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.

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.

Practical Bayesian tomography

NASA Astrophysics Data System (ADS)

Granade, Christopher; Combes, Joshua; Cory, D. G.

2016-03-01

In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Huszár and Houlsby (2012 Phys. Rev. A 85 052120) and by Ferrie (2014 New J. Phys. 16 093035), to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first priors on quantum states and channels that allow for including useful experimental insight. Finally, we develop a method that allows tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.

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.

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Basics of Bayesian methods.

PubMed

Ghosh, Sujit K

2010-01-01

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

Bayesian 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.

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

PubMed

Molitor, John

2012-03-01

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

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.

Posterior Predictive Bayesian Phylogenetic Model Selection

PubMed Central

Lewis, Paul O.; Xie, Wangang; Chen, Ming-Hui; Fan, Yu; Kuo, Lynn

2014-01-01

We present two distinctly different posterior predictive approaches to Bayesian phylogenetic model selection and illustrate these methods using examples from green algal protein-coding cpDNA sequences and flowering plant rDNA sequences. The Gelfand–Ghosh (GG) approach allows dissection of an overall measure of model fit into components due to posterior predictive variance (GGp) and goodness-of-fit (GGg), which distinguishes this method from the posterior predictive P-value approach. The conditional predictive ordinate (CPO) method provides a site-specific measure of model fit useful for exploratory analyses and can be combined over sites yielding the log pseudomarginal likelihood (LPML) which is useful as an overall measure of model fit. CPO provides a useful cross-validation approach that is computationally efficient, requiring only a sample from the posterior distribution (no additional simulation is required). Both GG and CPO add new perspectives to Bayesian phylogenetic model selection based on the predictive abilities of models and complement the perspective provided by the marginal likelihood (including Bayes Factor comparisons) based solely on the fit of competing models to observed data. [Bayesian; conditional predictive ordinate; CPO; L-measure; LPML; model selection; phylogenetics; posterior predictive.] PMID:24193892

Variational learning and bits-back coding: an information-theoretic view to Bayesian learning.

PubMed

Honkela, Antti; Valpola, Harri

2004-07-01

The bits-back coding first introduced by Wallace in 1990 and later by Hinton and van Camp in 1993 provides an interesting link between Bayesian learning and information-theoretic minimum-description-length (MDL) learning approaches. The bits-back coding allows interpreting the cost function used in the variational Bayesian method called ensemble learning as a code length in addition to the Bayesian view of misfit of the posterior approximation and a lower bound of model evidence. Combining these two viewpoints provides interesting insights to the learning process and the functions of different parts of the model. In this paper, the problem of variational Bayesian learning of hierarchical latent variable models is used to demonstrate the benefits of the two views. The code-length interpretation provides new views to many parts of the problem such as model comparison and pruning and helps explain many phenomena occurring in learning.

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

Bayesian flood forecasting methods: A review

NASA Astrophysics Data System (ADS)

Han, Shasha; Coulibaly, Paulin

2017-08-01

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

Bayesian 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

A Bayesian Approach to Determination of F, D, and Z Values Used in Steam Sterilization Validation.

PubMed

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

2017-01-01

For manufacturers of sterile drug products, steam sterilization is a common method used to provide assurance of the sterility of manufacturing equipment and products. The validation of sterilization processes is a regulatory requirement and relies upon the estimation of key resistance parameters of microorganisms. Traditional methods have relied upon point estimates for the resistance parameters. In this paper, we propose a Bayesian method for estimation of the well-known D T , z , and F o values that are used in the development and validation of sterilization processes. A Bayesian approach allows the uncertainty about these values to be modeled using probability distributions, thereby providing a fully risk-based approach to measures of sterility assurance. An example is given using the survivor curve and fraction negative methods for estimation of resistance parameters, and we present a means by which a probabilistic conclusion can be made regarding the ability of a process to achieve a specified sterility criterion. LAY ABSTRACT: For manufacturers of sterile drug products, steam sterilization is a common method used to provide assurance of the sterility of manufacturing equipment and products. The validation of sterilization processes is a regulatory requirement and relies upon the estimation of key resistance parameters of microorganisms. Traditional methods have relied upon point estimates for the resistance parameters. In this paper, we propose a Bayesian method for estimation of the critical process parameters that are evaluated in the development and validation of sterilization processes. A Bayesian approach allows the uncertainty about these parameters to be modeled using probability distributions, thereby providing a fully risk-based approach to measures of sterility assurance. An example is given using the survivor curve and fraction negative methods for estimation of resistance parameters, and we present a means by which a probabilistic conclusion can be made regarding the ability of a process to achieve a specified sterility criterion. © PDA, Inc. 2017.

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.

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.

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

Bayes and the Law

PubMed Central

Fenton, Norman; Neil, Martin; Berger, Daniel

2016-01-01

Although the last forty years has seen considerable growth in the use of statistics in legal proceedings, it is primarily classical statistical methods rather than Bayesian methods that have been used. Yet the Bayesian approach avoids many of the problems of classical statistics and is also well suited to a broader range of problems. This paper reviews the potential and actual use of Bayes in the law and explains the main reasons for its lack of impact on legal practice. These include misconceptions by the legal community about Bayes’ theorem, over-reliance on the use of the likelihood ratio and the lack of adoption of modern computational methods. We argue that Bayesian Networks (BNs), which automatically produce the necessary Bayesian calculations, provide an opportunity to address most concerns about using Bayes in the law. PMID:27398389

Bayes and the Law.

PubMed

Fenton, Norman; Neil, Martin; Berger, Daniel

2016-06-01

Although the last forty years has seen considerable growth in the use of statistics in legal proceedings, it is primarily classical statistical methods rather than Bayesian methods that have been used. Yet the Bayesian approach avoids many of the problems of classical statistics and is also well suited to a broader range of problems. This paper reviews the potential and actual use of Bayes in the law and explains the main reasons for its lack of impact on legal practice. These include misconceptions by the legal community about Bayes' theorem, over-reliance on the use of the likelihood ratio and the lack of adoption of modern computational methods. We argue that Bayesian Networks (BNs), which automatically produce the necessary Bayesian calculations, provide an opportunity to address most concerns about using Bayes in the law.

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

Semisupervised learning using Bayesian interpretation: application to LS-SVM.

PubMed

Adankon, Mathias M; Cheriet, Mohamed; Biem, Alain

2011-04-01

Bayesian reasoning provides an ideal basis for representing and manipulating uncertain knowledge, with the result that many interesting algorithms in machine learning are based on Bayesian inference. In this paper, we use the Bayesian approach with one and two levels of inference to model the semisupervised learning problem and give its application to the successful kernel classifier support vector machine (SVM) and its variant least-squares SVM (LS-SVM). Taking advantage of Bayesian interpretation of LS-SVM, we develop a semisupervised learning algorithm for Bayesian LS-SVM using our approach based on two levels of inference. Experimental results on both artificial and real pattern recognition problems show the utility of our method.

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.

Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

PubMed Central

Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass. PMID:24278198

Tree biomass estimation of Chinese fir (Cunninghamia lanceolata) based on Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation W = a(D2H)b was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.

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.

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.

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

PubMed

Moscoso del Prado Martín, Fermín

2013-12-01

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

Bayesian Inference in the Modern Design of Experiments

NASA Technical Reports Server (NTRS)

DeLoach, Richard

2008-01-01

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

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

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...

Using SAS PROC MCMC for Item Response Theory Models

PubMed Central

Samonte, Kelli

2014-01-01

Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian methods in the context of item response theory to serve as a useful guide for practitioners in estimating and interpreting item response theory (IRT) models. Included is a description of the estimation procedure used by SAS PROC MCMC. Syntax is provided for estimation of both dichotomous and polytomous IRT models, as well as a discussion on how to extend the syntax to accommodate more complex IRT models. PMID:29795834

Win-Stay, Lose-Sample: a simple sequential algorithm for approximating Bayesian inference.

PubMed

Bonawitz, Elizabeth; Denison, Stephanie; Gopnik, Alison; Griffiths, Thomas L

2014-11-01

People can behave in a way that is consistent with Bayesian models of cognition, despite the fact that performing exact Bayesian inference is computationally challenging. What algorithms could people be using to make this possible? We show that a simple sequential algorithm "Win-Stay, Lose-Sample", inspired by the Win-Stay, Lose-Shift (WSLS) principle, can be used to approximate Bayesian inference. We investigate the behavior of adults and preschoolers on two causal learning tasks to test whether people might use a similar algorithm. These studies use a "mini-microgenetic method", investigating how people sequentially update their beliefs as they encounter new evidence. Experiment 1 investigates a deterministic causal learning scenario and Experiments 2 and 3 examine how people make inferences in a stochastic scenario. The behavior of adults and preschoolers in these experiments is consistent with our Bayesian version of the WSLS principle. This algorithm provides both a practical method for performing Bayesian inference and a new way to understand people's judgments. Copyright © 2014 Elsevier Inc. All rights reserved.

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

PubMed

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

2013-12-01

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

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.

Tracking composite material damage evolution using Bayesian filtering and flash thermography data

NASA Astrophysics Data System (ADS)

Gregory, Elizabeth D.; Holland, Steve D.

