experimental data and a careful treatment of systematic and probabilistic uncertainties. To analyze the experimental data, Coc et al. used results of ab initio models for the theoretical calculation of the energy dependence of S-factors in conjunction with traditional statistical methods based on χ 2 minimization. Bayesian methods have now spread to many scientific fields and provide numerous advantages in data analysis. Astrophysical S-factors and reaction rates using Bayesian statistics were calculated by Iliadis et al. Here we present a similar analysis for two d+d reactions, d(d, n)3He and d(d, p)3H, that has been translated into a total decrease of the predicted D/H value by 0.16%.

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

An absolute chronology for early Egypt using radiocarbon dating and Bayesian statistical modelling

PubMed Central

Dee, Michael; Wengrow, David; Shortland, Andrew; Stevenson, Alice; Brock, Fiona; Girdland Flink, Linus; Bronk Ramsey, Christopher

2013-01-01

The Egyptian state was formed prior to the existence of verifiable historical records. Conventional dates for its formation are based on the relative ordering of artefacts. This approach is no longer considered sufficient for cogent historical analysis. Here, we produce an absolute chronology for Early Egypt by combining radiocarbon and archaeological evidence within a Bayesian paradigm. Our data cover the full trajectory of Egyptian state formation and indicate that the process occurred more rapidly than previously thought. We provide a timeline for the First Dynasty of Egypt of generational-scale resolution that concurs with prevailing archaeological analysis and produce a chronometric date for the foundation of Egypt that distinguishes between historical estimates. PMID:24204188

Bayesian analysis of factors associated with fibromyalgia syndrome subjects

NASA Astrophysics Data System (ADS)

Jayawardana, Veroni; Mondal, Sumona; Russek, Leslie

2015-01-01

Factors contributing to movement-related fear were assessed by Russek, et al. 2014 for subjects with Fibromyalgia (FM) based on the collected data by a national internet survey of community-based individuals. The study focused on the variables, Activities-Specific Balance Confidence scale (ABC), Primary Care Post-Traumatic Stress Disorder screen (PC-PTSD), Tampa Scale of Kinesiophobia (TSK), a Joint Hypermobility Syndrome screen (JHS), Vertigo Symptom Scale (VSS-SF), Obsessive-Compulsive Personality Disorder (OCPD), Pain, work status and physical activity dependent from the "Revised Fibromyalgia Impact Questionnaire" (FIQR). The study presented in this paper revisits same data with a Bayesian analysis where appropriate priors were introduced for variables selected in the Russek's paper.

A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.

PubMed

Houseman, E Andres; Virji, M Abbas

2017-08-01

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates were significant in some frequentist models, but in the Bayesian model their credible intervals contained zero; such discrepancies were observed in multiple datasets. Variance components from the Bayesian model reflected substantial autocorrelation, consistent with the frequentist models, except for the auto-regressive moving average model. Plots of means from the Bayesian model showed good fit to the observed data. The proposed Bayesian model provides an approach for modeling non-stationary autocorrelation in a hierarchical modeling framework to estimate task means, standard deviations, quantiles, and parameter estimates for covariates that are less biased and have better performance characteristics than some of the contemporary methods. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

Flood quantile estimation at ungauged sites by Bayesian networks

NASA Astrophysics Data System (ADS)

Mediero, L.; Santillán, D.; Garrote, L.

2012-04-01

Estimating flood quantiles at a site for which no observed measurements are available is essential for water resources planning and management. Ungauged sites have no observations about the magnitude of floods, but some site and basin characteristics are known. The most common technique used is the multiple regression analysis, which relates physical and climatic basin characteristic to flood quantiles. Regression equations are fitted from flood frequency data and basin characteristics at gauged sites. Regression equations are a rigid technique that assumes linear relationships between variables and cannot take the measurement errors into account. In addition, the prediction intervals are estimated in a very simplistic way from the variance of the residuals in the estimated model. Bayesian networks are a probabilistic computational structure taken from the field of Artificial Intelligence, which have been widely and successfully applied to many scientific fields like medicine and informatics, but application to the field of hydrology is recent. Bayesian networks infer the joint probability distribution of several related variables from observations through nodes, which represent random variables, and links, which represent causal dependencies between them. A Bayesian network is more flexible than regression equations, as they capture non-linear relationships between variables. In addition, the probabilistic nature of Bayesian networks allows taking the different sources of estimation uncertainty into account, as they give a probability distribution as result. A homogeneous region in the Tagus Basin was selected as case study. A regression equation was fitted taking the basin area, the annual maximum 24-hour rainfall for a given recurrence interval and the mean height as explanatory variables. Flood quantiles at ungauged sites were estimated by Bayesian networks. Bayesian networks need to be learnt from a huge enough data set. As observational data are reduced, a stochastic generator of synthetic data was developed. Synthetic basin characteristics were randomised, keeping the statistical properties of observed physical and climatic variables in the homogeneous region. The synthetic flood quantiles were stochastically generated taking the regression equation as basis. The learnt Bayesian network was validated by the reliability diagram, the Brier Score and the ROC diagram, which are common measures used in the validation of probabilistic forecasts. Summarising, the flood quantile estimations through Bayesian networks supply information about the prediction uncertainty as a probability distribution function of discharges is given as result. Therefore, the Bayesian network model has application as a decision support for water resources and planning management.

BAYESIAN ANALYSIS TO EVALUATE TESTS FOR THE DETECTION OF MYCOBACTERIUM BOVIS INFECTION IN FREE-RANGING WILD BISON (BISON BISON ATHABASCAE) IN THE ABSENCE OF A GOLD STANDARD.

PubMed

Chapinal, Núria; Schumaker, Brant A; Joly, Damien O; Elkin, Brett T; Stephen, Craig

2015-07-01

We estimated the sensitivity and specificity of the caudal-fold skin test (CFT), the fluorescent polarization assay (FPA), and the rapid lateral-flow test (RT) for the detection of Mycobacterium bovis in free-ranging wild wood bison (Bison bison athabascae), in the absence of a gold standard, by using Bayesian analysis, and then used those estimates to forecast the performance of a pairwise combination of tests in parallel. In 1998-99, 212 wood bison from Wood Buffalo National Park (Canada) were tested for M. bovis infection using CFT and two serologic tests (FPA and RT). The sensitivity and specificity of each test were estimated using a three-test, one-population, Bayesian model allowing for conditional dependence between FPA and RT. The sensitivity and specificity of the combination of CFT and each serologic test in parallel were calculated assuming conditional independence. The test performance estimates were influenced by the prior values chosen. However, the rank of tests and combinations of tests based on those estimates remained constant. The CFT was the most sensitive test and the FPA was the least sensitive, whereas RT was the most specific test and CFT was the least specific. In conclusion, given the fact that gold standards for the detection of M. bovis are imperfect and difficult to obtain in the field, Bayesian analysis holds promise as a tool to rank tests and combinations of tests based on their performance. Combining a skin test with an animal-side serologic test, such as RT, increases sensitivity in the detection of M. bovis and is a good approach to enhance disease eradication or control in wild bison.

Variational Bayesian Learning for Wavelet Independent Component Analysis

NASA Astrophysics Data System (ADS)

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

2005-11-01

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

A tutorial on Bayesian bivariate meta-analysis of mixed binary-continuous outcomes with missing treatment effects.

PubMed

Gajic-Veljanoski, Olga; Cheung, Angela M; Bayoumi, Ahmed M; Tomlinson, George

2016-05-30

Bivariate random-effects meta-analysis (BVMA) is a method of data synthesis that accounts for treatment effects measured on two outcomes. BVMA gives more precise estimates of the population mean and predicted values than two univariate random-effects meta-analyses (UVMAs). BVMA also addresses bias from incomplete reporting of outcomes. A few tutorials have covered technical details of BVMA of categorical or continuous outcomes. Limited guidance is available on how to analyze datasets that include trials with mixed continuous-binary outcomes where treatment effects on one outcome or the other are not reported. Given the advantages of Bayesian BVMA for handling missing outcomes, we present a tutorial for Bayesian BVMA of incompletely reported treatment effects on mixed bivariate outcomes. This step-by-step approach can serve as a model for our intended audience, the methodologist familiar with Bayesian meta-analysis, looking for practical advice on fitting bivariate models. To facilitate application of the proposed methods, we include our WinBUGS code. As an example, we use aggregate-level data from published trials to demonstrate the estimation of the effects of vitamin K and bisphosphonates on two correlated bone outcomes, fracture, and bone mineral density. We present datasets where reporting of the pairs of treatment effects on both outcomes was 'partially' complete (i.e., pairs completely reported in some trials), and we outline steps for modeling the incompletely reported data. To assess what is gained from the additional work required by BVMA, we compare the resulting estimates to those from separate UVMAs. We discuss methodological findings and make four recommendations. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Scheduling structural health monitoring activities for optimizing life-cycle costs and reliability of wind turbines

NASA Astrophysics Data System (ADS)

Hanish Nithin, Anu; Omenzetter, Piotr

2017-04-01

Optimization of the life-cycle costs and reliability of offshore wind turbines (OWTs) is an area of immense interest due to the widespread increase in wind power generation across the world. Most of the existing studies have used structural reliability and the Bayesian pre-posterior analysis for optimization. This paper proposes an extension to the previous approaches in a framework for probabilistic optimization of the total life-cycle costs and reliability of OWTs by combining the elements of structural reliability/risk analysis (SRA), the Bayesian pre-posterior analysis with optimization through a genetic algorithm (GA). The SRA techniques are adopted to compute the probabilities of damage occurrence and failure associated with the deterioration model. The probabilities are used in the decision tree and are updated using the Bayesian analysis. The output of this framework would determine the optimal structural health monitoring and maintenance schedules to be implemented during the life span of OWTs while maintaining a trade-off between the life-cycle costs and risk of the structural failure. Numerical illustrations with a generic deterioration model for one monitoring exercise in the life cycle of a system are demonstrated. Two case scenarios, namely to build initially an expensive and robust or a cheaper but more quickly deteriorating structures and to adopt expensive monitoring system, are presented to aid in the decision-making process.

Assessing compositional variability through graphical analysis and Bayesian statistical approaches: case studies on transgenic crops.

PubMed

Harrigan, George G; Harrison, Jay M

2012-01-01

New transgenic (GM) crops are subjected to extensive safety assessments that include compositional comparisons with conventional counterparts as a cornerstone of the process. The influence of germplasm, location, environment, and agronomic treatments on compositional variability is, however, often obscured in these pair-wise comparisons. Furthermore, classical statistical significance testing can often provide an incomplete and over-simplified summary of highly responsive variables such as crop composition. In order to more clearly describe the influence of the numerous sources of compositional variation we present an introduction to two alternative but complementary approaches to data analysis and interpretation. These include i) exploratory data analysis (EDA) with its emphasis on visualization and graphics-based approaches and ii) Bayesian statistical methodology that provides easily interpretable and meaningful evaluations of data in terms of probability distributions. The EDA case-studies include analyses of herbicide-tolerant GM soybean and insect-protected GM maize and soybean. Bayesian approaches are presented in an analysis of herbicide-tolerant GM soybean. Advantages of these approaches over classical frequentist significance testing include the more direct interpretation of results in terms of probabilities pertaining to quantities of interest and no confusion over the application of corrections for multiple comparisons. It is concluded that a standardized framework for these methodologies could provide specific advantages through enhanced clarity of presentation and interpretation in comparative assessments of crop composition.

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?

Bayesian bivariate meta-analysis of diagnostic test studies with interpretable priors.

PubMed

Guo, Jingyi; Riebler, Andrea; Rue, Håvard

2017-08-30

In a bivariate meta-analysis, the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Using Bayesian inference is particularly attractive as informative priors that add a small amount of information can stabilise the analysis without overwhelming the data. However, Bayesian analysis is often computationally demanding and the selection of the prior for the covariance matrix of the bivariate structure is crucial with little data. The integrated nested Laplace approximations method provides an efficient solution to the computational issues by avoiding any sampling, but the important question of priors remain. We explore the penalised complexity (PC) prior framework for specifying informative priors for the variance parameters and the correlation parameter. PC priors facilitate model interpretation and hyperparameter specification as expert knowledge can be incorporated intuitively. We conduct a simulation study to compare the properties and behaviour of differently defined PC priors to currently used priors in the field. The simulation study shows that the PC prior seems beneficial for the variance parameters. The use of PC priors for the correlation parameter results in more precise estimates when specified in a sensible neighbourhood around the truth. To investigate the usage of PC priors in practice, we reanalyse a meta-analysis using the telomerase marker for the diagnosis of bladder cancer and compare the results with those obtained by other commonly used modelling approaches. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

An efficient Bayesian data-worth analysis using a multilevel Monte Carlo method

NASA Astrophysics Data System (ADS)

Lu, Dan; Ricciuto, Daniel; Evans, Katherine

2018-03-01

Improving the understanding of subsurface systems and thus reducing prediction uncertainty requires collection of data. As the collection of subsurface data is costly, it is important that the data collection scheme is cost-effective. Design of a cost-effective data collection scheme, i.e., data-worth analysis, requires quantifying model parameter, prediction, and both current and potential data uncertainties. Assessment of these uncertainties in large-scale stochastic subsurface hydrological model simulations using standard Monte Carlo (MC) sampling or surrogate modeling is extremely computationally intensive, sometimes even infeasible. In this work, we propose an efficient Bayesian data-worth analysis using a multilevel Monte Carlo (MLMC) method. Compared to the standard MC that requires a significantly large number of high-fidelity model executions to achieve a prescribed accuracy in estimating expectations, the MLMC can substantially reduce computational costs using multifidelity approximations. Since the Bayesian data-worth analysis involves a great deal of expectation estimation, the cost saving of the MLMC in the assessment can be outstanding. While the proposed MLMC-based data-worth analysis is broadly applicable, we use it for a highly heterogeneous two-phase subsurface flow simulation to select an optimal candidate data set that gives the largest uncertainty reduction in predicting mass flow rates at four production wells. The choices made by the MLMC estimation are validated by the actual measurements of the potential data, and consistent with the standard MC estimation. But compared to the standard MC, the MLMC greatly reduces the computational costs.