2016-05-01

We propose a method for tracking the condition of a composite part using Bayesian filtering of ash thermography data over the lifetime of the part. In this demonstration, composite panels were fabricated; impacted to induce subsurface delaminations; and loaded in compression over multiple time steps, causing the delaminations to grow in size. Flash thermography data was collected between each damage event to serve as a time history of the part. The ash thermography indicated some areas of damage but provided little additional information as to the exact nature or depth of the damage. Computed tomography (CT) data was also collected after each damage event and provided a high resolution volume model of damage that acted as truth. After each cycle, the condition estimate, from the ash thermography data and the Bayesian filter, was compared to 'ground truth'. The Bayesian process builds on the lifetime history of ash thermography scans and can give better estimates of material condition as compared to the most recent scan alone, which is common practice in the aerospace industry. Bayesian inference provides probabilistic estimates of damage condition that are updated as each new set of data becomes available. The method was tested on simulated data and then on an experimental data set.

Unification of field theory and maximum entropy methods for learning probability densities

NASA Astrophysics Data System (ADS)

Kinney, Justin B.

2015-09-01

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

Unification of field theory and maximum entropy methods for learning probability densities.

PubMed

Kinney, Justin B

2015-09-01

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

When mechanism matters: Bayesian forecasting using models of ecological diffusion

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.

2017-01-01

Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.

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 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 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.

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.

Probabilistic inference using linear Gaussian importance sampling for hybrid Bayesian networks

NASA Astrophysics Data System (ADS)

Sun, Wei; Chang, K. C.

2005-05-01

Probabilistic inference for Bayesian networks is in general NP-hard using either exact algorithms or approximate methods. However, for very complex networks, only the approximate methods such as stochastic sampling could be used to provide a solution given any time constraint. There are several simulation methods currently available. They include logic sampling (the first proposed stochastic method for Bayesian networks, the likelihood weighting algorithm) the most commonly used simulation method because of its simplicity and efficiency, the Markov blanket scoring method, and the importance sampling algorithm. In this paper, we first briefly review and compare these available simulation methods, then we propose an improved importance sampling algorithm called linear Gaussian importance sampling algorithm for general hybrid model (LGIS). LGIS is aimed for hybrid Bayesian networks consisting of both discrete and continuous random variables with arbitrary distributions. It uses linear function and Gaussian additive noise to approximate the true conditional probability distribution for continuous variable given both its parents and evidence in a Bayesian network. One of the most important features of the newly developed method is that it can adaptively learn the optimal important function from the previous samples. We test the inference performance of LGIS using a 16-node linear Gaussian model and a 6-node general hybrid model. The performance comparison with other well-known methods such as Junction tree (JT) and likelihood weighting (LW) shows that LGIS-GHM is very promising.

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

PubMed

Bockman, Alexander; Fackler, Cameron; Xiang, Ning

2015-04-01

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

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.

Trans-dimensional and hierarchical Bayesian approaches toward rigorous estimation of seismic sources and structures in the Northeast Asia

NASA Astrophysics Data System (ADS)

Kim, Seongryong; Tkalčić, Hrvoje; Mustać, Marija; Rhie, Junkee; Ford, Sean

2016-04-01

A framework is presented within which we provide rigorous estimations for seismic sources and structures in the Northeast Asia. We use Bayesian inversion methods, which enable statistical estimations of models and their uncertainties based on data information. Ambiguities in error statistics and model parameterizations are addressed by hierarchical and trans-dimensional (trans-D) techniques, which can be inherently implemented in the Bayesian inversions. Hence reliable estimation of model parameters and their uncertainties is possible, thus avoiding arbitrary regularizations and parameterizations. Hierarchical and trans-D inversions are performed to develop a three-dimensional velocity model using ambient noise data. To further improve the model, we perform joint inversions with receiver function data using a newly developed Bayesian method. For the source estimation, a novel moment tensor inversion method is presented and applied to regional waveform data of the North Korean nuclear explosion tests. By the combination of new Bayesian techniques and the structural model, coupled with meaningful uncertainties related to each of the processes, more quantitative monitoring and discrimination of seismic events is possible.

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

Bayesian Estimation Supersedes the "t" Test

ERIC Educational Resources Information Center

Kruschke, John K.

2013-01-01

Bayesian estimation for 2 groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data. The method handles outliers. The decision rule can accept the null value (unlike traditional "t" tests) when certainty in the estimate is…

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.

A fast Bayesian approach to discrete object detection in astronomical data sets - PowellSnakes I

NASA Astrophysics Data System (ADS)

Carvalho, Pedro; Rocha, Graça; Hobson, M. P.

2009-03-01

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by (i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; (ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior and (iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of `100' as compared to existing Bayesian source extraction methods that use Monte Carlo Markov chain to explore the parameter space, such as that presented by Hobson & McLachlan. The method can be implemented in either real or Fourier space. In the case of objects embedded in a homogeneous random field, working in Fourier space provides a further speed up that takes advantage of the fact that the correlation matrix of the background is circulant. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore, PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (version I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.

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

NASA Astrophysics Data System (ADS)

Li, Qiaofeng; Lu, Qiuhai

2018-05-01

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

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.

A Gibbs sampler for Bayesian analysis of site-occupancy data

USGS Publications Warehouse

Dorazio, Robert M.; Rodriguez, Daniel Taylor

2012-01-01

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

A Bayesian 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.

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.

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.

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.

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 characterization of uncertainty in species interaction strengths.

PubMed

Wolf, Christopher; Novak, Mark; Gitelman, Alix I

2017-06-01

Considerable effort has been devoted to the estimation of species interaction strengths. This effort has focused primarily on statistical significance testing and obtaining point estimates of parameters that contribute to interaction strength magnitudes, leaving the characterization of uncertainty associated with those estimates unconsidered. We consider a means of characterizing the uncertainty of a generalist predator's interaction strengths by formulating an observational method for estimating a predator's prey-specific per capita attack rates as a Bayesian statistical model. This formulation permits the explicit incorporation of multiple sources of uncertainty. A key insight is the informative nature of several so-called non-informative priors that have been used in modeling the sparse data typical of predator feeding surveys. We introduce to ecology a new neutral prior and provide evidence for its superior performance. We use a case study to consider the attack rates in a New Zealand intertidal whelk predator, and we illustrate not only that Bayesian point estimates can be made to correspond with those obtained by frequentist approaches, but also that estimation uncertainty as described by 95% intervals is more useful and biologically realistic using the Bayesian method. In particular, unlike in bootstrap confidence intervals, the lower bounds of the Bayesian posterior intervals for attack rates do not include zero when a predator-prey interaction is in fact observed. We conclude that the Bayesian framework provides a straightforward, probabilistic characterization of interaction strength uncertainty, enabling future considerations of both the deterministic and stochastic drivers of interaction strength and their impact on food webs.

Construction of monitoring model and algorithm design on passenger security during shipping based on improved Bayesian network.

PubMed

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping.

Construction of Monitoring Model and Algorithm Design on Passenger Security during Shipping Based on Improved Bayesian Network

PubMed Central

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping. PMID:25254227

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.

Results of Bayesian methods depend on details of implementation: An example of estimating salmon escapement goals

USGS Publications Warehouse

Adkison, Milo D.; Peterman, R.M.

1996-01-01

Bayesian methods have been proposed to estimate optimal escapement goals, using both knowledge about physical determinants of salmon productivity and stock-recruitment data. The Bayesian approach has several advantages over many traditional methods for estimating stock productivity: it allows integration of information from diverse sources and provides a framework for decision-making that takes into account uncertainty reflected in the data. However, results can be critically dependent on details of implementation of this approach. For instance, unintended and unwarranted confidence about stock-recruitment relationships can arise if the range of relationships examined is too narrow, if too few discrete alternatives are considered, or if data are contradictory. This unfounded confidence can result in a suboptimal choice of a spawning escapement goal.

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

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).

Using SAS PROC MCMC for Item Response Theory Models

ERIC Educational Resources Information Center

Ames, Allison J.; Samonte, Kelli

2015-01-01

Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian…

BAYESIAN BICLUSTERING FOR PATIENT STRATIFICATION.

PubMed

Khakabimamaghani, Sahand; Ester, Martin

2016-01-01

The move from Empirical Medicine towards Personalized Medicine has attracted attention to Stratified Medicine (SM). Some methods are provided in the literature for patient stratification, which is the central task of SM, however, there are still significant open issues. First, it is still unclear if integrating different datatypes will help in detecting disease subtypes more accurately, and, if not, which datatype(s) are most useful for this task. Second, it is not clear how we can compare different methods of patient stratification. Third, as most of the proposed stratification methods are deterministic, there is a need for investigating the potential benefits of applying probabilistic methods. To address these issues, we introduce a novel integrative Bayesian biclustering method, called B2PS, for patient stratification and propose methods for evaluating the results. Our experimental results demonstrate the superiority of B2PS over a popular state-of-the-art method and the benefits of Bayesian approaches. Our results agree with the intuition that transcriptomic data forms a better basis for patient stratification than genomic data.

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.

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.

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.

Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data.

PubMed

Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

2017-01-01

Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

Hierarchical Bayesian sparse image reconstruction with application to MRFM.

PubMed

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

2009-09-01

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

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.

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

Brewer, Brendon J.; Foreman-Mackey, Daniel; Hogg, David W., E-mail: bj.brewer@auckland.ac.nz

We present and implement a probabilistic (Bayesian) method for producing catalogs from images of stellar fields. The method is capable of inferring the number of sources N in the image and can also handle the challenges introduced by noise, overlapping sources, and an unknown point-spread function. The luminosity function of the stars can also be inferred, even when the precise luminosity of each star is uncertain, via the use of a hierarchical Bayesian model. The computational feasibility of the method is demonstrated on two simulated images with different numbers of stars. We find that our method successfully recovers the inputmore » parameter values along with principled uncertainties even when the field is crowded. We also compare our results with those obtained from the SExtractor software. While the two approaches largely agree about the fluxes of the bright stars, the Bayesian approach provides more accurate inferences about the faint stars and the number of stars, particularly in the crowded case.« less

A Bayesian Model of the Memory Colour Effect.

PubMed

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

2018-01-01

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

A Bayesian Model of the Memory Colour Effect

PubMed Central

Olkkonen, Maria; Gegenfurtner, Karl R.

2018-01-01

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

A systematic review of Bayesian articles in psychology: The last 25 years.

PubMed

van de Schoot, Rens; Winter, Sonja D; Ryan, Oisín; Zondervan-Zwijnenburg, Mariëlle; Depaoli, Sarah

2017-06-01

Although the statistical tools most often used by researchers in the field of psychology over the last 25 years are based on frequentist statistics, it is often claimed that the alternative Bayesian approach to statistics is gaining in popularity. In the current article, we investigated this claim by performing the very first systematic review of Bayesian psychological articles published between 1990 and 2015 (n = 1,579). We aim to provide a thorough presentation of the role Bayesian statistics plays in psychology. This historical assessment allows us to identify trends and see how Bayesian methods have been integrated into psychological research in the context of different statistical frameworks (e.g., hypothesis testing, cognitive models, IRT, SEM, etc.). We also describe take-home messages and provide "big-picture" recommendations to the field as Bayesian statistics becomes more popular. Our review indicated that Bayesian statistics is used in a variety of contexts across subfields of psychology and related disciplines. There are many different reasons why one might choose to use Bayes (e.g., the use of priors, estimating otherwise intractable models, modeling uncertainty, etc.). We found in this review that the use of Bayes has increased and broadened in the sense that this methodology can be used in a flexible manner to tackle many different forms of questions. We hope this presentation opens the door for a larger discussion regarding the current state of Bayesian statistics, as well as future trends. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Prior approval: the growth of Bayesian methods in psychology.

PubMed

Andrews, Mark; Baguley, Thom

2013-02-01

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

Modeling and Bayesian parameter estimation for shape memory alloy bending actuators

NASA Astrophysics Data System (ADS)

Crews, John H.; Smith, Ralph C.

2012-04-01

In this paper, we employ a homogenized energy model (HEM) for shape memory alloy (SMA) bending actuators. Additionally, we utilize a Bayesian method for quantifying parameter uncertainty. The system consists of a SMA wire attached to a flexible beam. As the actuator is heated, the beam bends, providing endoscopic motion. The model parameters are fit to experimental data using an ordinary least-squares approach. The uncertainty in the fit model parameters is then quantified using Markov Chain Monte Carlo (MCMC) methods. The MCMC algorithm provides bounds on the parameters, which will ultimately be used in robust control algorithms. One purpose of the paper is to test the feasibility of the Random Walk Metropolis algorithm, the MCMC method used here.

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.

Predicting Drug Safety and Communicating Risk: Benefits of a Bayesian Approach.

PubMed

Lazic, Stanley E; Edmunds, Nicholas; Pollard, Christopher E

2018-03-01

Drug toxicity is a major source of attrition in drug discovery and development. Pharmaceutical companies routinely use preclinical data to predict clinical outcomes and continue to invest in new assays to improve predictions. However, there are many open questions about how to make the best use of available data, combine diverse data, quantify risk, and communicate risk and uncertainty to enable good decisions. The costs of suboptimal decisions are clear: resources are wasted and patients may be put at risk. We argue that Bayesian methods provide answers to all of these problems and use hERG-mediated QT prolongation as a case study. Benefits of Bayesian machine learning models include intuitive probabilistic statements of risk that incorporate all sources of uncertainty, the option to include diverse data and external information, and visualizations that have a clear link between the output from a statistical model and what this means for risk. Furthermore, Bayesian methods are easy to use with modern software, making their adoption for safety screening straightforward. We include R and Python code to encourage the adoption of these methods.

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

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

Moving in Parallel Toward a Modern Modeling Epistemology: Bayes Factors and Frequentist Modeling Methods.

PubMed

Rodgers, Joseph Lee

2016-01-01

The Bayesian-frequentist debate typically portrays these statistical perspectives as opposing views. However, both Bayesian and frequentist statisticians have expanded their epistemological basis away from a singular focus on the null hypothesis, to a broader perspective involving the development and comparison of competing statistical/mathematical models. For frequentists, statistical developments such as structural equation modeling and multilevel modeling have facilitated this transition. For Bayesians, the Bayes factor has facilitated this transition. The Bayes factor is treated in articles within this issue of Multivariate Behavioral Research. The current presentation provides brief commentary on those articles and more extended discussion of the transition toward a modern modeling epistemology. In certain respects, Bayesians and frequentists share common goals.

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

PubMed

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

2013-01-01

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

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.

BAM: Bayesian AMHG-Manning Inference of Discharge Using Remotely Sensed Stream Width, Slope, and Height

NASA Astrophysics Data System (ADS)

Hagemann, M. W.; Gleason, C. J.; Durand, M. T.

2017-11-01

The forthcoming Surface Water and Ocean Topography (SWOT) NASA satellite mission will measure water surface width, height, and slope of major rivers worldwide. The resulting data could provide an unprecedented account of river discharge at continental scales, but reliable methods need to be identified prior to launch. Here we present a novel algorithm for discharge estimation from only remotely sensed stream width, slope, and height at multiple locations along a mass-conserved river segment. The algorithm, termed the Bayesian AMHG-Manning (BAM) algorithm, implements a Bayesian formulation of streamflow uncertainty using a combination of Manning's equation and at-many-stations hydraulic geometry (AMHG). Bayesian methods provide a statistically defensible approach to generating discharge estimates in a physically underconstrained system but rely on prior distributions that quantify the a priori uncertainty of unknown quantities including discharge and hydraulic equation parameters. These were obtained from literature-reported values and from a USGS data set of acoustic Doppler current profiler (ADCP) measurements at USGS stream gauges. A data set of simulated widths, slopes, and heights from 19 rivers was used to evaluate the algorithms using a set of performance metrics. Results across the 19 rivers indicate an improvement in performance of BAM over previously tested methods and highlight a path forward in solving discharge estimation using solely satellite remote sensing.

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

PubMed

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

2013-01-01

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

Sparse Bayesian learning for DOA estimation with mutual coupling.

PubMed

Dai, Jisheng; Hu, Nan; Xu, Weichao; Chang, Chunqi

2015-10-16

Sparse Bayesian learning (SBL) has given renewed interest to the problem of direction-of-arrival (DOA) estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs). Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM) algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD) to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise.

A Bayesian approach to estimating variance components within a multivariate generalizability theory framework.

PubMed

Jiang, Zhehan; Skorupski, William

2017-12-12

In many behavioral research areas, multivariate generalizability theory (mG theory) has been typically used to investigate the reliability of certain multidimensional assessments. However, traditional mG-theory estimation-namely, using frequentist approaches-has limits, leading researchers to fail to take full advantage of the information that mG theory can offer regarding the reliability of measurements. Alternatively, Bayesian methods provide more information than frequentist approaches can offer. This article presents instructional guidelines on how to implement mG-theory analyses in a Bayesian framework; in particular, BUGS code is presented to fit commonly seen designs from mG theory, including single-facet designs, two-facet crossed designs, and two-facet nested designs. In addition to concrete examples that are closely related to the selected designs and the corresponding BUGS code, a simulated dataset is provided to demonstrate the utility and advantages of the Bayesian approach. This article is intended to serve as a tutorial reference for applied researchers and methodologists conducting mG-theory studies.

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

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.

Analyzing Single-Molecule Time Series via Nonparametric Bayesian Inference

PubMed Central

Hines, Keegan E.; Bankston, John R.; Aldrich, Richard W.

2015-01-01

The ability to measure the properties of proteins at the single-molecule level offers an unparalleled glimpse into biological systems at the molecular scale. The interpretation of single-molecule time series has often been rooted in statistical mechanics and the theory of Markov processes. While existing analysis methods have been useful, they are not without significant limitations including problems of model selection and parameter nonidentifiability. To address these challenges, we introduce the use of nonparametric Bayesian inference for the analysis of single-molecule time series. These methods provide a flexible way to extract structure from data instead of assuming models beforehand. We demonstrate these methods with applications to several diverse settings in single-molecule biophysics. This approach provides a well-constrained and rigorously grounded method for determining the number of biophysical states underlying single-molecule data. PMID:25650922

Teaching Bayesian Statistics in a Health Research Methodology Program

ERIC Educational Resources Information Center

Pullenayegum, Eleanor M.; Thabane, Lehana

2009-01-01

Despite the appeal of Bayesian methods in health research, they are not widely used. This is partly due to a lack of courses in Bayesian methods at an appropriate level for non-statisticians in health research. Teaching such a course can be challenging because most statisticians have been taught Bayesian methods using a mathematical approach, and…

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.

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.

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

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.

Enhancements to the Bayesian Infrasound Source Location Method

DTIC Science & Technology

2012-09-01

ENHANCEMENTS TO THE BAYESIAN INFRASOUND SOURCE LOCATION METHOD Omar E. Marcillo, Stephen J. Arrowsmith, Rod W. Whitaker, and Dale N. Anderson Los...ABSTRACT We report on R&D that is enabling enhancements to the Bayesian Infrasound Source Location (BISL) method for infrasound event location...the Bayesian Infrasound Source Location Method 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER

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.

Inference of epidemiological parameters from household stratified data

PubMed Central

Walker, James N.; Ross, Joshua V.