Selected aspects of prior and likelihood information for a Bayesian classifier in a road safety analysis.

PubMed

Nowakowska, Marzena

2017-04-01

The development of the Bayesian logistic regression model classifying the road accident severity is discussed. The already exploited informative priors (method of moments, maximum likelihood estimation, and two-stage Bayesian updating), along with the original idea of a Boot prior proposal, are investigated when no expert opinion has been available. In addition, two possible approaches to updating the priors, in the form of unbalanced and balanced training data sets, are presented. The obtained logistic Bayesian models are assessed on the basis of a deviance information criterion (DIC), highest probability density (HPD) intervals, and coefficients of variation estimated for the model parameters. The verification of the model accuracy has been based on sensitivity, specificity and the harmonic mean of sensitivity and specificity, all calculated from a test data set. The models obtained from the balanced training data set have a better classification quality than the ones obtained from the unbalanced training data set. The two-stage Bayesian updating prior model and the Boot prior model, both identified with the use of the balanced training data set, outperform the non-informative, method of moments, and maximum likelihood estimation prior models. It is important to note that one should be careful when interpreting the parameters since different priors can lead to different models. Copyright © 2017 Elsevier Ltd. All rights reserved.

Finite‐fault Bayesian inversion of teleseismic body waves

USGS Publications Warehouse

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

On selecting a prior for the precision parameter of Dirichlet process mixture models

USGS Publications Warehouse

Dorazio, R.M.

2009-01-01

In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter ?? and a base probability measure G0. In problems where ?? is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for ??. In this paper an approach is developed for computing a prior for the precision parameter ?? that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.

Probabilistic safety analysis of earth retaining structures during earthquakes

NASA Astrophysics Data System (ADS)

Grivas, D. A.; Souflis, C.

1982-07-01

A procedure is presented for determining the probability of failure of Earth retaining structures under static or seismic conditions. Four possible modes of failure (overturning, base sliding, bearing capacity, and overall sliding) are examined and their combined effect is evaluated with the aid of combinatorial analysis. The probability of failure is shown to be a more adequate measure of safety than the customary factor of safety. As Earth retaining structures may fail in four distinct modes, a system analysis can provide a single estimate for the possibility of failure. A Bayesian formulation of the safety retaining walls is found to provide an improved measure for the predicted probability of failure under seismic loading. The presented Bayesian analysis can account for the damage incurred to a retaining wall during an earthquake to provide an improved estimate for its probability of failure during future seismic events.

Application of Bayesian configural frequency analysis (BCFA) to determine characteristics user and non-user motor X

NASA Astrophysics Data System (ADS)

Mawardi, Muhamad Iqbal; Padmadisastra, Septiadi; Tantular, Bertho

2018-03-01

Configural Frequency Analysis is a method for cell-wise testing in contingency tables for exploratory search type and antitype, that can see the existence of discrepancy on the model by existence of a significant difference between the frequency of observation and frequency of expectation. This analysis focuses on whether or not the interaction among categories from different variables, and not the interaction among variables. One of the extensions of CFA method is Bayesian CFA, this alternative method pursue the same goal as frequentist version of CFA with the advantage that adjustment of the experiment-wise significance level α is not necessary and test whether groups of types and antitypes form composite types or composite antitypes. Hence, this research will present the concept of the Bayesian CFA and how it works for the real data. The data on this paper is based on case studies in a company about decrease Brand Awareness & Image motor X on Top Of Mind Unit indicator in Cirebon City for user 30.8% and non user 9.8%. From the result of B-CFA have four characteristics from deviation, one of the four characteristics above that is the configuration 2212 need more attention by company to determine promotion strategy to maintain and improve Top Of Mind Unit in Cirebon City.

Bayesian analysis of energy and count rate data for detection of low count rate radioactive sources

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

Klumpp, John

We propose a radiation detection system which generates its own discrete sampling distribution based on past measurements of background. The advantage to this approach is that it can take into account variations in background with respect to time, location, energy spectra, detector-specific characteristics (i.e. different efficiencies at different count rates and energies), etc. This would therefore be a 'machine learning' approach, in which the algorithm updates and improves its characterization of background over time. The system would have a 'learning mode,' in which it measures and analyzes background count rates, and a 'detection mode,' in which it compares measurements frommore » an unknown source against its unique background distribution. By characterizing and accounting for variations in the background, general purpose radiation detectors can be improved with little or no increase in cost. The statistical and computational techniques to perform this kind of analysis have already been developed. The necessary signal analysis can be accomplished using existing Bayesian algorithms which account for multiple channels, multiple detectors, and multiple time intervals. Furthermore, Bayesian machine-learning techniques have already been developed which, with trivial modifications, can generate appropriate decision thresholds based on the comparison of new measurements against a nonparametric sampling distribution. (authors)« less

Bayesian meta-analysis of Cronbach's coefficient alpha to evaluate informative hypotheses.

PubMed

Okada, Kensuke

2015-12-01

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 this test is greater than 0.8' or 'alpha of one form of a test is greater than the others.' The proposed method enables direct evaluation of these informative hypotheses. To this end, a Bayes factor is calculated to evaluate the informative hypothesis against its complement. It allows researchers to summarize the evidence provided by previous studies in favor of their informative hypothesis. The proposed approach can be seen as a natural extension of the Bayesian meta-analysis of coefficient alpha recently proposed in this journal (Brannick and Zhang, 2013). The proposed method is illustrated through two meta-analyses of real data that evaluate different kinds of informative hypotheses on superpopulation: one is that alpha of a particular test is above the criterion value, and the other is that alphas among different test versions have ordered relationships. Informative hypotheses are supported from the data in both cases, suggesting that the proposed approach is promising for application. Copyright © 2015 John Wiley & Sons, Ltd.

Influence of erroneous patient records on population pharmacokinetic modeling and individual bayesian estimation.

PubMed

van der Meer, Aize Franciscus; Touw, Daniël J; Marcus, Marco A E; Neef, Cornelis; Proost, Johannes H

2012-10-01

Observational data sets can be used for population pharmacokinetic (PK) modeling. However, these data sets are generally less precisely recorded than experimental data sets. This article aims to investigate the influence of erroneous records on population PK modeling and individual maximum a posteriori Bayesian (MAPB) estimation. A total of 1123 patient records of neonates who were administered vancomycin were used for population PK modeling by iterative 2-stage Bayesian (ITSB) analysis. Cut-off values for weighted residuals were tested for exclusion of records from the analysis. A simulation study was performed to assess the influence of erroneous records on population modeling and individual MAPB estimation. Also the cut-off values for weighted residuals were tested in the simulation study. Errors in registration have limited the influence on outcomes of population PK modeling but can have detrimental effects on individual MAPB estimation. A population PK model created from a data set with many registration errors has little influence on subsequent MAPB estimates for precisely recorded data. A weighted residual value of 2 for concentration measurements has good discriminative power for identification of erroneous records. ITSB analysis and its individual estimates are hardly affected by most registration errors. Large registration errors can be detected by weighted residuals of concentration.

Bayesian Estimation of Fish Disease Prevalence from Pooled Samples Incorporating Sensitivity and Specificity

NASA Astrophysics Data System (ADS)

Williams, Christopher J.; Moffitt, Christine M.

2003-03-01

An important emerging issue in fisheries biology is the health of free-ranging populations of fish, particularly with respect to the prevalence of certain pathogens. For many years, pathologists focused on captive populations and interest was in the presence or absence of certain pathogens, so it was economically attractive to test pooled samples of fish. Recently, investigators have begun to study individual fish prevalence from pooled samples. Estimation of disease prevalence from pooled samples is straightforward when assay sensitivity and specificity are perfect, but this assumption is unrealistic. Here we illustrate the use of a Bayesian approach for estimating disease prevalence from pooled samples when sensitivity and specificity are not perfect. We also focus on diagnostic plots to monitor the convergence of the Gibbs-sampling-based Bayesian analysis. The methods are illustrated with a sample data set.

Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Cheong, R. Y.; Gabda, D.

2017-09-01

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

Bayesian network modelling of upper gastrointestinal bleeding

NASA Astrophysics Data System (ADS)

Aisha, Nazziwa; Shohaimi, Shamarina; Adam, Mohd Bakri

2013-09-01

Bayesian networks are graphical probabilistic models that represent causal and other relationships between domain variables. In the context of medical decision making, these models have been explored to help in medical diagnosis and prognosis. In this paper, we discuss the Bayesian network formalism in building medical support systems and we learn a tree augmented naive Bayes Network (TAN) from gastrointestinal bleeding data. The accuracy of the TAN in classifying the source of gastrointestinal bleeding into upper or lower source is obtained. The TAN achieves a high classification accuracy of 86% and an area under curve of 92%. A sensitivity analysis of the model shows relatively high levels of entropy reduction for color of the stool, history of gastrointestinal bleeding, consistency and the ratio of blood urea nitrogen to creatinine. The TAN facilitates the identification of the source of GIB and requires further validation.

On the predictive information criteria for model determination in seismic hazard analysis

NASA Astrophysics Data System (ADS)

Varini, Elisa; Rotondi, Renata

2016-04-01

Many statistical tools have been developed for evaluating, understanding, and comparing models, from both frequentist and Bayesian perspectives. In particular, the problem of model selection can be addressed according to whether the primary goal is explanation or, alternatively, prediction. In the former case, the criteria for model selection are defined over the parameter space whose physical interpretation can be difficult; in the latter case, they are defined over the space of the observations, which has a more direct physical meaning. In the frequentist approaches, model selection is generally based on an asymptotic approximation which may be poor for small data sets (e.g. the F-test, the Kolmogorov-Smirnov test, etc.); moreover, these methods often apply under specific assumptions on models (e.g. models have to be nested in the likelihood ratio test). In the Bayesian context, among the criteria for explanation, the ratio of the observed marginal densities for two competing models, named Bayes Factor (BF), is commonly used for both model choice and model averaging (Kass and Raftery, J. Am. Stat. Ass., 1995). But BF does not apply to improper priors and, even when the prior is proper, it is not robust to the specification of the prior. These limitations can be extended to two famous penalized likelihood methods as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), since they are proved to be approximations of -2log BF . In the perspective that a model is as good as its predictions, the predictive information criteria aim at evaluating the predictive accuracy of Bayesian models or, in other words, at estimating expected out-of-sample prediction error using a bias-correction adjustment of within-sample error (Gelman et al., Stat. Comput., 2014). In particular, the Watanabe criterion is fully Bayesian because it averages the predictive distribution over the posterior distribution of parameters rather than conditioning on a point estimate, but it is hardly applicable to data which are not independent given parameters (Watanabe, J. Mach. Learn. Res., 2010). A solution is given by Ando and Tsay criterion where the joint density may be decomposed into the product of the conditional densities (Ando and Tsay, Int. J. Forecast., 2010). The above mentioned criteria are global summary measures of model performance, but more detailed analysis could be required to discover the reasons for poor global performance. In this latter case, a retrospective predictive analysis is performed on each individual observation. In this study we performed the Bayesian analysis of Italian data sets by four versions of a long-term hazard model known as the stress release model (Vere-Jones, J. Physics Earth, 1978; Bebbington and Harte, Geophys. J. Int., 2003; Varini and Rotondi, Environ. Ecol. Stat., 2015). Then we illustrate the results on their performance evaluated by Bayes Factor, predictive information criteria and retrospective predictive analysis.

Bayesian networks for evaluation of evidence from forensic entomology.

PubMed

Andersson, M Gunnar; Sundström, Anders; Lindström, Anders

2013-09-01

In the aftermath of a CBRN incident, there is an urgent need to reconstruct events in order to bring the perpetrators to court and to take preventive actions for the future. The challenge is to discriminate, based on available information, between alternative scenarios. Forensic interpretation is used to evaluate to what extent results from the forensic investigation favor the prosecutors' or the defendants' arguments, using the framework of Bayesian hypothesis testing. Recently, several new scientific disciplines have been used in a forensic context. In the AniBioThreat project, the framework was applied to veterinary forensic pathology, tracing of pathogenic microorganisms, and forensic entomology. Forensic entomology is an important tool for estimating the postmortem interval in, for example, homicide investigations as a complement to more traditional methods. In this article we demonstrate the applicability of the Bayesian framework for evaluating entomological evidence in a forensic investigation through the analysis of a hypothetical scenario involving suspect movement of carcasses from a clandestine laboratory. Probabilities of different findings under the alternative hypotheses were estimated using a combination of statistical analysis of data, expert knowledge, and simulation, and entomological findings are used to update the beliefs about the prosecutors' and defendants' hypotheses and to calculate the value of evidence. The Bayesian framework proved useful for evaluating complex hypotheses using findings from several insect species, accounting for uncertainty about development rate, temperature, and precolonization. The applicability of the forensic statistic approach to evaluating forensic results from a CBRN incident is discussed.

Cross-validation to select Bayesian hierarchical models in phylogenetics.

PubMed

Duchêne, Sebastián; Duchêne, David A; Di Giallonardo, Francesca; Eden, John-Sebastian; Geoghegan, Jemma L; Holt, Kathryn E; Ho, Simon Y W; Holmes, Edward C

2016-05-26

Recent developments in Bayesian phylogenetic models have increased the range of inferences that can be drawn from molecular sequence data. Accordingly, model selection has become an important component of phylogenetic analysis. Methods of model selection generally consider the likelihood of the data under the model in question. In the context of Bayesian phylogenetics, the most common approach involves estimating the marginal likelihood, which is typically done by integrating the likelihood across model parameters, weighted by the prior. Although this method is accurate, it is sensitive to the presence of improper priors. We explored an alternative approach based on cross-validation that is widely used in evolutionary analysis. This involves comparing models according to their predictive performance. We analysed simulated data and a range of viral and bacterial data sets using a cross-validation approach to compare a variety of molecular clock and demographic models. Our results show that cross-validation can be effective in distinguishing between strict- and relaxed-clock models and in identifying demographic models that allow growth in population size over time. In most of our empirical data analyses, the model selected using cross-validation was able to match that selected using marginal-likelihood estimation. The accuracy of cross-validation appears to improve with longer sequence data, particularly when distinguishing between relaxed-clock models. Cross-validation is a useful method for Bayesian phylogenetic model selection. This method can be readily implemented even when considering complex models where selecting an appropriate prior for all parameters may be difficult.

The importance of proving the null.

PubMed

Gallistel, C R

2009-04-01

Null hypotheses are simple, precise, and theoretically important. Conventional statistical analysis cannot support them; Bayesian analysis can. The challenge in a Bayesian analysis is to formulate a suitably vague alternative, because the vaguer the alternative is (the more it spreads out the unit mass of prior probability), the more the null is favored. A general solution is a sensitivity analysis: Compute the odds for or against the null as a function of the limit(s) on the vagueness of the alternative. If the odds on the null approach 1 from above as the hypothesized maximum size of the possible effect approaches 0, then the data favor the null over any vaguer alternative to it. The simple computations and the intuitive graphic representation of the analysis are illustrated by the analysis of diverse examples from the current literature. They pose 3 common experimental questions: (a) Are 2 means the same? (b) Is performance at chance? (c) Are factors additive? (c) 2009 APA, all rights reserved

OGLE-2008-BLG-355Lb: A massive planet around a late-type star

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

Koshimoto, N.; Sumi, T.; Fukagawa, M.

2014-06-20

We report the discovery of a massive planet, OGLE-2008-BLG-355Lb. The light curve analysis indicates a planet:host mass ratio of q = 0.0118 ± 0.0006 at a separation of 0.877 ± 0.010 Einstein radii. We do not measure a significant microlensing parallax signal and do not have high angular resolution images that could detect the planetary host star. Therefore, we do not have a direct measurement of the host star mass. A Bayesian analysis, assuming that all host stars have equal probability to host a planet with the measured mass ratio, implies a host star mass of M{sub h}=0.37{sub −0.17}{sup +0.30}more » M{sub ⊙} and a companion of mass M{sub P}=4.6{sub −2.2}{sup +3.7}M{sub J}, at a projected separation of r{sub ⊥}=1.70{sub −0.30}{sup +0.29} AU. The implied distance to the planetary system is D {sub L} = 6.8 ± 1.1 kpc. A planetary system with the properties preferred by the Bayesian analysis may be a challenge to the core accretion model of planet formation, as the core accretion model predicts that massive planets are far more likely to form around more massive host stars. This core accretion model prediction is not consistent with our Bayesian prior of an equal probability of host stars of all masses to host a planet with the measured mass ratio. Thus, if the core accretion model prediction is right, we should expect that follow-up high angular resolution observations will detect a host star with a mass in the upper part of the range allowed by the Bayesian analysis. That is, the host would probably be a K or G dwarf.« less

Towards a Fuzzy Bayesian Network Based Approach for Safety Risk Analysis of Tunnel-Induced Pipeline Damage.

PubMed

Zhang, Limao; Wu, Xianguo; Qin, Yawei; Skibniewski, Miroslaw J; Liu, Wenli

2016-02-01

Tunneling excavation is bound to produce significant disturbances to surrounding environments, and the tunnel-induced damage to adjacent underground buried pipelines is of considerable importance for geotechnical practice. A fuzzy Bayesian networks (FBNs) based approach for safety risk analysis is developed in this article with detailed step-by-step procedures, consisting of risk mechanism analysis, the FBN model establishment, fuzzification, FBN-based inference, defuzzification, and decision making. In accordance with the failure mechanism analysis, a tunnel-induced pipeline damage model is proposed to reveal the cause-effect relationships between the pipeline damage and its influential variables. In terms of the fuzzification process, an expert confidence indicator is proposed to reveal the reliability of the data when determining the fuzzy probability of occurrence of basic events, with both the judgment ability level and the subjectivity reliability level taken into account. By means of the fuzzy Bayesian inference, the approach proposed in this article is capable of calculating the probability distribution of potential safety risks and identifying the most likely potential causes of accidents under both prior knowledge and given evidence circumstances. A case concerning the safety analysis of underground buried pipelines adjacent to the construction of the Wuhan Yangtze River Tunnel is presented. The results demonstrate the feasibility of the proposed FBN approach and its application potential. The proposed approach can be used as a decision tool to provide support for safety assurance and management in tunnel construction, and thus increase the likelihood of a successful project in a complex project environment. © 2015 Society for Risk Analysis.

A Bayesian network coding scheme for annotating biomedical information presented to genetic counseling clients.

PubMed

Green, Nancy

2005-04-01

We developed a Bayesian network coding scheme for annotating biomedical content in layperson-oriented clinical genetics documents. The coding scheme supports the representation of probabilistic and causal relationships among concepts in this domain, at a high enough level of abstraction to capture commonalities among genetic processes and their relationship to health. We are using the coding scheme to annotate a corpus of genetic counseling patient letters as part of the requirements analysis and knowledge acquisition phase of a natural language generation project. This paper describes the coding scheme and presents an evaluation of intercoder reliability for its tag set. In addition to giving examples of use of the coding scheme for analysis of discourse and linguistic features in this genre, we suggest other uses for it in analysis of layperson-oriented text and dialogue in medical communication.

A New Bayesian Approach for Estimating the Presence of a Suspected Compound in Routine Screening Analysis.

PubMed

Woldegebriel, Michael; Vivó-Truyols, Gabriel

2016-10-04

A novel method for compound identification in liquid chromatography-high resolution mass spectrometry (LC-HRMS) is proposed. The method, based on Bayesian statistics, accommodates all possible uncertainties involved, from instrumentation up to data analysis into a single model yielding the probability of the compound of interest being present/absent in the sample. This approach differs from the classical methods in two ways. First, it is probabilistic (instead of deterministic); hence, it computes the probability that the compound is (or is not) present in a sample. Second, it answers the hypothesis "the compound is present", opposed to answering the question "the compound feature is present". This second difference implies a shift in the way data analysis is tackled, since the probability of interfering compounds (i.e., isomers and isobaric compounds) is also taken into account.

The Development of Bayesian Theory and Its Applications in Business and Bioinformatics

NASA Astrophysics Data System (ADS)

Zhang, Yifei

2018-03-01

Bayesian Theory originated from an Essay of a British mathematician named Thomas Bayes in 1763, and after its development in 20th century, Bayesian Statistics has been taking a significant part in statistical study of all fields. Due to the recent breakthrough of high-dimensional integral, Bayesian Statistics has been improved and perfected, and now it can be used to solve problems that Classical Statistics failed to solve. This paper summarizes Bayesian Statistics’ history, concepts and applications, which are illustrated in five parts: the history of Bayesian Statistics, the weakness of Classical Statistics, Bayesian Theory and its development and applications. The first two parts make a comparison between Bayesian Statistics and Classical Statistics in a macroscopic aspect. And the last three parts focus on Bayesian Theory in specific -- from introducing some particular Bayesian Statistics’ concepts to listing their development and finally their applications.

Bayesian demography 250 years after Bayes

PubMed Central

Bijak, Jakub; Bryant, John

2016-01-01

Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms. PMID:26902889

A comparison of machine learning and Bayesian modelling for molecular serotyping.

PubMed

Newton, Richard; Wernisch, Lorenz

2017-08-11

Streptococcus pneumoniae is a human pathogen that is a major cause of infant mortality. Identifying the pneumococcal serotype is an important step in monitoring the impact of vaccines used to protect against disease. Genomic microarrays provide an effective method for molecular serotyping. Previously we developed an empirical Bayesian model for the classification of serotypes from a molecular serotyping array. With only few samples available, a model driven approach was the only option. In the meanwhile, several thousand samples have been made available to us, providing an opportunity to investigate serotype classification by machine learning methods, which could complement the Bayesian model. We compare the performance of the original Bayesian model with two machine learning algorithms: Gradient Boosting Machines and Random Forests. We present our results as an example of a generic strategy whereby a preliminary probabilistic model is complemented or replaced by a machine learning classifier once enough data are available. Despite the availability of thousands of serotyping arrays, a problem encountered when applying machine learning methods is the lack of training data containing mixtures of serotypes; due to the large number of possible combinations. Most of the available training data comprises samples with only a single serotype. To overcome the lack of training data we implemented an iterative analysis, creating artificial training data of serotype mixtures by combining raw data from single serotype arrays. With the enhanced training set the machine learning algorithms out perform the original Bayesian model. However, for serotypes currently lacking sufficient training data the best performing implementation was a combination of the results of the Bayesian Model and the Gradient Boosting Machine. As well as being an effective method for classifying biological data, machine learning can also be used as an efficient method for revealing subtle biological insights, which we illustrate with an example.

Source Detection with Bayesian Inference on ROSAT All-Sky Survey Data Sample

NASA Astrophysics Data System (ADS)

Guglielmetti, F.; Voges, W.; Fischer, R.; Boese, G.; Dose, V.

2004-07-01

We employ Bayesian inference for the joint estimation of sources and background on ROSAT All-Sky Survey (RASS) data. The probabilistic method allows for detection improvement of faint extended celestial sources compared to the Standard Analysis Software System (SASS). Background maps were estimated in a single step together with the detection of sources without pixel censoring. Consistent uncertainties of background and sources are provided. The source probability is evaluated for single pixels as well as for pixel domains to enhance source detection of weak and extended sources.

A Bayesian network model for predicting pregnancy after in vitro fertilization.

PubMed

Corani, G; Magli, C; Giusti, A; Gianaroli, L; Gambardella, L M

2013-11-01

We present a Bayesian network model for predicting the outcome of in vitro fertilization (IVF). The problem is characterized by a particular missingness process; we propose a simple but effective averaging approach which improves parameter estimates compared to the traditional MAP estimation. We present results with generated data and the analysis of a real data set. Moreover, we assess by means of a simulation study the effectiveness of the model in supporting the selection of the embryos to be transferred. © 2013 Elsevier Ltd. All rights reserved.

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1972-01-01

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

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

NASA Astrophysics Data System (ADS)

Zhu, Yi-Chen; Au, Siu-Kui

2018-01-01

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

Markov Random Fields, Stochastic Quantization and Image Analysis

DTIC Science & Technology

1990-01-01

Markov random fields based on the lattice Z2 have been extensively used in image analysis in a Bayesian framework as a-priori models for the...of Image Analysis can be given some fundamental justification then there is a remarkable connection between Probabilistic Image Analysis , Statistical Mechanics and Lattice-based Euclidean Quantum Field Theory.

Hybrid ICA-Bayesian network approach reveals distinct effective connectivity differences in schizophrenia.

PubMed

Kim, D; Burge, J; Lane, T; Pearlson, G D; Kiehl, K A; Calhoun, V D

2008-10-01

We utilized a discrete dynamic Bayesian network (dDBN) approach (Burge, J., Lane, T., Link, H., Qiu, S., Clark, V.P., 2007. Discrete dynamic Bayesian network analysis of fMRI data. Hum Brain Mapp.) to determine differences in brain regions between patients with schizophrenia and healthy controls on a measure of effective connectivity, termed the approximate conditional likelihood score (ACL) (Burge, J., Lane, T., 2005. Learning Class-Discriminative Dynamic Bayesian Networks. Proceedings of the International Conference on Machine Learning, Bonn, Germany, pp. 97-104.). The ACL score represents a class-discriminative measure of effective connectivity by measuring the relative likelihood of the correlation between brain regions in one group versus another. The algorithm is capable of finding non-linear relationships between brain regions because it uses discrete rather than continuous values and attempts to model temporal relationships with a first-order Markov and stationary assumption constraint (Papoulis, A., 1991. Probability, random variables, and stochastic processes. McGraw-Hill, New York.). Since Bayesian networks are overly sensitive to noisy data, we introduced an independent component analysis (ICA) filtering approach that attempted to reduce the noise found in fMRI data by unmixing the raw datasets into a set of independent spatial component maps. Components that represented noise were removed and the remaining components reconstructed into the dimensions of the original fMRI datasets. We applied the dDBN algorithm to a group of 35 patients with schizophrenia and 35 matched healthy controls using an ICA filtered and unfiltered approach. We determined that filtering the data significantly improved the magnitude of the ACL score. Patients showed the greatest ACL scores in several regions, most markedly the cerebellar vermis and hemispheres. Our findings suggest that schizophrenia patients exhibit weaker connectivity than healthy controls in multiple regions, including bilateral temporal, frontal, and cerebellar regions during an auditory paradigm.

Using protein-protein interactions for refining gene networks estimated from microarray data by Bayesian networks.

PubMed

Nariai, N; Kim, S; Imoto, S; Miyano, S

2004-01-01

We propose a statistical method to estimate gene networks from DNA microarray data and protein-protein interactions. Because physical interactions between proteins or multiprotein complexes are likely to regulate biological processes, using only mRNA expression data is not sufficient for estimating a gene network accurately. Our method adds knowledge about protein-protein interactions to the estimation method of gene networks under a Bayesian statistical framework. In the estimated gene network, a protein complex is modeled as a virtual node based on principal component analysis. We show the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae cell cycle data. The proposed method improves the accuracy of the estimated gene networks, and successfully identifies some biological facts.

Charged particle tracking without magnetic field: Optimal measurement of track momentum by a Bayesian analysis of the multiple measurements of deflections due to multiple scattering

NASA Astrophysics Data System (ADS)

Frosini, Mikael; Bernard, Denis

2017-09-01

We revisit the precision of the measurement of track parameters (position, angle) with optimal methods in the presence of detector resolution, multiple scattering and zero magnetic field. We then obtain an optimal estimator of the track momentum by a Bayesian analysis of the filtering innovations of a series of Kalman filters applied to the track. This work could pave the way to the development of autonomous high-performance gas time-projection chambers (TPC) or silicon wafer γ-ray space telescopes and be a powerful guide in the optimization of the design of the multi-kilo-ton liquid argon TPCs that are under development for neutrino studies.

System Analysis by Mapping a Fault-tree into a Bayesian-network

NASA Astrophysics Data System (ADS)

Sheng, B.; Deng, C.; Wang, Y. H.; Tang, L. H.