2017-01-01

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

BMDS: A Collection of R Functions for Bayesian Multidimensional Scaling

ERIC Educational Resources Information Center

Okada, Kensuke; Shigemasu, Kazuo

2009-01-01

Bayesian multidimensional scaling (MDS) has attracted a great deal of attention because: (1) it provides a better fit than do classical MDS and ALSCAL; (2) it provides estimation errors of the distances; and (3) the Bayesian dimension selection criterion, MDSIC, provides a direct indication of optimal dimensionality. However, Bayesian MDS is not…

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.

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.

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

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

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

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

PubMed

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

2015-10-01

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

A comparison of confidence interval methods for the concordance correlation coefficient and intraclass correlation coefficient with small number of raters.

PubMed

Feng, Dai; Svetnik, Vladimir; Coimbra, Alexandre; Baumgartner, Richard

2014-01-01

The intraclass correlation coefficient (ICC) with fixed raters or, equivalently, the concordance correlation coefficient (CCC) for continuous outcomes is a widely accepted aggregate index of agreement in settings with small number of raters. Quantifying the precision of the CCC by constructing its confidence interval (CI) is important in early drug development applications, in particular in qualification of biomarker platforms. In recent years, there have been several new methods proposed for construction of CIs for the CCC, but their comprehensive comparison has not been attempted. The methods consisted of the delta method and jackknifing with and without Fisher's Z-transformation, respectively, and Bayesian methods with vague priors. In this study, we carried out a simulation study, with data simulated from multivariate normal as well as heavier tailed distribution (t-distribution with 5 degrees of freedom), to compare the state-of-the-art methods for assigning CI to the CCC. When the data are normally distributed, the jackknifing with Fisher's Z-transformation (JZ) tended to provide superior coverage and the difference between it and the closest competitor, the Bayesian method with the Jeffreys prior was in general minimal. For the nonnormal data, the jackknife methods, especially the JZ method, provided the coverage probabilities closest to the nominal in contrast to the others which yielded overly liberal coverage. Approaches based upon the delta method and Bayesian method with conjugate prior generally provided slightly narrower intervals and larger lower bounds than others, though this was offset by their poor coverage. Finally, we illustrated the utility of the CIs for the CCC in an example of a wake after sleep onset (WASO) biomarker, which is frequently used in clinical sleep studies of drugs for treatment of insomnia.

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.

Hypothesis Testing, "p" Values, Confidence Intervals, Measures of Effect Size, and Bayesian Methods in Light of Modern Robust Techniques

ERIC Educational Resources Information Center

Wilcox, Rand R.; Serang, Sarfaraz

2017-01-01

The article provides perspectives on p values, null hypothesis testing, and alternative techniques in light of modern robust statistical methods. Null hypothesis testing and "p" values can provide useful information provided they are interpreted in a sound manner, which includes taking into account insights and advances that have…

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.

SensibleSleep: A Bayesian Model for Learning Sleep Patterns from Smartphone Events

PubMed Central

Sekara, Vedran; Jonsson, Håkan; Larsen, Jakob Eg; Lehmann, Sune

2017-01-01

We propose a Bayesian model for extracting sleep patterns from smartphone events. Our method is able to identify individuals’ daily sleep periods and their evolution over time, and provides an estimation of the probability of sleep and wake transitions. The model is fitted to more than 400 participants from two different datasets, and we verify the results against ground truth from dedicated armband sleep trackers. We show that the model is able to produce reliable sleep estimates with an accuracy of 0.89, both at the individual and at the collective level. Moreover the Bayesian model is able to quantify uncertainty and encode prior knowledge about sleep patterns. Compared with existing smartphone-based systems, our method requires only screen on/off events, and is therefore much less intrusive in terms of privacy and more battery-efficient. PMID:28076375

SensibleSleep: A Bayesian Model for Learning Sleep Patterns from Smartphone Events.

PubMed

Cuttone, Andrea; Bækgaard, Per; Sekara, Vedran; Jonsson, Håkan; Larsen, Jakob Eg; Lehmann, Sune

2017-01-01

We propose a Bayesian model for extracting sleep patterns from smartphone events. Our method is able to identify individuals' daily sleep periods and their evolution over time, and provides an estimation of the probability of sleep and wake transitions. The model is fitted to more than 400 participants from two different datasets, and we verify the results against ground truth from dedicated armband sleep trackers. We show that the model is able to produce reliable sleep estimates with an accuracy of 0.89, both at the individual and at the collective level. Moreover the Bayesian model is able to quantify uncertainty and encode prior knowledge about sleep patterns. Compared with existing smartphone-based systems, our method requires only screen on/off events, and is therefore much less intrusive in terms of privacy and more battery-efficient.

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.

SELFI: an object-based, Bayesian method for faint emission line source detection in MUSE deep field data cubes

NASA Astrophysics Data System (ADS)

Meillier, Céline; Chatelain, Florent; Michel, Olivier; Bacon, Roland; Piqueras, Laure; Bacher, Raphael; Ayasso, Hacheme

2016-04-01

We present SELFI, the Source Emission Line FInder, a new Bayesian method optimized for detection of faint galaxies in Multi Unit Spectroscopic Explorer (MUSE) deep fields. MUSE is the new panoramic integral field spectrograph at the Very Large Telescope (VLT) that has unique capabilities for spectroscopic investigation of the deep sky. It has provided data cubes with 324 million voxels over a single 1 arcmin2 field of view. To address the challenge of faint-galaxy detection in these large data cubes, we developed a new method that processes 3D data either for modeling or for estimation and extraction of source configurations. This object-based approach yields a natural sparse representation of the sources in massive data fields, such as MUSE data cubes. In the Bayesian framework, the parameters that describe the observed sources are considered random variables. The Bayesian model leads to a general and robust algorithm where the parameters are estimated in a fully data-driven way. This detection algorithm was applied to the MUSE observation of Hubble Deep Field-South. With 27 h total integration time, these observations provide a catalog of 189 sources of various categories and with secured redshift. The algorithm retrieved 91% of the galaxies with only 9% false detection. This method also allowed the discovery of three new Lyα emitters and one [OII] emitter, all without any Hubble Space Telescope counterpart. We analyzed the reasons for failure for some targets, and found that the most important limitation of the method is when faint sources are located in the vicinity of bright spatially resolved galaxies that cannot be approximated by the Sérsic elliptical profile. The software and its documentation are available on the MUSE science web service (muse-vlt.eu/science).

Estimating Tree Height-Diameter Models with the Bayesian Method

PubMed Central

Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

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

Estimating tree height-diameter models with the Bayesian method.

PubMed

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

2014-01-01

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

Additive Genetic Variability and the Bayesian Alphabet

PubMed Central

Gianola, Daniel; de los Campos, Gustavo; Hill, William G.; Manfredi, Eduardo; Fernando, Rohan

2009-01-01

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called “Bayes A”) with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly. PMID:19620397

Statistical Bayesian method for reliability evaluation based on ADT data

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

Quantitative comparison of alternative methods for coarse-graining biological networks

PubMed Central

Bowman, Gregory R.; Meng, Luming; Huang, Xuhui

2013-01-01

Markov models and master equations are a powerful means of modeling dynamic processes like protein conformational changes. However, these models are often difficult to understand because of the enormous number of components and connections between them. Therefore, a variety of methods have been developed to facilitate understanding by coarse-graining these complex models. Here, we employ Bayesian model comparison to determine which of these coarse-graining methods provides the models that are most faithful to the original set of states. We find that the Bayesian agglomerative clustering engine and the hierarchical Nyström expansion graph (HNEG) typically provide the best performance. Surprisingly, the original Perron cluster cluster analysis (PCCA) method often provides the next best results, outperforming the newer PCCA+ method and the most probable paths algorithm. We also show that the differences between the models are qualitatively significant, rather than being minor shifts in the boundaries between states. The performance of the methods correlates well with the entropy of the resulting coarse-grainings, suggesting that finding states with more similar populations (i.e., avoiding low population states that may just be noise) gives better results. PMID:24089717

A SAS Interface for Bayesian Analysis with WinBUGS

ERIC Educational Resources Information Center

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

2008-01-01

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

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

PubMed

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

2013-04-01

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

How Many Batches Are Needed for Process Validation under the New FDA Guidance?

PubMed

Yang, Harry

2013-01-01

The newly updated FDA Guidance for Industry on Process Validation: General Principles and Practices ushers in a life cycle approach to process validation. While the guidance no longer considers the use of traditional three-batch validation appropriate, it does not prescribe the number of validation batches for a prospective validation protocol, nor does it provide specific methods to determine it. This potentially could leave manufacturers in a quandary. In this paper, I develop a Bayesian method to address the issue. By combining process knowledge gained from Stage 1 Process Design (PD) with expected outcomes of Stage 2 Process Performance Qualification (PPQ), the number of validation batches for PPQ is determined to provide a high level of assurance that the process will consistently produce future batches meeting quality standards. Several examples based on simulated data are presented to illustrate the use of the Bayesian method in helping manufacturers make risk-based decisions for Stage 2 PPQ, and they highlight the advantages of the method over traditional Frequentist approaches. The discussions in the paper lend support for a life cycle and risk-based approach to process validation recommended in the new FDA guidance. The newly updated FDA Guidance for Industry on Process Validation: General Principles and Practices ushers in a life cycle approach to process validation. While the guidance no longer considers the use of traditional three-batch validation appropriate, it does not prescribe the number of validation batches for a prospective validation protocol, nor does it provide specific methods to determine it. This potentially could leave manufacturers in a quandary. In this paper, I develop a Bayesian method to address the issue. By combining process knowledge gained from Stage 1 Process Design (PD) with expected outcomes of Stage 2 Process Performance Qualification (PPQ), the number of validation batches for PPQ is determined to provide a high level of assurance that the process will consistently produce future batches meeting quality standards. Several examples based on simulated data are presented to illustrate the use of the Bayesian method in helping manufacturers make risk-based decisions for Stage 2 PPQ, and THEY highlight the advantages of the method over traditional Frequentist approaches. The discussions in the paper lend support for a life cycle and risk-based approach to process validation recommended in the new FDA guidance.

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…

On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood

ERIC Educational Resources Information Center

Karabatsos, George

2017-01-01

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…

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.

Predicting Software Suitability Using a Bayesian Belief Network

NASA Technical Reports Server (NTRS)

Beaver, Justin M.; Schiavone, Guy A.; Berrios, Joseph S.

2005-01-01

The ability to reliably predict the end quality of software under development presents a significant advantage for a development team. It provides an opportunity to address high risk components earlier in the development life cycle, when their impact is minimized. This research proposes a model that captures the evolution of the quality of a software product, and provides reliable forecasts of the end quality of the software being developed in terms of product suitability. Development team skill, software process maturity, and software problem complexity are hypothesized as driving factors of software product quality. The cause-effect relationships between these factors and the elements of software suitability are modeled using Bayesian Belief Networks, a machine learning method. This research presents a Bayesian Network for software quality, and the techniques used to quantify the factors that influence and represent software quality. The developed model is found to be effective in predicting the end product quality of small-scale software development efforts.

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.

bnstruct: an R package for Bayesian Network structure learning in the presence of missing data.

PubMed

Franzin, Alberto; Sambo, Francesco; Di Camillo, Barbara

2017-04-15

A Bayesian Network is a probabilistic graphical model that encodes probabilistic dependencies between a set of random variables. We introduce bnstruct, an open source R package to (i) learn the structure and the parameters of a Bayesian Network from data in the presence of missing values and (ii) perform reasoning and inference on the learned Bayesian Networks. To the best of our knowledge, there is no other open source software that provides methods for all of these tasks, particularly the manipulation of missing data, which is a common situation in practice. The software is implemented in R and C and is available on CRAN under a GPL licence. francesco.sambo@unipd.it. Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

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

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.

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

PubMed

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

2015-08-07

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

Probabilistic mapping of descriptive health status responses onto health state utilities using Bayesian networks: an empirical analysis converting SF-12 into EQ-5D utility index in a national US sample.

PubMed

Le, Quang A; Doctor, Jason N

2011-05-01

As quality-adjusted life years have become the standard metric in health economic evaluations, mapping health-profile or disease-specific measures onto preference-based measures to obtain quality-adjusted life years has become a solution when health utilities are not directly available. However, current mapping methods are limited due to their predictive validity, reliability, and/or other methodological issues. We employ probability theory together with a graphical model, called a Bayesian network, to convert health-profile measures into preference-based measures and to compare the results to those estimated with current mapping methods. A sample of 19,678 adults who completed both the 12-item Short Form Health Survey (SF-12v2) and EuroQoL 5D (EQ-5D) questionnaires from the 2003 Medical Expenditure Panel Survey was split into training and validation sets. Bayesian networks were constructed to explore the probabilistic relationships between each EQ-5D domain and 12 items of the SF-12v2. The EQ-5D utility scores were estimated on the basis of the predicted probability of each response level of the 5 EQ-5D domains obtained from the Bayesian inference process using the following methods: Monte Carlo simulation, expected utility, and most-likely probability. Results were then compared with current mapping methods including multinomial logistic regression, ordinary least squares, and censored least absolute deviations. The Bayesian networks consistently outperformed other mapping models in the overall sample (mean absolute error=0.077, mean square error=0.013, and R overall=0.802), in different age groups, number of chronic conditions, and ranges of the EQ-5D index. Bayesian networks provide a new robust and natural approach to map health status responses into health utility measures for health economic evaluations.

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

PubMed

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

2015-11-01

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 R(2) 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 R(2) (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R(2) 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. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Bayesian ionospheric multi-instrument 3D tomography

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Vierinen, Juha; Roininen, Lassi

2017-04-01

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

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

PubMed Central

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

2013-01-01

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

Model Diagnostics for Bayesian Networks

ERIC Educational Resources Information Center

Sinharay, Sandip

2006-01-01

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

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

PubMed

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

2015-01-01

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

A Bayesian comparative effectiveness trial in action: developing a platform for multisite study adaptive randomization.

PubMed

Brown, Alexandra R; Gajewski, Byron J; Aaronson, Lauren S; Mudaranthakam, Dinesh Pal; Hunt, Suzanne L; Berry, Scott M; Quintana, Melanie; Pasnoor, Mamatha; Dimachkie, Mazen M; Jawdat, Omar; Herbelin, Laura; Barohn, Richard J

2016-08-31

In the last few decades, the number of trials using Bayesian methods has grown rapidly. Publications prior to 1990 included only three clinical trials that used Bayesian methods, but that number quickly jumped to 19 in the 1990s and to 99 from 2000 to 2012. While this literature provides many examples of Bayesian Adaptive Designs (BAD), none of the papers that are available walks the reader through the detailed process of conducting a BAD. This paper fills that gap by describing the BAD process used for one comparative effectiveness trial (Patient Assisted Intervention for Neuropathy: Comparison of Treatment in Real Life Situations) that can be generalized for use by others. A BAD was chosen with efficiency in mind. Response-adaptive randomization allows the potential for substantially smaller sample sizes, and can provide faster conclusions about which treatment or treatments are most effective. An Internet-based electronic data capture tool, which features a randomization module, facilitated data capture across study sites and an in-house computation software program was developed to implement the response-adaptive randomization. A process for adapting randomization with minimal interruption to study sites was developed. A new randomization table can be generated quickly and can be seamlessly integrated in the data capture tool with minimal interruption to study sites. This manuscript is the first to detail the technical process used to evaluate a multisite comparative effectiveness trial using adaptive randomization. An important opportunity for the application of Bayesian trials is in comparative effectiveness trials. The specific case study presented in this paper can be used as a model for conducting future clinical trials using a combination of statistical software and a web-based application. ClinicalTrials.gov Identifier: NCT02260388 , registered on 6 October 2014.

Parameter inference in small world network disease models with approximate Bayesian Computational methods

NASA Astrophysics Data System (ADS)

Walker, David M.; Allingham, David; Lee, Heung Wing Joseph; Small, Michael

2010-02-01

Small world network models have been effective in capturing the variable behaviour of reported case data of the SARS coronavirus outbreak in Hong Kong during 2003. Simulations of these models have previously been realized using informed “guesses” of the proposed model parameters and tested for consistency with the reported data by surrogate analysis. In this paper we attempt to provide statistically rigorous parameter distributions using Approximate Bayesian Computation sampling methods. We find that such sampling schemes are a useful framework for fitting parameters of stochastic small world network models where simulation of the system is straightforward but expressing a likelihood is cumbersome.

Exposure Models for the Prior Distribution in Bayesian Decision Analysis for Occupational Hygiene Decision Making

PubMed Central

Lee, Eun Gyung; Kim, Seung Won; Feigley, Charles E.; Harper, Martin

2015-01-01

This study introduces two semi-quantitative methods, Structured Subjective Assessment (SSA) and Control of Substances Hazardous to Health (COSHH) Essentials, in conjunction with two-dimensional Monte Carlo simulations for determining prior probabilities. Prior distribution using expert judgment was included for comparison. Practical applications of the proposed methods were demonstrated using personal exposure measurements of isoamyl acetate in an electronics manufacturing facility and of isopropanol in a printing shop. Applicability of these methods in real workplaces was discussed based on the advantages and disadvantages of each method. Although these methods could not be completely independent of expert judgments, this study demonstrated a methodological improvement in the estimation of the prior distribution for the Bayesian decision analysis tool. The proposed methods provide a logical basis for the decision process by considering determinants of worker exposure. PMID:23252451

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.

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?

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

Advances in Applications of Hierarchical Bayesian Methods with Hydrological Models

NASA Astrophysics Data System (ADS)

Alexander, R. B.; Schwarz, G. E.; Boyer, E. W.

2017-12-01

Mechanistic and empirical watershed models are increasingly used to inform water resource decisions. Growing access to historical stream measurements and data from in-situ sensor technologies has increased the need for improved techniques for coupling models with hydrological measurements. Techniques that account for the intrinsic uncertainties of both models and measurements are especially needed. Hierarchical Bayesian methods provide an efficient modeling tool for quantifying model and prediction uncertainties, including those associated with measurements. Hierarchical methods can also be used to explore spatial and temporal variations in model parameters and uncertainties that are informed by hydrological measurements. We used hierarchical Bayesian methods to develop a hybrid (statistical-mechanistic) SPARROW (SPAtially Referenced Regression On Watershed attributes) model of long-term mean annual streamflow across diverse environmental and climatic drainages in 18 U.S. hydrological regions. Our application illustrates the use of a new generation of Bayesian methods that offer more advanced computational efficiencies than the prior generation. Evaluations of the effects of hierarchical (regional) variations in model coefficients and uncertainties on model accuracy indicates improved prediction accuracies (median of 10-50%) but primarily in humid eastern regions, where model uncertainties are one-third of those in arid western regions. Generally moderate regional variability is observed for most hierarchical coefficients. Accounting for measurement and structural uncertainties, using hierarchical state-space techniques, revealed the effects of spatially-heterogeneous, latent hydrological processes in the "localized" drainages between calibration sites; this improved model precision, with only minor changes in regional coefficients. Our study can inform advances in the use of hierarchical methods with hydrological models to improve their integration with stream measurements.