2018-05-01

In view of the limitations of fault tree analysis in reliability assessment, Bayesian Network (BN) has been studied as an alternative technology. After a brief introduction to the method for mapping a Fault Tree (FT) into an equivalent BN, equations used to calculate the structure importance degree, the probability importance degree and the critical importance degree are presented. Furthermore, the correctness of these equations is proved mathematically. Combining with an aircraft landing gear’s FT, an equivalent BN is developed and analysed. The results show that richer and more accurate information have been achieved through the BN method than the FT, which demonstrates that the BN is a superior technique in both reliability assessment and fault diagnosis.

Research on Risk Manage of Power Construction Project Based on Bayesian Network

NASA Astrophysics Data System (ADS)

Jia, Zhengyuan; Fan, Zhou; Li, Yong

With China's changing economic structure and increasingly fierce competition in the market, the uncertainty and risk factors in the projects of electric power construction are increasingly complex, the projects will face huge risks or even fail if we don't consider or ignore these risk factors. Therefore, risk management in the projects of electric power construction plays an important role. The paper emphatically elaborated the influence of cost risk in electric power projects through study overall risk management and the behavior of individual in risk management, and introduced the Bayesian network to the project risk management. The paper obtained the order of key factors according to both scene analysis and causal analysis for effective risk management.

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.

Bayesian multivariate hierarchical transformation models for ROC analysis.

PubMed

O'Malley, A James; Zou, Kelly H

2006-02-15

A Bayesian multivariate hierarchical transformation model (BMHTM) is developed for receiver operating characteristic (ROC) curve analysis based on clustered continuous diagnostic outcome data with covariates. Two special features of this model are that it incorporates non-linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed. The mean, variance, and transformation components are all modelled parametrically, enabling a wide range of inferences. The general framework is illustrated by focusing on two problems: (1) analysis of the diagnostic accuracy of a covariate-dependent univariate test outcome requiring a Box-Cox transformation within each cluster to map the test outcomes to a common family of distributions; (2) development of an optimal composite diagnostic test using multivariate clustered outcome data. In the second problem, the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome. The proposed methodology is illustrated on prostate cancer biopsy data from a multi-centre clinical trial.

Bayesian multivariate hierarchical transformation models for ROC analysis

PubMed Central

O'Malley, A. James; Zou, Kelly H.

2006-01-01

SUMMARY A Bayesian multivariate hierarchical transformation model (BMHTM) is developed for receiver operating characteristic (ROC) curve analysis based on clustered continuous diagnostic outcome data with covariates. Two special features of this model are that it incorporates non-linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed. The mean, variance, and transformation components are all modelled parametrically, enabling a wide range of inferences. The general framework is illustrated by focusing on two problems: (1) analysis of the diagnostic accuracy of a covariate-dependent univariate test outcome requiring a Box–Cox transformation within each cluster to map the test outcomes to a common family of distributions; (2) development of an optimal composite diagnostic test using multivariate clustered outcome data. In the second problem, the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome. The proposed methodology is illustrated on prostate cancer biopsy data from a multi-centre clinical trial. PMID:16217836

A Rational Analysis of the Acquisition of Multisensory Representations

ERIC Educational Resources Information Center

Yildirim, Ilker; Jacobs, Robert A.

2012-01-01

How do people learn multisensory, or amodal, representations, and what consequences do these representations have for perceptual performance? We address this question by performing a rational analysis of the problem of learning multisensory representations. This analysis makes use of a Bayesian nonparametric model that acquires latent multisensory…

BAT - The Bayesian analysis toolkit

NASA Astrophysics Data System (ADS)

Caldwell, Allen; Kollár, Daniel; Kröninger, Kevin

2009-11-01

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

Bayesian Propensity Score Analysis: Simulation and Case Study

ERIC Educational Resources Information Center

Kaplan, David; Chen, Cassie J. S.

2011-01-01

Propensity score analysis (PSA) has been used in a variety of settings, such as education, epidemiology, and sociology. Most typically, propensity score analysis has been implemented within the conventional frequentist perspective of statistics. This perspective, as is well known, does not account for uncertainty in either the parameters of the…

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

The effect of iconicity of visual displays on statistical reasoning: evidence in favor of the null hypothesis.

PubMed

Sirota, Miroslav; Kostovičová, Lenka; Juanchich, Marie

2014-08-01

Knowing which properties of visual displays facilitate statistical reasoning bears practical and theoretical implications. Therefore, we studied the effect of one property of visual diplays - iconicity (i.e., the resemblance of a visual sign to its referent) - on Bayesian reasoning. Two main accounts of statistical reasoning predict different effect of iconicity on Bayesian reasoning. The ecological-rationality account predicts a positive iconicity effect, because more highly iconic signs resemble more individuated objects, which tap better into an evolutionary-designed frequency-coding mechanism that, in turn, facilitates Bayesian reasoning. The nested-sets account predicts a null iconicity effect, because iconicity does not affect the salience of a nested-sets structure-the factor facilitating Bayesian reasoning processed by a general reasoning mechanism. In two well-powered experiments (N = 577), we found no support for a positive iconicity effect across different iconicity levels that were manipulated in different visual displays (meta-analytical overall effect: log OR = -0.13, 95% CI [-0.53, 0.28]). A Bayes factor analysis provided strong evidence in favor of the null hypothesis-the null iconicity effect. Thus, these findings corroborate the nested-sets rather than the ecological-rationality account of statistical reasoning.

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

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

Bayesian Computation Emerges in Generic Cortical Microcircuits through Spike-Timing-Dependent Plasticity

PubMed Central

Nessler, Bernhard; Pfeiffer, Michael; Buesing, Lars; Maass, Wolfgang

2013-01-01

The principles by which networks of neurons compute, and how spike-timing dependent plasticity (STDP) of synaptic weights generates and maintains their computational function, are unknown. Preceding work has shown that soft winner-take-all (WTA) circuits, where pyramidal neurons inhibit each other via interneurons, are a common motif of cortical microcircuits. We show through theoretical analysis and computer simulations that Bayesian computation is induced in these network motifs through STDP in combination with activity-dependent changes in the excitability of neurons. The fundamental components of this emergent Bayesian computation are priors that result from adaptation of neuronal excitability and implicit generative models for hidden causes that are created in the synaptic weights through STDP. In fact, a surprising result is that STDP is able to approximate a powerful principle for fitting such implicit generative models to high-dimensional spike inputs: Expectation Maximization. Our results suggest that the experimentally observed spontaneous activity and trial-to-trial variability of cortical neurons are essential features of their information processing capability, since their functional role is to represent probability distributions rather than static neural codes. Furthermore it suggests networks of Bayesian computation modules as a new model for distributed information processing in the cortex. PMID:23633941

Bayesian Inference of Physics Parameters in the DIII-D Charge-Exchange Recombination Spectroscopy System

NASA Astrophysics Data System (ADS)

Bowman, C.; Gibson, K. J.; La Haye, R. J.; Groebner, R. J.; Taylor, N. Z.; Grierson, B. A.

2014-10-01

A Bayesian inference framework has been developed for the DIII-D charge-exchange recombination (CER) system, capable of computing probability distribution functions (PDFs) for desired parameters. CER is a key diagnostic system at DIII-D, measuring important physics parameters such as plasma rotation and impurity ion temperature. This work is motivated by a case in which the CER system was used to probe the plasma rotation radial profile around an m/n = 2/1 tearing mode island rotating at ~ 1 kHz. Due to limited resolution in the tearing mode phase and short integration time, it has proven challenging to observe the structure of the rotation profile across the island. We seek to solve this problem by using the Bayesian framework to improve the estimation accuracy of the plasma rotation, helping to reveal details of how it is perturbed in the magnetic island vicinity. Examples of the PDFs obtained through the Bayesian framework will be presented, and compared with results from a conventional least-squares analysis of the CER data. Work supported by the US DOE under DE-FC02-04ER54698 and DE-AC02-09CH11466.

Comparison Analysis of Recognition Algorithms of Forest-Cover Objects on Hyperspectral Air-Borne and Space-Borne Images

NASA Astrophysics Data System (ADS)

Kozoderov, V. V.; Kondranin, T. V.; Dmitriev, E. V.

2017-12-01

The basic model for the recognition of natural and anthropogenic objects using their spectral and textural features is described in the problem of hyperspectral air-borne and space-borne imagery processing. The model is based on improvements of the Bayesian classifier that is a computational procedure of statistical decision making in machine-learning methods of pattern recognition. The principal component method is implemented to decompose the hyperspectral measurements on the basis of empirical orthogonal functions. Application examples are shown of various modifications of the Bayesian classifier and Support Vector Machine method. Examples are provided of comparing these classifiers and a metrical classifier that operates on finding the minimal Euclidean distance between different points and sets in the multidimensional feature space. A comparison is also carried out with the " K-weighted neighbors" method that is close to the nonparametric Bayesian classifier.

Neglected chaos in international stock markets: Bayesian analysis of the joint return-volatility dynamical system

NASA Astrophysics Data System (ADS)

Tsionas, Mike G.; Michaelides, Panayotis G.

2017-09-01

We use a novel Bayesian inference procedure for the Lyapunov exponent in the dynamical system of returns and their unobserved volatility. In the dynamical system, computation of largest Lyapunov exponent by traditional methods is impossible as the stochastic nature has to be taken explicitly into account due to unobserved volatility. We apply the new techniques to daily stock return data for a group of six countries, namely USA, UK, Switzerland, Netherlands, Germany and France, from 2003 to 2014, by means of Sequential Monte Carlo for Bayesian inference. The evidence points to the direction that there is indeed noisy chaos both before and after the recent financial crisis. However, when a much simpler model is examined where the interaction between returns and volatility is not taken into consideration jointly, the hypothesis of chaotic dynamics does not receive much support by the data ("neglected chaos").

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

USGS Publications Warehouse

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

2014-01-01

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

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

PubMed

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence

2012-12-01

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

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

PubMed

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

2008-04-01

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

A Bayesian sequential processor approach to spectroscopic portal system decisions

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

Sale, K; Candy, J; Breitfeller, E

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

Overlapping community detection in weighted networks via a Bayesian approach

NASA Astrophysics Data System (ADS)

Chen, Yi; Wang, Xiaolong; Xiang, Xin; Tang, Buzhou; Chen, Qingcai; Fan, Shixi; Bu, Junzhao

2017-02-01

Complex networks as a powerful way to represent complex systems have been widely studied during the past several years. One of the most important tasks of complex network analysis is to detect communities embedded in networks. In the real world, weighted networks are very common and may contain overlapping communities where a node is allowed to belong to multiple communities. In this paper, we propose a novel Bayesian approach, called the Bayesian mixture network (BMN) model, to detect overlapping communities in weighted networks. The advantages of our method are (i) providing soft-partition solutions in weighted networks; (ii) providing soft memberships, which quantify 'how strongly' a node belongs to a community. Experiments on a large number of real and synthetic networks show that our model has the ability in detecting overlapping communities in weighted networks and is competitive with other state-of-the-art models at shedding light on community partition.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

Bayesian spatio-temporal modeling of particulate matter concentrations in Peninsular Malaysia

NASA Astrophysics Data System (ADS)

Manga, Edna; Awang, Norhashidah

2016-06-01

This article presents an application of a Bayesian spatio-temporal Gaussian process (GP) model on particulate matter concentrations from Peninsular Malaysia. We analyze daily PM10 concentration levels from 35 monitoring sites in June and July 2011. The spatiotemporal model set in a Bayesian hierarchical framework allows for inclusion of informative covariates, meteorological variables and spatiotemporal interactions. Posterior density estimates of the model parameters are obtained by Markov chain Monte Carlo methods. Preliminary data analysis indicate information on PM10 levels at sites classified as industrial locations could explain part of the space time variations. We include the site-type indicator in our modeling efforts. Results of the parameter estimates for the fitted GP model show significant spatio-temporal structure and positive effect of the location-type explanatory variable. We also compute some validation criteria for the out of sample sites that show the adequacy of the model for predicting PM10 at unmonitored sites.

F-MAP: A Bayesian approach to infer the gene regulatory network using external hints

PubMed Central

Shahdoust, Maryam; Mahjub, Hossein; Sadeghi, Mehdi

2017-01-01

The Common topological features of related species gene regulatory networks suggest reconstruction of the network of one species by using the further information from gene expressions profile of related species. We present an algorithm to reconstruct the gene regulatory network named; F-MAP, which applies the knowledge about gene interactions from related species. Our algorithm sets a Bayesian framework to estimate the precision matrix of one species microarray gene expressions dataset to infer the Gaussian Graphical model of the network. The conjugate Wishart prior is used and the information from related species is applied to estimate the hyperparameters of the prior distribution by using the factor analysis. Applying the proposed algorithm on six related species of drosophila shows that the precision of reconstructed networks is improved considerably compared to the precision of networks constructed by other Bayesian approaches. PMID:28938012

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

Jesus, J.F.; Valentim, R.; Andrade-Oliveira, F., E-mail: jfjesus@itapeva.unesp.br, E-mail: valentim.rodolfo@unifesp.br, E-mail: felipe.oliveira@port.ac.uk

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 Γmore » = 3α H {sub 0} 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.« less

Modular analysis of the probabilistic genetic interaction network.

PubMed

Hou, Lin; Wang, Lin; Qian, Minping; Li, Dong; Tang, Chao; Zhu, Yunping; Deng, Minghua; Li, Fangting

2011-03-15

Epistatic Miniarray Profiles (EMAP) has enabled the mapping of large-scale genetic interaction networks; however, the quantitative information gained from EMAP cannot be fully exploited since the data are usually interpreted as a discrete network based on an arbitrary hard threshold. To address such limitations, we adopted a mixture modeling procedure to construct a probabilistic genetic interaction network and then implemented a Bayesian approach to identify densely interacting modules in the probabilistic network. Mixture modeling has been demonstrated as an effective soft-threshold technique of EMAP measures. The Bayesian approach was applied to an EMAP dataset studying the early secretory pathway in Saccharomyces cerevisiae. Twenty-seven modules were identified, and 14 of those were enriched by gold standard functional gene sets. We also conducted a detailed comparison with state-of-the-art algorithms, hierarchical cluster and Markov clustering. The experimental results show that the Bayesian approach outperforms others in efficiently recovering biologically significant modules.

Bayesian Analysis of the Power Spectrum of the Cosmic Microwave Background

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Eriksen, H. K.; O'Dwyer, I. J.; Wandelt, B. D.

2005-01-01

There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background. The sky, when viewed in the microwave, is very uniform, with a nearly perfect blackbody spectrum at 2.7 degrees. Very small amplitude brightness fluctuations (to one part in a million!!) trace small density perturbations in the early universe (roughly 300,000 years after the Big Bang), which later grow through gravitational instability to the large-scale structure seen in redshift surveys... In this talk, I will discuss a Bayesian formulation of this problem; discuss a Gibbs sampling approach to numerically sampling from the Bayesian posterior, and the application of this approach to the first-year data from the Wilkinson Microwave Anisotropy Probe. I will also comment on recent algorithmic developments for this approach to be tractable for the even more massive data set to be returned from the Planck satellite.

BATMAN: Bayesian Technique for Multi-image Analysis

NASA Astrophysics Data System (ADS)

Casado, J.; Ascasibar, Y.; García-Benito, R.; Guidi, G.; Choudhury, O. S.; Bellocchi, E.; Sánchez, S. F.; Díaz, A. I.

2017-04-01

This paper describes the Bayesian Technique for Multi-image Analysis (BATMAN), a novel image-segmentation technique based on Bayesian statistics that characterizes any astronomical data set containing spatial information and performs a tessellation based on the measurements and errors provided as input. The algorithm iteratively merges spatial elements as long as they are statistically consistent with carrying the same information (I.e. identical signal within the errors). We illustrate its operation and performance with a set of test cases including both synthetic and real integral-field spectroscopic data. The output segmentations adapt to the underlying spatial structure, regardless of its morphology and/or the statistical properties of the noise. The quality of the recovered signal represents an improvement with respect to the input, especially in regions with low signal-to-noise ratio. However, the algorithm may be sensitive to small-scale random fluctuations, and its performance in presence of spatial gradients is limited. Due to these effects, errors may be underestimated by as much as a factor of 2. Our analysis reveals that the algorithm prioritizes conservation of all the statistically significant information over noise reduction, and that the precise choice of the input data has a crucial impact on the results. Hence, the philosophy of BaTMAn is not to be used as a 'black box' to improve the signal-to-noise ratio, but as a new approach to characterize spatially resolved data prior to its analysis. The source code is publicly available at http://astro.ft.uam.es/SELGIFS/BaTMAn.

Uncertainty Reduction using Bayesian Inference and Sensitivity Analysis: A Sequential Approach to the NASA Langley Uncertainty Quantification Challenge

NASA Technical Reports Server (NTRS)

Sankararaman, Shankar

2016-01-01

This paper presents a computational framework for uncertainty characterization and propagation, and sensitivity analysis under the presence of aleatory and epistemic un- certainty, and develops a rigorous methodology for efficient refinement of epistemic un- certainty by identifying important epistemic variables that significantly affect the overall performance of an engineering system. The proposed methodology is illustrated using the NASA Langley Uncertainty Quantification Challenge (NASA-LUQC) problem that deals with uncertainty analysis of a generic transport model (GTM). First, Bayesian inference is used to infer subsystem-level epistemic quantities using the subsystem-level model and corresponding data. Second, tools of variance-based global sensitivity analysis are used to identify four important epistemic variables (this limitation specified in the NASA-LUQC is reflective of practical engineering situations where not all epistemic variables can be refined due to time/budget constraints) that significantly affect system-level performance. The most significant contribution of this paper is the development of the sequential refine- ment methodology, where epistemic variables for refinement are not identified all-at-once. Instead, only one variable is first identified, and then, Bayesian inference and global sensi- tivity calculations are repeated to identify the next important variable. This procedure is continued until all 4 variables are identified and the refinement in the system-level perfor- mance is computed. The advantages of the proposed sequential refinement methodology over the all-at-once uncertainty refinement approach are explained, and then applied to the NASA Langley Uncertainty Quantification Challenge problem.

Cyber-T web server: differential analysis of high-throughput data.

PubMed

Kayala, Matthew A; Baldi, Pierre

2012-07-01

The Bayesian regularization method for high-throughput differential analysis, described in Baldi and Long (A Bayesian framework for the analysis of microarray expression data: regularized t-test and statistical inferences of gene changes. Bioinformatics 2001: 17: 509-519) and implemented in the Cyber-T web server, is one of the most widely validated. Cyber-T implements a t-test using a Bayesian framework to compute a regularized variance of the measurements associated with each probe under each condition. This regularized estimate is derived by flexibly combining the empirical measurements with a prior, or background, derived from pooling measurements associated with probes in the same neighborhood. This approach flexibly addresses problems associated with low replication levels and technology biases, not only for DNA microarrays, but also for other technologies, such as protein arrays, quantitative mass spectrometry and next-generation sequencing (RNA-seq). Here we present an update to the Cyber-T web server, incorporating several useful new additions and improvements. Several preprocessing data normalization options including logarithmic and (Variance Stabilizing Normalization) VSN transforms are included. To augment two-sample t-tests, a one-way analysis of variance is implemented. Several methods for multiple tests correction, including standard frequentist methods and a probabilistic mixture model treatment, are available. Diagnostic plots allow visual assessment of the results. The web server provides comprehensive documentation and example data sets. The Cyber-T web server, with R source code and data sets, is publicly available at http://cybert.ics.uci.edu/.

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.

BM-Map: Bayesian Mapping of Multireads for Next-Generation Sequencing Data

PubMed Central

Ji, Yuan; Xu, Yanxun; Zhang, Qiong; Tsui, Kam-Wah; Yuan, Yuan; Norris, Clift; Liang, Shoudan; Liang, Han

2011-01-01

Summary Next-generation sequencing (NGS) technology generates millions of short reads, which provide valuable information for various aspects of cellular activities and biological functions. A key step in NGS applications (e.g., RNA-Seq) is to map short reads to correct genomic locations within the source genome. While most reads are mapped to a unique location, a significant proportion of reads align to multiple genomic locations with equal or similar numbers of mismatches; these are called multireads. The ambiguity in mapping the multireads may lead to bias in downstream analyses. Currently, most practitioners discard the multireads in their analysis, resulting in a loss of valuable information, especially for the genes with similar sequences. To refine the read mapping, we develop a Bayesian model that computes the posterior probability of mapping a multiread to each competing location. The probabilities are used for downstream analyses, such as the quantification of gene expression. We show through simulation studies and RNA-Seq analysis of real life data that the Bayesian method yields better mapping than the current leading methods. We provide a C++ program for downloading that is being packaged into a user-friendly software. PMID:21517792

Uncertainty analysis of depth predictions from seismic reflection data using Bayesian statistics

NASA Astrophysics Data System (ADS)

Michelioudakis, Dimitrios G.; Hobbs, Richard W.; Caiado, Camila C. S.

2018-03-01

Estimating the depths of target horizons from seismic reflection data is an important task in exploration geophysics. To constrain these depths we need a reliable and accurate velocity model. Here, we build an optimum 2D seismic reflection data processing flow focused on pre - stack deghosting filters and velocity model building and apply Bayesian methods, including Gaussian process emulation and Bayesian History Matching (BHM), to estimate the uncertainties of the depths of key horizons near the borehole DSDP-258 located in the Mentelle Basin, south west of Australia, and compare the results with the drilled core from that well. Following this strategy, the tie between the modelled and observed depths from DSDP-258 core was in accordance with the ± 2σ posterior credibility intervals and predictions for depths to key horizons were made for the two new drill sites, adjacent the existing borehole of the area. The probabilistic analysis allowed us to generate multiple realizations of pre-stack depth migrated images, these can be directly used to better constrain interpretation and identify potential risk at drill sites. The method will be applied to constrain the drilling targets for the upcoming International Ocean Discovery Program (IODP), leg 369.

Uncertainty analysis of depth predictions from seismic reflection data using Bayesian statistics

NASA Astrophysics Data System (ADS)

Michelioudakis, Dimitrios G.; Hobbs, Richard W.; Caiado, Camila C. S.

2018-06-01

Estimating the depths of target horizons from seismic reflection data is an important task in exploration geophysics. To constrain these depths we need a reliable and accurate velocity model. Here, we build an optimum 2-D seismic reflection data processing flow focused on pre-stack deghosting filters and velocity model building and apply Bayesian methods, including Gaussian process emulation and Bayesian History Matching, to estimate the uncertainties of the depths of key horizons near the Deep Sea Drilling Project (DSDP) borehole 258 (DSDP-258) located in the Mentelle Basin, southwest of Australia, and compare the results with the drilled core from that well. Following this strategy, the tie between the modelled and observed depths from DSDP-258 core was in accordance with the ±2σ posterior credibility intervals and predictions for depths to key horizons were made for the two new drill sites, adjacent to the existing borehole of the area. The probabilistic analysis allowed us to generate multiple realizations of pre-stack depth migrated images, these can be directly used to better constrain interpretation and identify potential risk at drill sites. The method will be applied to constrain the drilling targets for the upcoming International Ocean Discovery Program, leg 369.

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

PubMed Central

2011-01-01

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

Bayesian analysis of U.S. hurricane climate

USGS Publications Warehouse

Elsner, James B.; Bossak, Brian H.

2001-01-01

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

GO-Bayes: Gene Ontology-based overrepresentation analysis using a Bayesian approach.

PubMed

Zhang, Song; Cao, Jing; Kong, Y Megan; Scheuermann, Richard H

2010-04-01

A typical approach for the interpretation of high-throughput experiments, such as gene expression microarrays, is to produce groups of genes based on certain criteria (e.g. genes that are differentially expressed). To gain more mechanistic insights into the underlying biology, overrepresentation analysis (ORA) is often conducted to investigate whether gene sets associated with particular biological functions, for example, as represented by Gene Ontology (GO) annotations, are statistically overrepresented in the identified gene groups. However, the standard ORA, which is based on the hypergeometric test, analyzes each GO term in isolation and does not take into account the dependence structure of the GO-term hierarchy. We have developed a Bayesian approach (GO-Bayes) to measure overrepresentation of GO terms that incorporates the GO dependence structure by taking into account evidence not only from individual GO terms, but also from their related terms (i.e. parents, children, siblings, etc.). The Bayesian framework borrows information across related GO terms to strengthen the detection of overrepresentation signals. As a result, this method tends to identify sets of closely related GO terms rather than individual isolated GO terms. The advantage of the GO-Bayes approach is demonstrated with a simulation study and an application example.

Calculating shock arrival in expansion tubes and shock tunnels using Bayesian changepoint analysis

NASA Astrophysics Data System (ADS)

James, Christopher M.; Bourke, Emily J.; Gildfind, David E.

2018-06-01

To understand the flow conditions generated in expansion tubes and shock tunnels, shock speeds are generally calculated based on shock arrival times at high-frequency wall-mounted pressure transducers. These calculations require that the shock arrival times are obtained accurately. This can be non-trivial for expansion tubes especially because pressure rises may be small and shock speeds high. Inaccurate shock arrival times can be a significant source of uncertainty. To help address this problem, this paper investigates two separate but complimentary techniques. Principally, it proposes using a Bayesian changepoint detection method to automatically calculate shock arrival, potentially reducing error and simplifying the shock arrival finding process. To compliment this, a technique for filtering the raw data without losing the shock arrival time is also presented and investigated. To test the validity of the proposed techniques, tests are performed using both a theoretical step change with different levels of noise and real experimental data. It was found that with conditions added to ensure that a real shock arrival time was found, the Bayesian changepoint analysis method was able to automatically find the shock arrival time, even for noisy signals.

Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

NASA Astrophysics Data System (ADS)

Li, Zhiqiang; Xu, Tingxue; Gu, Junyuan; Dong, Qi; Fu, Linyu

2018-04-01

This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables, can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit.

BASiCS: Bayesian Analysis of Single-Cell Sequencing Data

PubMed Central

Vallejos, Catalina A.; Marioni, John C.; Richardson, Sylvia

2015-01-01

Single-cell mRNA sequencing can uncover novel cell-to-cell heterogeneity in gene expression levels in seemingly homogeneous populations of cells. However, these experiments are prone to high levels of unexplained technical noise, creating new challenges for identifying genes that show genuine heterogeneous expression within the population of cells under study. BASiCS (Bayesian Analysis of Single-Cell Sequencing data) is an integrated Bayesian hierarchical model where: (i) cell-specific normalisation constants are estimated as part of the model parameters, (ii) technical variability is quantified based on spike-in genes that are artificially introduced to each analysed cell’s lysate and (iii) the total variability of the expression counts is decomposed into technical and biological components. BASiCS also provides an intuitive detection criterion for highly (or lowly) variable genes within the population of cells under study. This is formalised by means of tail posterior probabilities associated to high (or low) biological cell-to-cell variance contributions, quantities that can be easily interpreted by users. We demonstrate our method using gene expression measurements from mouse Embryonic Stem Cells. Cross-validation and meaningful enrichment of gene ontology categories within genes classified as highly (or lowly) variable supports the efficacy of our approach. PMID:26107944

BASiCS: Bayesian Analysis of Single-Cell Sequencing Data.

PubMed

Vallejos, Catalina A; Marioni, John C; Richardson, Sylvia

2015-06-01

Single-cell mRNA sequencing can uncover novel cell-to-cell heterogeneity in gene expression levels in seemingly homogeneous populations of cells. However, these experiments are prone to high levels of unexplained technical noise, creating new challenges for identifying genes that show genuine heterogeneous expression within the population of cells under study. BASiCS (Bayesian Analysis of Single-Cell Sequencing data) is an integrated Bayesian hierarchical model where: (i) cell-specific normalisation constants are estimated as part of the model parameters, (ii) technical variability is quantified based on spike-in genes that are artificially introduced to each analysed cell's lysate and (iii) the total variability of the expression counts is decomposed into technical and biological components. BASiCS also provides an intuitive detection criterion for highly (or lowly) variable genes within the population of cells under study. This is formalised by means of tail posterior probabilities associated to high (or low) biological cell-to-cell variance contributions, quantities that can be easily interpreted by users. We demonstrate our method using gene expression measurements from mouse Embryonic Stem Cells. Cross-validation and meaningful enrichment of gene ontology categories within genes classified as highly (or lowly) variable supports the efficacy of our approach.