Meta-Analysis of a Continuous Outcome Combining Individual Patient Data and Aggregate Data: A Method Based on Simulated Individual Patient Data

ERIC Educational Resources Information Center

Yamaguchi, Yusuke; Sakamoto, Wataru; Goto, Masashi; Staessen, Jan A.; Wang, Jiguang; Gueyffier, Francois; Riley, Richard D.

2014-01-01

When some trials provide individual patient data (IPD) and the others provide only aggregate data (AD), meta-analysis methods for combining IPD and AD are required. We propose a method that reconstructs the missing IPD for AD trials by a Bayesian sampling procedure and then applies an IPD meta-analysis model to the mixture of simulated IPD and…

Order priors for Bayesian network discovery with an application to malware phylogeny

DOE PAGES

Oyen, Diane; Anderson, Blake; Sentz, Kari; ...

2017-09-15

Here, Bayesian networks have been used extensively to model and discover dependency relationships among sets of random variables. We learn Bayesian network structure with a combination of human knowledge about the partial ordering of variables and statistical inference of conditional dependencies from observed data. Our approach leverages complementary information from human knowledge and inference from observed data to produce networks that reflect human beliefs about the system as well as to fit the observed data. Applying prior beliefs about partial orderings of variables is an approach distinctly different from existing methods that incorporate prior beliefs about direct dependencies (or edges)more » in a Bayesian network. We provide an efficient implementation of the partial-order prior in a Bayesian structure discovery learning algorithm, as well as an edge prior, showing that both priors meet the local modularity requirement necessary for an efficient Bayesian discovery algorithm. In benchmark studies, the partial-order prior improves the accuracy of Bayesian network structure learning as well as the edge prior, even though order priors are more general. Our primary motivation is in characterizing the evolution of families of malware to aid cyber security analysts. For the problem of malware phylogeny discovery, we find that our algorithm, compared to existing malware phylogeny algorithms, more accurately discovers true dependencies that are missed by other algorithms.« less

Order priors for Bayesian network discovery with an application to malware phylogeny

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

Oyen, Diane; Anderson, Blake; Sentz, Kari

Here, Bayesian networks have been used extensively to model and discover dependency relationships among sets of random variables. We learn Bayesian network structure with a combination of human knowledge about the partial ordering of variables and statistical inference of conditional dependencies from observed data. Our approach leverages complementary information from human knowledge and inference from observed data to produce networks that reflect human beliefs about the system as well as to fit the observed data. Applying prior beliefs about partial orderings of variables is an approach distinctly different from existing methods that incorporate prior beliefs about direct dependencies (or edges)more » in a Bayesian network. We provide an efficient implementation of the partial-order prior in a Bayesian structure discovery learning algorithm, as well as an edge prior, showing that both priors meet the local modularity requirement necessary for an efficient Bayesian discovery algorithm. In benchmark studies, the partial-order prior improves the accuracy of Bayesian network structure learning as well as the edge prior, even though order priors are more general. Our primary motivation is in characterizing the evolution of families of malware to aid cyber security analysts. For the problem of malware phylogeny discovery, we find that our algorithm, compared to existing malware phylogeny algorithms, more accurately discovers true dependencies that are missed by other algorithms.« less

Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

QUEST+: A general multidimensional Bayesian adaptive psychometric method.

PubMed

Watson, Andrew B

2017-03-01

QUEST+ is a Bayesian adaptive psychometric testing method that allows an arbitrary number of stimulus dimensions, psychometric function parameters, and trial outcomes. It is a generalization and extension of the original QUEST procedure and incorporates many subsequent developments in the area of parametric adaptive testing. With a single procedure, it is possible to implement a wide variety of experimental designs, including conventional threshold measurement; measurement of psychometric function parameters, such as slope and lapse; estimation of the contrast sensitivity function; measurement of increment threshold functions; measurement of noise-masking functions; Thurstone scale estimation using pair comparisons; and categorical ratings on linear and circular stimulus dimensions. QUEST+ provides a general method to accelerate data collection in many areas of cognitive and perceptual science.

Resolution analysis of marine seismic full waveform data by Bayesian inversion

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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

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.

Quantification of downscaled precipitation uncertainties via Bayesian inference

NASA Astrophysics Data System (ADS)

Nury, A. H.; Sharma, A.; Marshall, L. A.

2017-12-01

Prediction of precipitation from global climate model (GCM) outputs remains critical to decision-making in water-stressed regions. In this regard, downscaling of GCM output has been a useful tool for analysing future hydro-climatological states. Several downscaling approaches have been developed for precipitation downscaling, including those using dynamical or statistical downscaling methods. Frequently, outputs from dynamical downscaling are not readily transferable across regions for significant methodical and computational difficulties. Statistical downscaling approaches provide a flexible and efficient alternative, providing hydro-climatological outputs across multiple temporal and spatial scales in many locations. However these approaches are subject to significant uncertainty, arising due to uncertainty in the downscaled model parameters and in the use of different reanalysis products for inferring appropriate model parameters. Consequently, these will affect the performance of simulation in catchment scale. This study develops a Bayesian framework for modelling downscaled daily precipitation from GCM outputs. This study aims to introduce uncertainties in downscaling evaluating reanalysis datasets against observational rainfall data over Australia. In this research a consistent technique for quantifying downscaling uncertainties by means of Bayesian downscaling frame work has been proposed. The results suggest that there are differences in downscaled precipitation occurrences and extremes.

Evidence reasoning method for constructing conditional probability tables in a Bayesian network of multimorbidity.

PubMed

Du, Yuanwei; Guo, Yubin

2015-01-01

The intrinsic mechanism of multimorbidity is difficult to recognize and prediction and diagnosis are difficult to carry out accordingly. Bayesian networks can help to diagnose multimorbidity in health care, but it is difficult to obtain the conditional probability table (CPT) because of the lack of clinically statistical data. Today, expert knowledge and experience are increasingly used in training Bayesian networks in order to help predict or diagnose diseases, but the CPT in Bayesian networks is usually irrational or ineffective for ignoring realistic constraints especially in multimorbidity. In order to solve these problems, an evidence reasoning (ER) approach is employed to extract and fuse inference data from experts using a belief distribution and recursive ER algorithm, based on which evidence reasoning method for constructing conditional probability tables in Bayesian network of multimorbidity is presented step by step. A multimorbidity numerical example is used to demonstrate the method and prove its feasibility and application. Bayesian network can be determined as long as the inference assessment is inferred by each expert according to his/her knowledge or experience. Our method is more effective than existing methods for extracting expert inference data accurately and is fused effectively for constructing CPTs in a Bayesian network of multimorbidity.

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.

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

PubMed

Mila, A L; Ngugi, H K

2011-01-01

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

A Hierarchical Multivariate Bayesian Approach to Ensemble Model output Statistics in Atmospheric Prediction

DTIC Science & Technology

2017-09-01

efficacy of statistical post-processing methods downstream of these dynamical model components with a hierarchical multivariate Bayesian approach to...Bayesian hierarchical modeling, Markov chain Monte Carlo methods , Metropolis algorithm, machine learning, atmospheric prediction 15. NUMBER OF PAGES...scale processes. However, this dissertation explores the efficacy of statistical post-processing methods downstream of these dynamical model components

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

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

Karagiannis, Georgios, E-mail: georgios.karagiannis@pnnl.gov; Lin, Guang, E-mail: guang.lin@pnnl.gov

2014-02-15

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, bymore » coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.« less

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

NASA Astrophysics Data System (ADS)

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

2013-08-01

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

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

PubMed

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

2013-08-01

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

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

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.

Ultrafast current imaging by Bayesian inversion

DOE Data Explorer

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

2016-01-01

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

Gaussian process tomography for soft x-ray spectroscopy at WEST without equilibrium information

NASA Astrophysics Data System (ADS)

Wang, T.; Mazon, D.; Svensson, J.; Li, D.; Jardin, A.; Verdoolaege, G.

2018-06-01

Gaussian process tomography (GPT) is a recently developed tomography method based on the Bayesian probability theory [J. Svensson, JET Internal Report EFDA-JET-PR(11)24, 2011 and Li et al., Rev. Sci. Instrum. 84, 083506 (2013)]. By modeling the soft X-ray (SXR) emissivity field in a poloidal cross section as a Gaussian process, the Bayesian SXR tomography can be carried out in a robust and extremely fast way. Owing to the short execution time of the algorithm, GPT is an important candidate for providing real-time reconstructions with a view to impurity transport and fast magnetohydrodynamic control. In addition, the Bayesian formalism allows quantifying uncertainty on the inferred parameters. In this paper, the GPT technique is validated using a synthetic data set expected from the WEST tokamak, and the results are shown of its application to the reconstruction of SXR emissivity profiles measured on Tore Supra. The method is compared with the standard algorithm based on minimization of the Fisher information.

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.

Dissolution curve comparisons through the F(2) parameter, a Bayesian extension of the f(2) statistic.