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

NASA Astrophysics Data System (ADS)

Taylor, Stephen; Ellis, Justin; Gair, Jonathan

2014-11-01

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

Bayesian networks of age estimation and classification based on dental evidence: A study on the third molar mineralization.

PubMed

Sironi, Emanuele; Pinchi, Vilma; Pradella, Francesco; Focardi, Martina; Bozza, Silvia; Taroni, Franco

2018-04-01

Not only does the Bayesian approach offer a rational and logical environment for evidence evaluation in a forensic framework, but it also allows scientists to coherently deal with uncertainty related to a collection of multiple items of evidence, due to its flexible nature. Such flexibility might come at the expense of elevated computational complexity, which can be handled by using specific probabilistic graphical tools, namely Bayesian networks. In the current work, such probabilistic tools are used for evaluating dental evidence related to the development of third molars. A set of relevant properties characterizing the graphical models are discussed and Bayesian networks are implemented to deal with the inferential process laying beyond the estimation procedure, as well as to provide age estimates. Such properties include operationality, flexibility, coherence, transparence and sensitivity. A data sample composed of Italian subjects was employed for the analysis; results were in agreement with previous studies in terms of point estimate and age classification. The influence of the prior probability elicitation in terms of Bayesian estimate and classifies was also analyzed. Findings also supported the opportunity to take into consideration multiple teeth in the evaluative procedure, since it can be shown this results in an increased robustness towards the prior probability elicitation process, as well as in more favorable outcomes from a forensic perspective. Copyright © 2018 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

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 Bayesian approach to reliability and confidence

NASA Technical Reports Server (NTRS)

Barnes, Ron

1989-01-01

The historical evolution of NASA's interest in quantitative measures of reliability assessment is outlined. The introduction of some quantitative methodologies into the Vehicle Reliability Branch of the Safety, Reliability and Quality Assurance (SR and QA) Division at Johnson Space Center (JSC) was noted along with the development of the Extended Orbiter Duration--Weakest Link study which will utilize quantitative tools for a Bayesian statistical analysis. Extending the earlier work of NASA sponsor, Richard Heydorn, researchers were able to produce a consistent Bayesian estimate for the reliability of a component and hence by a simple extension for a system of components in some cases where the rate of failure is not constant but varies over time. Mechanical systems in general have this property since the reliability usually decreases markedly as the parts degrade over time. While they have been able to reduce the Bayesian estimator to a simple closed form for a large class of such systems, the form for the most general case needs to be attacked by the computer. Once a table is generated for this form, researchers will have a numerical form for the general solution. With this, the corresponding probability statements about the reliability of a system can be made in the most general setting. Note that the utilization of uniform Bayesian priors represents a worst case scenario in the sense that as researchers incorporate more expert opinion into the model, they will be able to improve the strength of the probability calculations.

Aphis (Hemiptera: Aphididae) species groups found in the Midwestern United States and their contribution to the phylogenetic knowledge of the genus.

PubMed

Lagos, Doris M; Voegtlin, David J; Coeur d'acier, Armelle; Giordano, Rosanna

2014-06-01

A phylogeny of the genus Aphis Linnaeus, 1 758 was built primarily from specimens collected in the Midwest of the United States. A data matrix was constructed with 68 species and 41 morphological characters with respective character states of alate and apterous viviparous females. Dendrogram topologies of analyses performed using UPGMA (Unweighted Pair Group Method with Arithmetic Mean), Maximum Parsimony and Bayesian analysis of Cytochrome Oxidase I, Elongation Factor 1-α and primary endosymbiont Buchnera aphidicola 16S sequences were not congruent. Bayesian analysis strongly supported most terminal nodes of the phylogenetic trees. The phylogeny was strongly supported by EF1-α, and analysis of COI and EF1-α molecular data combined with morphological characters. It was not supported by single analysis of COI or Buchnera aphidicola 16S. Results from the Bayesian phylogeny show 4 main species groups: asclepiadis, fabae, gossypii, and middletonii. Results place Aphis and species of the genera Protaphis Börner, 1952, Toxoptera Koch, and Xerobion Nevsky, 1928 in a monophyletic clade. Morphological characters support this monophyly as well. The phylogeny shows that the monophyletic clade of the North American middletonii species group belong to the genus Protaphis: P. debilicornis (Gillette & Palmer, 1929), comb. nov., P. echinaceae (Lagos and Voegtlin, 2009), comb. nov., and P. middletonii (Thomas, 1879). The genus Toxoptera should be considered a subgenus of Aphis (stat. nov.). The analysis also indicates that the current genus Iowana Frison, 1954 should be considered a subgenus of Aphis (stat. nov.). © 2013 Institute of Zoology, Chinese Academy of Sciences.

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times.

PubMed

dos Reis, Mario; Yang, Ziheng

2011-07-01

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.

Extracting a Whisper from the DIN: A Bayesian-Inductive Approach to Learning an Anticipatory Model of Cavitation

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

Kercel, S.W.

1999-11-07

For several reasons, Bayesian parameter estimation is superior to other methods for inductively learning a model for an anticipatory system. Since it exploits prior knowledge, the analysis begins from a more advantageous starting point than other methods. Also, since "nuisance parameters" can be removed from the Bayesian analysis, the description of the model need not be as complete as is necessary for such methods as matched filtering. In the limit of perfectly random noise and a perfect description of the model, the signal-to-noise ratio improves as the square root of the number of samples in the data. Even with themore » imperfections of real-world data, Bayesian methods approach this ideal limit of performance more closely than other methods. These capabilities provide a strategy for addressing a major unsolved problem in pump operation: the identification of precursors of cavitation. Cavitation causes immediate degradation of pump performance and ultimate destruction of the pump. However, the most efficient point to operate a pump is just below the threshold of cavitation. It might be hoped that a straightforward method to minimize pump cavitation damage would be to simply adjust the operating point until the inception of cavitation is detected and then to slightly readjust the operating point to let the cavitation vanish. However, due to the continuously evolving state of the fluid moving through the pump, the threshold of cavitation tends to wander. What is needed is to anticipate cavitation, and this requires the detection and identification of precursor features that occur just before cavitation starts.« less

Meta-analysis of the effect of natural frequencies on Bayesian reasoning.

PubMed

McDowell, Michelle; Jacobs, Perke

2017-12-01

The natural frequency facilitation effect describes the finding that people are better able to solve descriptive Bayesian inference tasks when represented as joint frequencies obtained through natural sampling, known as natural frequencies, than as conditional probabilities. The present meta-analysis reviews 20 years of research seeking to address when, why, and for whom natural frequency formats are most effective. We review contributions from research associated with the 2 dominant theoretical perspectives, the ecological rationality framework and nested-sets theory, and test potential moderators of the effect. A systematic review of relevant literature yielded 35 articles representing 226 performance estimates. These estimates were statistically integrated using a bivariate mixed-effects model that yields summary estimates of average performances across the 2 formats and estimates of the effects of different study characteristics on performance. These study characteristics range from moderators representing individual characteristics (e.g., numeracy, expertise), to methodological differences (e.g., use of incentives, scoring criteria) and features of problem representation (e.g., short menu format, visual aid). Short menu formats (less computationally complex representations showing joint-events) and visual aids demonstrated some of the strongest moderation effects, improving performance for both conditional probability and natural frequency formats. A number of methodological factors (e.g., exposure to both problem formats) were also found to affect performance rates, emphasizing the importance of a systematic approach. We suggest how research on Bayesian reasoning can be strengthened by broadening the definition of successful Bayesian reasoning to incorporate choice and process and by applying different research methodologies. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Eyewitness identification: Bayesian information gain, base-rate effect equivalency curves, and reasonable suspicion.

PubMed

Wells, Gary L; Yang, Yueran; Smalarz, Laura

2015-04-01

We provide a novel Bayesian treatment of the eyewitness identification problem as it relates to various system variables, such as instruction effects, lineup presentation format, lineup-filler similarity, lineup administrator influence, and show-ups versus lineups. We describe why eyewitness identification is a natural Bayesian problem and how numerous important observations require careful consideration of base rates. Moreover, we argue that the base rate in eyewitness identification should be construed as a system variable (under the control of the justice system). We then use prior-by-posterior curves and information-gain curves to examine data obtained from a large number of published experiments. Next, we show how information-gain curves are moderated by system variables and by witness confidence and we note how information-gain curves reveal that lineups are consistently more proficient at incriminating the guilty than they are at exonerating the innocent. We then introduce a new type of analysis that we developed called base rate effect-equivalency (BREE) curves. BREE curves display how much change in the base rate is required to match the impact of any given system variable. The results indicate that even relatively modest changes to the base rate can have more impact on the reliability of eyewitness identification evidence than do the traditional system variables that have received so much attention in the literature. We note how this Bayesian analysis of eyewitness identification has implications for the question of whether there ought to be a reasonable-suspicion criterion for placing a person into the jeopardy of an identification procedure. (c) 2015 APA, all rights reserved).

Model Diagnostics for Bayesian Networks

ERIC Educational Resources Information Center

Sinharay, Sandip

2006-01-01

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

Multi-angle backscatter classification and sub-bottom profiling for improved seafloor characterization

NASA Astrophysics Data System (ADS)

Alevizos, Evangelos; Snellen, Mirjam; Simons, Dick; Siemes, Kerstin; Greinert, Jens

2018-06-01

This study applies three classification methods exploiting the angular dependence of acoustic seafloor backscatter along with high resolution sub-bottom profiling for seafloor sediment characterization in the Eckernförde Bay, Baltic Sea Germany. This area is well suited for acoustic backscatter studies due to its shallowness, its smooth bathymetry and the presence of a wide range of sediment types. Backscatter data were acquired using a Seabeam1180 (180 kHz) multibeam echosounder and sub-bottom profiler data were recorded using a SES-2000 parametric sonar transmitting 6 and 12 kHz. The high density of seafloor soundings allowed extracting backscatter layers for five beam angles over a large part of the surveyed area. A Bayesian probability method was employed for sediment classification based on the backscatter variability at a single incidence angle, whereas Maximum Likelihood Classification (MLC) and Principal Components Analysis (PCA) were applied to the multi-angle layers. The Bayesian approach was used for identifying the optimum number of acoustic classes because cluster validation is carried out prior to class assignment and class outputs are ordinal categorical values. The method is based on the principle that backscatter values from a single incidence angle express a normal distribution for a particular sediment type. The resulting Bayesian classes were well correlated to median grain sizes and the percentage of coarse material. The MLC method uses angular response information from five layers of training areas extracted from the Bayesian classification map. The subsequent PCA analysis is based on the transformation of these five layers into two principal components that comprise most of the data variability. These principal components were clustered in five classes after running an external cluster validation test. In general both methods MLC and PCA, separated the various sediment types effectively, showing good agreement (kappa >0.7) with the Bayesian approach which also correlates well with ground truth data (r2 > 0.7). In addition, sub-bottom data were used in conjunction with the Bayesian classification results to characterize acoustic classes with respect to their geological and stratigraphic interpretation. The joined interpretation of seafloor and sub-seafloor data sets proved to be an efficient approach for a better understanding of seafloor backscatter patchiness and to discriminate acoustically similar classes in different geological/bathymetric settings.

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Empirical Bayes estimation of proportions with application to cowbird parasitism rates

USGS Publications Warehouse

Link, W.A.; Hahn, D.C.

1996-01-01

Bayesian models provide a structure for studying collections of parameters such as are considered in the investigation of communities, ecosystems, and landscapes. This structure allows for improved estimation of individual parameters, by considering them in the context of a group of related parameters. Individual estimates are differentially adjusted toward an overall mean, with the magnitude of their adjustment based on their precision. Consequently, Bayesian estimation allows for a more credible identification of extreme values in a collection of estimates. Bayesian models regard individual parameters as values sampled from a specified probability distribution, called a prior. The requirement that the prior be known is often regarded as an unattractive feature of Bayesian analysis and may be the reason why Bayesian analyses are not frequently applied in ecological studies. Empirical Bayes methods provide an alternative approach that incorporates the structural advantages of Bayesian models while requiring a less stringent specification of prior knowledge. Rather than requiring that the prior distribution be known, empirical Bayes methods require only that it be in a certain family of distributions, indexed by hyperparameters that can be estimated from the available data. This structure is of interest per se, in addition to its value in allowing for improved estimation of individual parameters; for example, hypotheses regarding the existence of distinct subgroups in a collection of parameters can be considered under the empirical Bayes framework by allowing the hyperparameters to vary among subgroups. Though empirical Bayes methods have been applied in a variety of contexts, they have received little attention in the ecological literature. We describe the empirical Bayes approach in application to estimation of proportions, using data obtained in a community-wide study of cowbird parasitism rates for illustration. Since observed proportions based on small sample sizes are heavily adjusted toward the mean, extreme values among empirical Bayes estimates identify those species for which there is the greatest evidence of extreme parasitism rates. Applying a subgroup analysis to our data on cowbird parasitism rates, we conclude that parasitism rates for Neotropical Migrants as a group are no greater than those of Resident/Short-distance Migrant species in this forest community. Our data and analyses demonstrate that the parasitism rates for certain Neotropical Migrant species are remarkably low (Wood Thrush and Rose-breasted Grosbeak) while those for others are remarkably high (Ovenbird and Red-eyed Vireo).

Bayesian network analysis revealed the connectivity difference of the default mode network from the resting-state to task-state

PubMed Central

Wu, Xia; Yu, Xinyu; Yao, Li; Li, Rui

2014-01-01

Functional magnetic resonance imaging (fMRI) studies have converged to reveal the default mode network (DMN), a constellation of regions that display co-activation during resting-state but co-deactivation during attention-demanding tasks in the brain. Here, we employed a Bayesian network (BN) analysis method to construct a directed effective connectivity model of the DMN and compared the organizational architecture and interregional directed connections under both resting-state and task-state. The analysis results indicated that the DMN was consistently organized into two closely interacting subsystems in both resting-state and task-state. The directed connections between DMN regions, however, changed significantly from the resting-state to task-state condition. The results suggest that the DMN intrinsically maintains a relatively stable structure whether at rest or performing tasks but has different information processing mechanisms under varied states. PMID:25309414

Unmasking the masked Universe: the 2M++ catalogue through Bayesian eyes

NASA Astrophysics Data System (ADS)

Lavaux, Guilhem; Jasche, Jens

2016-01-01

This work describes a full Bayesian analysis of the Nearby Universe as traced by galaxies of the 2M++ survey. The analysis is run in two sequential steps. The first step self-consistently derives the luminosity-dependent galaxy biases, the power spectrum of matter fluctuations and matter density fields within a Gaussian statistic approximation. The second step makes a detailed analysis of the three-dimensional large-scale structures, assuming a fixed bias model and a fixed cosmology. This second step allows for the reconstruction of both the final density field and the initial conditions at z = 1000 assuming a fixed bias model. From these, we derive fields that self-consistently extrapolate the observed large-scale structures. We give two examples of these extrapolation and their utility for the detection of structures: the visibility of the Sloan Great Wall, and the detection and characterization of the Local Void using DIVA, a Lagrangian based technique to classify structures.

Testing non-minimally coupled inflation with CMB data: a Bayesian analysis

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

Campista, Marcela; Benetti, Micol; Alcaniz, Jailson, E-mail: campista@on.br, E-mail: micolbenetti@on.br, E-mail: alcaniz@on.br

2017-09-01

We use the most recent cosmic microwave background (CMB) data to perform a Bayesian statistical analysis and discuss the observational viability of inflationary models with a non-minimal coupling, ξ, between the inflaton field and the Ricci scalar. We particularize our analysis to two examples of small and large field inflationary models, namely, the Coleman-Weinberg and the chaotic quartic potentials. We find that ( i ) the ξ parameter is closely correlated with the primordial amplitude ; ( ii ) although improving the agreement with the CMB data in the r − n {sub s} plane, where r is the tensor-to-scalarmore » ratio and n {sub s} the primordial spectral index, a non-null coupling is strongly disfavoured with respect to the minimally coupled standard ΛCDM model, since the upper bounds of the Bayes factor (odds) for ξ parameter are greater than 150:1.« less

Factors affecting GEBV accuracy with single-step Bayesian models.

PubMed

Zhou, Lei; Mrode, Raphael; Zhang, Shengli; Zhang, Qin; Li, Bugao; Liu, Jian-Feng

2018-01-01

A single-step approach to obtain genomic prediction was first proposed in 2009. Many studies have investigated the components of GEBV accuracy in genomic selection. However, it is still unclear how the population structure and the relationships between training and validation populations influence GEBV accuracy in terms of single-step analysis. Here, we explored the components of GEBV accuracy in single-step Bayesian analysis with a simulation study. Three scenarios with various numbers of QTL (5, 50, and 500) were simulated. Three models were implemented to analyze the simulated data: single-step genomic best linear unbiased prediction (GBLUP; SSGBLUP), single-step BayesA (SS-BayesA), and single-step BayesB (SS-BayesB). According to our results, GEBV accuracy was influenced by the relationships between the training and validation populations more significantly for ungenotyped animals than for genotyped animals. SS-BayesA/BayesB showed an obvious advantage over SSGBLUP with the scenarios of 5 and 50 QTL. SS-BayesB model obtained the lowest accuracy with the 500 QTL in the simulation. SS-BayesA model was the most efficient and robust considering all QTL scenarios. Generally, both the relationships between training and validation populations and LD between markers and QTL contributed to GEBV accuracy in the single-step analysis, and the advantages of single-step Bayesian models were more apparent when the trait is controlled by fewer QTL.

Bayesian analysis of biogeography when the number of areas is large.

PubMed

Landis, Michael J; Matzke, Nicholas J; Moore, Brian R; Huelsenbeck, John P

2013-11-01

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.

A phylogenetic study of Laeliinae (Orchidaceae) based on combined nuclear and plastid DNA sequences

PubMed Central

van den Berg, Cássio; Higgins, Wesley E.; Dressler, Robert L.; Whitten, W. Mark; Soto-Arenas, Miguel A.; Chase, Mark W.

2009-01-01

Background and Aims Laeliinae are a neotropical orchid subtribe with approx. 1500 species in 50 genera. In this study, an attempt is made to assess generic alliances based on molecular phylogenetic analysis of DNA sequence data. Methods Six DNA datasets were gathered: plastid trnL intron, trnL-F spacer, matK gene and trnK introns upstream and dowstream from matK and nuclear ITS rDNA. Data were analysed with maximum parsimony (MP) and Bayesian analysis with mixed models (BA). Key Results Although relationships between Laeliinae and outgroups are well supported, within the subtribe sequence variation is low considering the broad taxonomic range covered. Localized incongruence between the ITS and plastid trees was found. A combined tree followed the ITS trees more closely, but the levels of support obtained with MP were low. The Bayesian analysis recovered more well-supported nodes. The trees from combined MP and BA allowed eight generic alliances to be recognized within Laeliinae, all of which show trends in morphological characters but lack unambiguous synapomorphies. Conclusions By using combined plastid and nuclear DNA data in conjunction with mixed-models Bayesian inference, it is possible to delimit smaller groups within Laeliinae and discuss general patterns of pollination and hybridization compatibility. Furthermore, these small groups can now be used for further detailed studies to explain morphological evolution and diversification patterns within the subtribe. PMID:19423551

Selecting Strategies to Reduce High-Risk Unsafe Work Behaviors Using the Safety Behavior Sampling Technique and Bayesian Network Analysis.

PubMed

Ghasemi, Fakhradin; Kalatpour, Omid; Moghimbeigi, Abbas; Mohammadfam, Iraj

2017-03-04

High-risk unsafe behaviors (HRUBs) have been known as the main cause of occupational accidents. Considering the financial and societal costs of accidents and the limitations of available resources, there is an urgent need for managing unsafe behaviors at workplaces. The aim of the present study was to find strategies for decreasing the rate of HRUBs using an integrated approach of safety behavior sampling technique and Bayesian networks analysis. A cross-sectional study. The Bayesian network was constructed using a focus group approach. The required data was collected using the safety behavior sampling, and the parameters of the network were estimated using Expectation-Maximization algorithm. Using sensitivity analysis and belief updating, it was determined that which factors had the highest influences on unsafe behavior. Based on BN analyses, safety training was the most important factor influencing employees' behavior at the workplace. High quality safety training courses can reduce the rate of HRUBs about 10%. Moreover, the rate of HRUBs increased by decreasing the age of employees. The rate of HRUBs was higher in the afternoon and last days of a week. Among the investigated variables, training was the most important factor affecting safety behavior of employees. By holding high quality safety training courses, companies would be able to reduce the rate of HRUBs significantly.

Bayesian Nonparametric Ordination for the Analysis of Microbial Communities.

PubMed

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

2017-01-01

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

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.

Evaluating Mixture Modeling for Clustering: Recommendations and Cautions

ERIC Educational Resources Information Center

Steinley, Douglas; Brusco, Michael J.

2011-01-01

This article provides a large-scale investigation into several of the properties of mixture-model clustering techniques (also referred to as latent class cluster analysis, latent profile analysis, model-based clustering, probabilistic clustering, Bayesian classification, unsupervised learning, and finite mixture models; see Vermunt & Magdison,…

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

PubMed

Arenas, Miguel

2015-04-01

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

Significance testing of clinical data using virus dynamics models with a Markov chain Monte Carlo method: application to emergence of lamivudine-resistant hepatitis B virus.

PubMed Central

Burroughs, N J; Pillay, D; Mutimer, D

1999-01-01

Bayesian analysis using a virus dynamics model is demonstrated to facilitate hypothesis testing of patterns in clinical time-series. Our Markov chain Monte Carlo implementation demonstrates that the viraemia time-series observed in two sets of hepatitis B patients on antiviral (lamivudine) therapy, chronic carriers and liver transplant patients, are significantly different, overcoming clinical trial design differences that question the validity of non-parametric tests. We show that lamivudine-resistant mutants grow faster in transplant patients than in chronic carriers, which probably explains the differences in emergence times and failure rates between these two sets of patients. Incorporation of dynamic models into Bayesian parameter analysis is of general applicability in medical statistics. PMID:10643081

Data set for phylogenetic tree and RAMPAGE Ramachandran plot analysis of SODs in Gossypium raimondii and G. arboreum.

PubMed

Wang, Wei; Xia, Minxuan; Chen, Jie; Deng, Fenni; Yuan, Rui; Zhang, Xiaopei; Shen, Fafu

2016-12-01

The data presented in this paper is supporting the research article "Genome-Wide Analysis of Superoxide Dismutase Gene Family in Gossypium raimondii and G. arboreum" [1]. In this data article, we present phylogenetic tree showing dichotomy with two different clusters of SODs inferred by the Bayesian method of MrBayes (version 3.2.4), "Bayesian phylogenetic inference under mixed models" [2], Ramachandran plots of G. raimondii and G. arboreum SODs, the protein sequence used to generate 3D sructure of proteins and the template accession via SWISS-MODEL server, "SWISS-MODEL: modelling protein tertiary and quaternary structure using evolutionary information." [3] and motif sequences of SODs identified by InterProScan (version 4.8) with the Pfam database, "Pfam: the protein families database" [4].

A Bayesian deconvolution strategy for immunoprecipitation-based DNA methylome analysis

PubMed Central

Down, Thomas A.; Rakyan, Vardhman K.; Turner, Daniel J.; Flicek, Paul; Li, Heng; Kulesha, Eugene; Gräf, Stefan; Johnson, Nathan; Herrero, Javier; Tomazou, Eleni M.; Thorne, Natalie P.; Bäckdahl, Liselotte; Herberth, Marlis; Howe, Kevin L.; Jackson, David K.; Miretti, Marcos M.; Marioni, John C.; Birney, Ewan; Hubbard, Tim J. P.; Durbin, Richard; Tavaré, Simon; Beck, Stephan

2009-01-01

DNA methylation is an indispensible epigenetic modification of mammalian genomes. Consequently there is great interest in strategies for genome-wide/whole-genome DNA methylation analysis, and immunoprecipitation-based methods have proven to be a powerful option. Such methods are rapidly shifting the bottleneck from data generation to data analysis, necessitating the development of better analytical tools. Until now, a major analytical difficulty associated with immunoprecipitation-based DNA methylation profiling has been the inability to estimate absolute methylation levels. Here we report the development of a novel cross-platform algorithm – Bayesian Tool for Methylation Analysis (Batman) – for analyzing Methylated DNA Immunoprecipitation (MeDIP) profiles generated using arrays (MeDIP-chip) or next-generation sequencing (MeDIP-seq). The latter is an approach we have developed to elucidate the first high-resolution whole-genome DNA methylation profile (DNA methylome) of any mammalian genome. MeDIP-seq/MeDIP-chip combined with Batman represent robust, quantitative, and cost-effective functional genomic strategies for elucidating the function of DNA methylation. PMID:18612301

A Bayesian technique for improving the sensitivity of the atmospheric neutrino L/E analysis

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

Blake, A. S. T.; Chapman, J. D.; Thomson, M. A.

Tmore » his paper outlines a method for improving the precision of atmospheric neutrino oscillation measurements. One experimental signature for these oscillations is an observed deficit in the rate of ν μ charged-current interactions with an oscillatory dependence on L ν / E ν , where L ν is the neutrino propagation distance and E mrow is="true"> ν is the neutrino energy. For contained-vertex atmospheric neutrino interactions, the L ν / E ν resolution varies significantly from event to event. he precision of the oscillation measurement can be improved by incorporating information on L ν / E ν resolution into the oscillation analysis. In the analysis presented here, a Bayesian technique is used to estimate the L ν / E ν resolution of observed atmospheric neutrinos on an event-by-event basis. By separating the events into bins of L ν / E ν resolution in the oscillation analysis, a significant improvement in oscillation sensitivity can be achieved.« less

Quantitative analysis of factors that affect oil pipeline network accident based on Bayesian networks: A case study in China

NASA Astrophysics Data System (ADS)

Zhang, Chao; Qin, Ting Xin; Huang, Shuai; Wu, Jian Song; Meng, Xin Yan

2018-06-01

Some factors can affect the consequences of oil pipeline accident and their effects should be analyzed to improve emergency preparation and emergency response. Although there are some qualitative analysis models of risk factors' effects, the quantitative analysis model still should be researched. In this study, we introduce a Bayesian network (BN) model of risk factors' effects analysis in an oil pipeline accident case that happened in China. The incident evolution diagram is built to identify the risk factors. And the BN model is built based on the deployment rule for factor nodes in BN and the expert knowledge by Dempster-Shafer evidence theory. Then the probabilities of incident consequences and risk factors' effects can be calculated. The most likely consequences given by this model are consilient with the case. Meanwhile, the quantitative estimations of risk factors' effects may provide a theoretical basis to take optimal risk treatment measures for oil pipeline management, which can be used in emergency preparation and emergency response.

Problems in the fingerprints based polycyclic aromatic hydrocarbons source apportionment analysis and a practical solution.

PubMed

Zou, Yonghong; Wang, Lixia; Christensen, Erik R

2015-10-01

This work intended to explain the challenges of the fingerprints based source apportionment method for polycyclic aromatic hydrocarbons (PAH) in the aquatic environment, and to illustrate a practical and robust solution. The PAH data detected in the sediment cores from the Illinois River provide the basis of this study. Principal component analysis (PCA) separates PAH compounds into two groups reflecting their possible airborne transport patterns; but it is not able to suggest specific sources. Not all positive matrix factorization (PMF) determined sources are distinguishable due to the variability of source fingerprints. However, they constitute useful suggestions for inputs for a Bayesian chemical mass balance (CMB) analysis. The Bayesian CMB analysis takes into account the measurement errors as well as the variations of source fingerprints, and provides a credible source apportionment. Major PAH sources for Illinois River sediments are traffic (35%), coke oven (24%), coal combustion (18%), and wood combustion (14%). Copyright © 2015. Published by Elsevier Ltd.

Case studies in Bayesian microbial risk assessments.