PubMed

Novick, Steven; Shen, Yan; Yang, Harry; Peterson, John; LeBlond, Dave; Altan, Stan

2015-01-01

Dissolution (or in vitro release) studies constitute an important aspect of pharmaceutical drug development. One important use of such studies is for justifying a biowaiver for post-approval changes which requires establishing equivalence between the new and old product. We propose a statistically rigorous modeling approach for this purpose based on the estimation of what we refer to as the F2 parameter, an extension of the commonly used f2 statistic. A Bayesian test procedure is proposed in relation to a set of composite hypotheses that capture the similarity requirement on the absolute mean differences between test and reference dissolution profiles. Several examples are provided to illustrate the application. Results of our simulation study comparing the performance of f2 and the proposed method show that our Bayesian approach is comparable to or in many cases superior to the f2 statistic as a decision rule. Further useful extensions of the method, such as the use of continuous-time dissolution modeling, are considered.

A Bayesian Approach for Measurements of Stray Neutrons at Proton Therapy Facilities: Quantifying Neutron Dose Uncertainty.

PubMed

Dommert, M; Reginatto, M; Zboril, M; Fiedler, F; Helmbrecht, S; Enghardt, W; Lutz, B

2017-11-28

Bonner sphere measurements are typically analyzed using unfolding codes. It is well known that it is difficult to get reliable estimates of uncertainties for standard unfolding procedures. An alternative approach is to analyze the data using Bayesian parameter estimation. This method provides reliable estimates of the uncertainties of neutron spectra leading to rigorous estimates of uncertainties of the dose. We extend previous Bayesian approaches and apply the method to stray neutrons in proton therapy environments by introducing a new parameterized model which describes the main features of the expected neutron spectra. The parameterization is based on information that is available from measurements and detailed Monte Carlo simulations. The validity of this approach has been validated with results of an experiment using Bonner spheres carried out at the experimental hall of the OncoRay proton therapy facility in Dresden. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Bayesian Methods and Universal Darwinism

NASA Astrophysics Data System (ADS)

Campbell, John

2009-12-01

Bayesian methods since the time of Laplace have been understood by their practitioners as closely aligned to the scientific method. Indeed a recent Champion of Bayesian methods, E. T. Jaynes, titled his textbook on the subject Probability Theory: the Logic of Science. Many philosophers of science including Karl Popper and Donald Campbell have interpreted the evolution of Science as a Darwinian process consisting of a `copy with selective retention' algorithm abstracted from Darwin's theory of Natural Selection. Arguments are presented for an isomorphism between Bayesian Methods and Darwinian processes. Universal Darwinism, as the term has been developed by Richard Dawkins, Daniel Dennett and Susan Blackmore, is the collection of scientific theories which explain the creation and evolution of their subject matter as due to the Operation of Darwinian processes. These subject matters span the fields of atomic physics, chemistry, biology and the social sciences. The principle of Maximum Entropy states that Systems will evolve to states of highest entropy subject to the constraints of scientific law. This principle may be inverted to provide illumination as to the nature of scientific law. Our best cosmological theories suggest the universe contained much less complexity during the period shortly after the Big Bang than it does at present. The scientific subject matter of atomic physics, chemistry, biology and the social sciences has been created since that time. An explanation is proposed for the existence of this subject matter as due to the evolution of constraints in the form of adaptations imposed on Maximum Entropy. It is argued these adaptations were discovered and instantiated through the Operations of a succession of Darwinian processes.

New insights into faster computation of uncertainties

NASA Astrophysics Data System (ADS)

Bhattacharya, Atreyee

2012-11-01

Heavy computation power, lengthy simulations, and an exhaustive number of model runs—often these seem like the only statistical tools that scientists have at their disposal when computing uncertainties associated with predictions, particularly in cases of environmental processes such as groundwater movement. However, calculation of uncertainties need not be as lengthy, a new study shows. Comparing two approaches—the classical Bayesian “credible interval” and a less commonly used regression-based “confidence interval” method—Lu et al. show that for many practical purposes both methods provide similar estimates of uncertainties. The advantage of the regression method is that it demands 10-1000 model runs, whereas the classical Bayesian approach requires 10,000 to millions of model runs.

Bayesian data augmentation methods for the synthesis of qualitative and quantitative research findings

PubMed Central

Crandell, Jamie L.; Voils, Corrine I.; Chang, YunKyung; Sandelowski, Margarete

2010-01-01

The possible utility of Bayesian methods for the synthesis of qualitative and quantitative research has been repeatedly suggested but insufficiently investigated. In this project, we developed and used a Bayesian method for synthesis, with the goal of identifying factors that influence adherence to HIV medication regimens. We investigated the effect of 10 factors on adherence. Recognizing that not all factors were examined in all studies, we considered standard methods for dealing with missing data and chose a Bayesian data augmentation method. We were able to summarize, rank, and compare the effects of each of the 10 factors on medication adherence. This is a promising methodological development in the synthesis of qualitative and quantitative research. PMID:21572970

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.

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.

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…

Mean Field Variational Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

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).

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

Bayesian Inference for NASA Probabilistic Risk and Reliability Analysis

NASA Technical Reports Server (NTRS)

Dezfuli, Homayoon; Kelly, Dana; Smith, Curtis; Vedros, Kurt; Galyean, William

2009-01-01

This document, Bayesian Inference for NASA Probabilistic Risk and Reliability Analysis, is intended to provide guidelines for the collection and evaluation of risk and reliability-related data. It is aimed at scientists and engineers familiar with risk and reliability methods and provides a hands-on approach to the investigation and application of a variety of risk and reliability data assessment methods, tools, and techniques. This document provides both: A broad perspective on data analysis collection and evaluation issues. A narrow focus on the methods to implement a comprehensive information repository. The topics addressed herein cover the fundamentals of how data and information are to be used in risk and reliability analysis models and their potential role in decision making. Understanding these topics is essential to attaining a risk informed decision making environment that is being sought by NASA requirements and procedures such as 8000.4 (Agency Risk Management Procedural Requirements), NPR 8705.05 (Probabilistic Risk Assessment Procedures for NASA Programs and Projects), and the System Safety requirements of NPR 8715.3 (NASA General Safety Program Requirements).

Geostatistics and Bayesian updating for transmissivity estimation in a multiaquifer system in Manitoba, Canada.

PubMed

Kennedy, Paula L; Woodbury, Allan D

2002-01-01

In ground water flow and transport modeling, the heterogeneous nature of porous media has a considerable effect on the resulting flow and solute transport. Some method of generating the heterogeneous field from a limited dataset of uncertain measurements is required. Bayesian updating is one method that interpolates from an uncertain dataset using the statistics of the underlying probability distribution function. In this paper, Bayesian updating was used to determine the heterogeneous natural log transmissivity field for a carbonate and a sandstone aquifer in southern Manitoba. It was determined that the transmissivity in m2/sec followed a natural log normal distribution for both aquifers with a mean of -7.2 and - 8.0 for the carbonate and sandstone aquifers, respectively. The variograms were calculated using an estimator developed by Li and Lake (1994). Fractal nature was not evident in the variogram from either aquifer. The Bayesian updating heterogeneous field provided good results even in cases where little data was available. A large transmissivity zone in the sandstone aquifer was created by the Bayesian procedure, which is not a reflection of any deterministic consideration, but is a natural outcome of updating a prior probability distribution function with observations. The statistical model returns a result that is very reasonable; that is homogeneous in regions where little or no information is available to alter an initial state. No long range correlation trends or fractal behavior of the log-transmissivity field was observed in either aquifer over a distance of about 300 km.

Bayesian techniques for analyzing group differences in the Iowa Gambling Task: A case study of intuitive and deliberate decision-makers.

PubMed

Steingroever, Helen; Pachur, Thorsten; Šmíra, Martin; Lee, Michael D

2018-06-01

The Iowa Gambling Task (IGT) is one of the most popular experimental paradigms for comparing complex decision-making across groups. Most commonly, IGT behavior is analyzed using frequentist tests to compare performance across groups, and to compare inferred parameters of cognitive models developed for the IGT. Here, we present a Bayesian alternative based on Bayesian repeated-measures ANOVA for comparing performance, and a suite of three complementary model-based methods for assessing the cognitive processes underlying IGT performance. The three model-based methods involve Bayesian hierarchical parameter estimation, Bayes factor model comparison, and Bayesian latent-mixture modeling. We illustrate these Bayesian methods by applying them to test the extent to which differences in intuitive versus deliberate decision style are associated with differences in IGT performance. The results show that intuitive and deliberate decision-makers behave similarly on the IGT, and the modeling analyses consistently suggest that both groups of decision-makers rely on similar cognitive processes. Our results challenge the notion that individual differences in intuitive and deliberate decision styles have a broad impact on decision-making. They also highlight the advantages of Bayesian methods, especially their ability to quantify evidence in favor of the null hypothesis, and that they allow model-based analyses to incorporate hierarchical and latent-mixture structures.

Development of uncertainty-based work injury model using Bayesian structural equation modelling.

PubMed

Chatterjee, Snehamoy

2014-01-01

This paper proposed a Bayesian method-based structural equation model (SEM) of miners' work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts' opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts' opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

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

USGS Publications Warehouse

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

2013-01-01

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

Bayesian logistic regression approaches to predict incorrect DRG assignment.