PubMed

Kennedy, Marc C; Clough, Helen E; Turner, Joanne

2009-12-21

The quantification of uncertainty and variability is a key component of quantitative risk analysis. Recent advances in Bayesian statistics make it ideal for integrating multiple sources of information, of different types and quality, and providing a realistic estimate of the combined uncertainty in the final risk estimates. We present two case studies related to foodborne microbial risks. In the first, we combine models to describe the sequence of events resulting in illness from consumption of milk contaminated with VTEC O157. We used Monte Carlo simulation to propagate uncertainty in some of the inputs to computer models describing the farm and pasteurisation process. Resulting simulated contamination levels were then assigned to consumption events from a dietary survey. Finally we accounted for uncertainty in the dose-response relationship and uncertainty due to limited incidence data to derive uncertainty about yearly incidences of illness in young children. Options for altering the risk were considered by running the model with different hypothetical policy-driven exposure scenarios. In the second case study we illustrate an efficient Bayesian sensitivity analysis for identifying the most important parameters of a complex computer code that simulated VTEC O157 prevalence within a managed dairy herd. This was carried out in 2 stages, first to screen out the unimportant inputs, then to perform a more detailed analysis on the remaining inputs. The method works by building a Bayesian statistical approximation to the computer code using a number of known code input/output pairs (training runs). We estimated that the expected total number of children aged 1.5-4.5 who become ill due to VTEC O157 in milk is 8.6 per year, with 95% uncertainty interval (0,11.5). The most extreme policy we considered was banning on-farm pasteurisation of milk, which reduced the estimate to 6.4 with 95% interval (0,11). In the second case study the effective number of inputs was reduced from 30 to 7 in the screening stage, and just 2 inputs were found to explain 82.8% of the output variance. A combined total of 500 runs of the computer code were used. These case studies illustrate the use of Bayesian statistics to perform detailed uncertainty and sensitivity analyses, integrating multiple information sources in a way that is both rigorous and efficient.

A Bayesian analysis of the impact of air pollution episodes on cardio-respiratory hospital admissions in the Greater London area.

PubMed

Blangiardo, Marta; Richardson, Sylvia; Gulliver, John; Hansell, Anna

2011-02-01

In this paper, we present a Bayesian hierarchical model to evaluate the effect of long-range and local range PM(10) during air pollution episodes on hospital admissions for cardio-respiratory diseases in Greater London. These episodes in 2003 are matched with the same periods during the previous year, used as a control. A baseline dose-response function is estimated for the controls and carried forward in the episodes, which are characterised by an additional component that estimates their specific effect on the health outcome.

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

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

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

2015-02-01

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

The current state of Bayesian methods in medical product development: survey results and recommendations from the DIA Bayesian Scientific Working Group.

PubMed

Natanegara, Fanni; Neuenschwander, Beat; Seaman, John W; Kinnersley, Nelson; Heilmann, Cory R; Ohlssen, David; Rochester, George

2014-01-01

Bayesian applications in medical product development have recently gained popularity. Despite many advances in Bayesian methodology and computations, increase in application across the various areas of medical product development has been modest. The DIA Bayesian Scientific Working Group (BSWG), which includes representatives from industry, regulatory agencies, and academia, has adopted the vision to ensure Bayesian methods are well understood, accepted more broadly, and appropriately utilized to improve decision making and enhance patient outcomes. As Bayesian applications in medical product development are wide ranging, several sub-teams were formed to focus on various topics such as patient safety, non-inferiority, prior specification, comparative effectiveness, joint modeling, program-wide decision making, analytical tools, and education. The focus of this paper is on the recent effort of the BSWG Education sub-team to administer a Bayesian survey to statisticians across 17 organizations involved in medical product development. We summarize results of this survey, from which we provide recommendations on how to accelerate progress in Bayesian applications throughout medical product development. The survey results support findings from the literature and provide additional insight on regulatory acceptance of Bayesian methods and information on the need for a Bayesian infrastructure within an organization. The survey findings support the claim that only modest progress in areas of education and implementation has been made recently, despite substantial progress in Bayesian statistical research and software availability. Copyright © 2013 John Wiley & Sons, Ltd.

Univariate and bivariate likelihood-based meta-analysis methods performed comparably when marginal sensitivity and specificity were the targets of inference.

PubMed

Dahabreh, Issa J; Trikalinos, Thomas A; Lau, Joseph; Schmid, Christopher H

2017-03-01

To compare statistical methods for meta-analysis of sensitivity and specificity of medical tests (e.g., diagnostic or screening tests). We constructed a database of PubMed-indexed meta-analyses of test performance from which 2 × 2 tables for each included study could be extracted. We reanalyzed the data using univariate and bivariate random effects models fit with inverse variance and maximum likelihood methods. Analyses were performed using both normal and binomial likelihoods to describe within-study variability. The bivariate model using the binomial likelihood was also fit using a fully Bayesian approach. We use two worked examples-thoracic computerized tomography to detect aortic injury and rapid prescreening of Papanicolaou smears to detect cytological abnormalities-to highlight that different meta-analysis approaches can produce different results. We also present results from reanalysis of 308 meta-analyses of sensitivity and specificity. Models using the normal approximation produced sensitivity and specificity estimates closer to 50% and smaller standard errors compared to models using the binomial likelihood; absolute differences of 5% or greater were observed in 12% and 5% of meta-analyses for sensitivity and specificity, respectively. Results from univariate and bivariate random effects models were similar, regardless of estimation method. Maximum likelihood and Bayesian methods produced almost identical summary estimates under the bivariate model; however, Bayesian analyses indicated greater uncertainty around those estimates. Bivariate models produced imprecise estimates of the between-study correlation of sensitivity and specificity. Differences between methods were larger with increasing proportion of studies that were small or required a continuity correction. The binomial likelihood should be used to model within-study variability. Univariate and bivariate models give similar estimates of the marginal distributions for sensitivity and specificity. Bayesian methods fully quantify uncertainty and their ability to incorporate external evidence may be useful for imprecisely estimated parameters. Copyright © 2017 Elsevier Inc. All rights reserved.

Improved Determination of the Myelin Water Fraction in Human Brain using Magnetic Resonance Imaging through Bayesian Analysis of mcDESPOT

PubMed Central

Bouhrara, Mustapha; Spencer, Richard G.

2015-01-01

Myelin water fraction (MWF) mapping with magnetic resonance imaging has led to the ability to directly observe myelination and demyelination in both the developing brain and in disease. Multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) has been proposed as a rapid approach for multicomponent relaxometry and has been applied to map MWF in human brain. However, even for the simplest two-pool signal model consisting of MWF and non-myelin-associated water, the dimensionality of the parameter space for obtaining MWF estimates remains high. This renders parameter estimation difficult, especially at low-to-moderate signal-to-noise ratios (SNR), due to the presence of local minima and the flatness of the fit residual energy surface used for parameter determination using conventional nonlinear least squares (NLLS)-based algorithms. In this study, we introduce three Bayesian approaches for analysis of the mcDESPOT signal model to determine MWF. Given the high dimensional nature of mcDESPOT signal model, and, thereby, the high dimensional marginalizations over nuisance parameters needed to derive the posterior probability distribution of MWF parameter, the introduced Bayesian analyses use different approaches to reduce the dimensionality of the parameter space. The first approach uses normalization by average signal amplitude, and assumes that noise can be accurately estimated from signal-free regions of the image. The second approach likewise uses average amplitude normalization, but incorporates a full treatment of noise as an unknown variable through marginalization. The third approach does not use amplitude normalization and incorporates marginalization over both noise and signal amplitude. Through extensive Monte Carlo numerical simulations and analysis of in-vivo human brain datasets exhibiting a range of SNR and spatial resolution, we demonstrated the markedly improved accuracy and precision in the estimation of MWF using these Bayesian methods as compared to the stochastic region contraction (SRC) implementation of NLLS. PMID:26499810

Bayesian multimodel inference of soil microbial respiration models: Theory, application and future prospective

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2015-12-01

Models in biogeoscience involve uncertainties in observation data, model inputs, model structure, model processes and modeling scenarios. To accommodate for different sources of uncertainty, multimodal analysis such as model combination, model selection, model elimination or model discrimination are becoming more popular. To illustrate theoretical and practical challenges of multimodal analysis, we use an example about microbial soil respiration modeling. Global soil respiration releases more than ten times more carbon dioxide to the atmosphere than all anthropogenic emissions. Thus, improving our understanding of microbial soil respiration is essential for improving climate change models. This study focuses on a poorly understood phenomena, which is the soil microbial respiration pulses in response to episodic rainfall pulses (the "Birch effect"). We hypothesize that the "Birch effect" is generated by the following three mechanisms. To test our hypothesis, we developed and assessed five evolving microbial-enzyme models against field measurements from a semiarid Savannah that is characterized by pulsed precipitation. These five model evolve step-wise such that the first model includes none of these three mechanism, while the fifth model includes the three mechanisms. The basic component of Bayesian multimodal analysis is the estimation of marginal likelihood to rank the candidate models based on their overall likelihood with respect to observation data. The first part of the study focuses on using this Bayesian scheme to discriminate between these five candidate models. The second part discusses some theoretical and practical challenges, which are mainly the effect of likelihood function selection and the marginal likelihood estimation methods on both model ranking and Bayesian model averaging. The study shows that making valid inference from scientific data is not a trivial task, since we are not only uncertain about the candidate scientific models, but also about the statistical methods that are used to discriminate between these models.

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.

On the Adequacy of Bayesian Evaluations of Categorization Models: Reply to Vanpaemel and Lee (2012)

ERIC Educational Resources Information Center

Wills, Andy J.; Pothos, Emmanuel M.

2012-01-01

Vanpaemel and Lee (2012) argued, and we agree, that the comparison of formal models can be facilitated by Bayesian methods. However, Bayesian methods neither precede nor supplant our proposals (Wills & Pothos, 2012), as Bayesian methods can be applied both to our proposals and to their polar opposites. Furthermore, the use of Bayesian methods to…

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data

PubMed Central

Ferragina, A.; de los Campos, G.; Vazquez, A. I.; Cecchinato, A.; Bittante, G.

2017-01-01

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict “difficult-to-predict” dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm−1 were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R2 value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R2 (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R2 of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations. PMID:26387015

Effective Online Bayesian Phylogenetics via Sequential Monte Carlo with Guided Proposals

PubMed Central

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

2018-01-01

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

Simultaneous Force Regression and Movement Classification of Fingers via Surface EMG within a Unified Bayesian Framework.

PubMed

Baldacchino, Tara; Jacobs, William R; Anderson, Sean R; Worden, Keith; Rowson, Jennifer

2018-01-01

This contribution presents a novel methodology for myolectric-based control using surface electromyographic (sEMG) signals recorded during finger movements. A multivariate Bayesian mixture of experts (MoE) model is introduced which provides a powerful method for modeling force regression at the fingertips, while also performing finger movement classification as a by-product of the modeling algorithm. Bayesian inference of the model allows uncertainties to be naturally incorporated into the model structure. This method is tested using data from the publicly released NinaPro database which consists of sEMG recordings for 6 degree-of-freedom force activations for 40 intact subjects. The results demonstrate that the MoE model achieves similar performance compared to the benchmark set by the authors of NinaPro for finger force regression. Additionally, inherent to the Bayesian framework is the inclusion of uncertainty in the model parameters, naturally providing confidence bounds on the force regression predictions. Furthermore, the integrated clustering step allows a detailed investigation into classification of the finger movements, without incurring any extra computational effort. Subsequently, a systematic approach to assessing the importance of the number of electrodes needed for accurate control is performed via sensitivity analysis techniques. A slight degradation in regression performance is observed for a reduced number of electrodes, while classification performance is unaffected.

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.

An Open-Source Bayesian Atmospheric Radiative Transfer (BART) Code, with Application to WASP-12b

NASA Astrophysics Data System (ADS)

Harrington, Joseph; Blecic, Jasmina; Cubillos, Patricio; Rojo, Patricio; Loredo, Thomas J.; Bowman, M. Oliver; Foster, Andrew S. D.; Stemm, Madison M.; Lust, Nate B.

2015-01-01

Atmospheric retrievals for solar-system planets typically fit, either with a minimizer or by eye, a synthetic spectrum to high-resolution (Δλ/λ ~ 1000-100,000) data with S/N > 100 per point. In contrast, exoplanet data often have S/N ~ 10 per point, and may have just a few points representing bandpasses larger than 1 um. To derive atmospheric constraints and robust parameter uncertainty estimates from such data requires a Bayesian approach. To date there are few investigators with the relevant codes, none of which are publicly available. We are therefore pleased to announce the open-source Bayesian Atmospheric Radiative Transfer (BART) code. BART uses a Bayesian phase-space explorer to drive a radiative-transfer model through the parameter phase space, producing the most robust estimates available for the thermal profile and chemical abundances in the atmosphere. We present an overview of the code and an initial application to Spitzer eclipse data for WASP-12b. We invite the community to use and improve BART via the open-source development site GitHub.com. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G. JB holds a NASA Earth and Space Science Fellowship.

An Open-Source Bayesian Atmospheric Radiative Transfer (BART) Code, and Application to WASP-12b

NASA Astrophysics Data System (ADS)

Harrington, Joseph; Blecic, Jasmina; Cubillos, Patricio; Rojo, Patricio M.; Loredo, Thomas J.; Bowman, Matthew O.; Foster, Andrew S.; Stemm, Madison M.; Lust, Nate B.

2014-11-01

Atmospheric retrievals for solar-system planets typically fit, either with a minimizer or by eye, a synthetic spectrum to high-resolution (Δλ/λ ~ 1000-100,000) data with S/N > 100 per point. In contrast, exoplanet data often have S/N ~ 10 per point, and may have just a few points representing bandpasses larger than 1 um. To derive atmospheric constraints and robust parameter uncertainty estimates from such data requires a Bayesian approach. To date there are few investigators with the relevant codes, none of which are publicly available. We are therefore pleased to announce the open-source Bayesian Atmospheric Radiative Transfer (BART) code. BART uses a Bayesian phase-space explorer to drive a radiative-transfer model through the parameter phase space, producing the most robust estimates available for the thermal profile and chemical abundances in the atmosphere. We present an overview of the code and an initial application to Spitzer eclipse data for WASP-12b. We invite the community to use and improve BART via the open-source development site GitHub.com. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G. JB holds a NASA Earth and Space Science Fellowship.