PubMed

Suleiman, Mani; Demirhan, Haydar; Boyd, Leanne; Girosi, Federico; Aksakalli, Vural

2018-05-07

Episodes of care involving similar diagnoses and treatments and requiring similar levels of resource utilisation are grouped to the same Diagnosis-Related Group (DRG). In jurisdictions which implement DRG based payment systems, DRGs are a major determinant of funding for inpatient care. Hence, service providers often dedicate auditing staff to the task of checking that episodes have been coded to the correct DRG. The use of statistical models to estimate an episode's probability of DRG error can significantly improve the efficiency of clinical coding audits. This study implements Bayesian logistic regression models with weakly informative prior distributions to estimate the likelihood that episodes require a DRG revision, comparing these models with each other and to classical maximum likelihood estimates. All Bayesian approaches had more stable model parameters than maximum likelihood. The best performing Bayesian model improved overall classification per- formance by 6% compared to maximum likelihood, with a 34% gain compared to random classification, respectively. We found that the original DRG, coder and the day of coding all have a significant effect on the likelihood of DRG error. Use of Bayesian approaches has improved model parameter stability and classification accuracy. This method has already lead to improved audit efficiency in an operational capacity.

Bayesian Inference and Online Learning in Poisson Neuronal Networks.

PubMed

Huang, Yanping; Rao, Rajesh P N

2016-08-01

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

Near Real-Time Probabilistic Damage Diagnosis Using Surrogate Modeling and High Performance Computing

NASA Technical Reports Server (NTRS)

Warner, James E.; Zubair, Mohammad; Ranjan, Desh

2017-01-01

This work investigates novel approaches to probabilistic damage diagnosis that utilize surrogate modeling and high performance computing (HPC) to achieve substantial computational speedup. Motivated by Digital Twin, a structural health management (SHM) paradigm that integrates vehicle-specific characteristics with continual in-situ damage diagnosis and prognosis, the methods studied herein yield near real-time damage assessments that could enable monitoring of a vehicle's health while it is operating (i.e. online SHM). High-fidelity modeling and uncertainty quantification (UQ), both critical to Digital Twin, are incorporated using finite element method simulations and Bayesian inference, respectively. The crux of the proposed Bayesian diagnosis methods, however, is the reformulation of the numerical sampling algorithms (e.g. Markov chain Monte Carlo) used to generate the resulting probabilistic damage estimates. To this end, three distinct methods are demonstrated for rapid sampling that utilize surrogate modeling and exploit various degrees of parallelism for leveraging HPC. The accuracy and computational efficiency of the methods are compared on the problem of strain-based crack identification in thin plates. While each approach has inherent problem-specific strengths and weaknesses, all approaches are shown to provide accurate probabilistic damage diagnoses and several orders of magnitude computational speedup relative to a baseline Bayesian diagnosis implementation.

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.

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

PubMed

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

2016-10-01

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

Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Markley, F. Landis

2010-01-01

When facing a conjunction between space objects, decision makers must chose whether to maneuver for collision avoidance or not. We apply a well-known decision procedure, the sequential probability ratio test, to this problem. We propose two approaches to the problem solution, one based on a frequentist method, and the other on a Bayesian method. The frequentist method does not require any prior knowledge concerning the conjunction, while the Bayesian method assumes knowledge of prior probability densities. Our results show that both methods achieve desired missed detection rates, but the frequentist method's false alarm performance is inferior to the Bayesian method's

Informative priors on fetal fraction increase power of the noninvasive prenatal screen.

PubMed

Xu, Hanli; Wang, Shaowei; Ma, Lin-Lin; Huang, Shuai; Liang, Lin; Liu, Qian; Liu, Yang-Yang; Liu, Ke-Di; Tan, Ze-Min; Ban, Hao; Guan, Yongtao; Lu, Zuhong

2017-11-09

PurposeNoninvasive prenatal screening (NIPS) sequences a mixture of the maternal and fetal cell-free DNA. Fetal trisomy can be detected by examining chromosomal dosages estimated from sequencing reads. The traditional method uses the Z-test, which compares a subject against a set of euploid controls, where the information of fetal fraction is not fully utilized. Here we present a Bayesian method that leverages informative priors on the fetal fraction.MethodOur Bayesian method combines the Z-test likelihood and informative priors of the fetal fraction, which are learned from the sex chromosomes, to compute Bayes factors. Bayesian framework can account for nongenetic risk factors through the prior odds, and our method can report individual positive/negative predictive values.ResultsOur Bayesian method has more power than the Z-test method. We analyzed 3,405 NIPS samples and spotted at least 9 (of 51) possible Z-test false positives.ConclusionBayesian NIPS is more powerful than the Z-test method, is able to account for nongenetic risk factors through prior odds, and can report individual positive/negative predictive values.Genetics in Medicine advance online publication, 9 November 2017; doi:10.1038/gim.2017.186.

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 outcome-based strategy classification.

PubMed

Lee, Michael D

2016-03-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2008-11-01

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

Bayesian methods in reliability

NASA Astrophysics Data System (ADS)

Sander, P.; Badoux, R.

1991-11-01

The present proceedings from a course on Bayesian methods in reliability encompasses Bayesian statistical methods and their computational implementation, models for analyzing censored data from nonrepairable systems, the traits of repairable systems and growth models, the use of expert judgment, and a review of the problem of forecasting software reliability. Specific issues addressed include the use of Bayesian methods to estimate the leak rate of a gas pipeline, approximate analyses under great prior uncertainty, reliability estimation techniques, and a nonhomogeneous Poisson process. Also addressed are the calibration sets and seed variables of expert judgment systems for risk assessment, experimental illustrations of the use of expert judgment for reliability testing, and analyses of the predictive quality of software-reliability growth models such as the Weibull order statistics.

Efficient fuzzy Bayesian inference algorithms for incorporating expert knowledge in parameter estimation

NASA Astrophysics Data System (ADS)

Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad

2016-05-01

Bayesian inference has traditionally been conceived as the proper framework for the formal incorporation of expert knowledge in parameter estimation of groundwater models. However, conventional Bayesian inference is incapable of taking into account the imprecision essentially embedded in expert provided information. In order to solve this problem, a number of extensions to conventional Bayesian inference have been introduced in recent years. One of these extensions is 'fuzzy Bayesian inference' which is the result of integrating fuzzy techniques into Bayesian statistics. Fuzzy Bayesian inference has a number of desirable features which makes it an attractive approach for incorporating expert knowledge in the parameter estimation process of groundwater models: (1) it is well adapted to the nature of expert provided information, (2) it allows to distinguishably model both uncertainty and imprecision, and (3) it presents a framework for fusing expert provided information regarding the various inputs of the Bayesian inference algorithm. However an important obstacle in employing fuzzy Bayesian inference in groundwater numerical modeling applications is the computational burden, as the required number of numerical model simulations often becomes extremely exhaustive and often computationally infeasible. In this paper, a novel approach of accelerating the fuzzy Bayesian inference algorithm is proposed which is based on using approximate posterior distributions derived from surrogate modeling, as a screening tool in the computations. The proposed approach is first applied to a synthetic test case of seawater intrusion (SWI) in a coastal aquifer. It is shown that for this synthetic test case, the proposed approach decreases the number of required numerical simulations by an order of magnitude. Then the proposed approach is applied to a real-world test case involving three-dimensional numerical modeling of SWI in Kish Island, located in the Persian Gulf. An expert elicitation methodology is developed and applied to the real-world test case in order to provide a road map for the use of fuzzy Bayesian inference in groundwater modeling applications.

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.

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.

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

PubMed

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

2004-10-01

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

Bayesian data analysis for newcomers.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.

Assessing Argumentative Representation with Bayesian Network Models in Debatable Social Issues

ERIC Educational Resources Information Center

Zhang, Zhidong; Lu, Jingyan

2014-01-01

This study seeks to obtain argumentation models, which represent argumentative processes and an assessment structure in secondary school debatable issues in the social sciences. The argumentation model was developed based on mixed methods, a combination of both theory-driven and data-driven methods. The coding system provided a combing point by…

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.

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…

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.

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.

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

PubMed Central

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

2016-01-01

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

[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.

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

The Psychology of Bayesian Reasoning

DTIC Science & Technology

2014-10-21

The psychology of Bayesian reasoning David R. Mandel* Socio-Cognitive Systems Section, Defence Research and Development Canada and Department...belief revision, subjective probability, human judgment, psychological methods. Most psychological research on Bayesian reasoning since the 1970s has...attention to some important problems with the conventional approach to studying Bayesian reasoning in psychology that has been dominant since the

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

PubMed

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

2017-02-01

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

UQTk Version 3.0.3 User Manual

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

Sargsyan, Khachik; Safta, Cosmin; Chowdhary, Kamaljit Singh

2017-05-01

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.0.3 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sen- sitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

Probability, statistics, and computational science.

PubMed

Beerenwinkel, Niko; Siebourg, Juliane

2012-01-01

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

Bayesian Decision Support for Adaptive Lung Treatments

NASA Astrophysics Data System (ADS)

McShan, Daniel; Luo, Yi; Schipper, Matt; TenHaken, Randall

2014-03-01

Purpose: A Bayesian Decision Network will be demonstrated to provide clinical decision support for adaptive lung response-driven treatment management based on evidence that physiologic metrics may correlate better with individual patient response than traditional (population-based) dose and volume-based metrics. Further, there is evidence that information obtained during the course of radiation therapy may further improve response predictions. Methods: Clinical factors were gathered for 58 patients including planned mean lung dose, and the bio-markers IL-8 and TGF-β1 obtained prior to treatment and two weeks into treatment along with complication outcomes for these patients. A Bayesian Decision Network was constructed using Netica 5.0.2 from Norsys linking these clinical factors to obtain a prediction of radiation induced lung disese (RILD) complication. A decision node was added to the network to provide a plan adaption recommendation based on the trade-off between the RILD prediction and complexity of replanning. A utility node provides the weighting cost between the competing factors. Results: The decision node predictions were optimized against the data for the 58 cases. With this decision network solution, one can consider the decision result for a new patient with specific findings to obtain a recommendation to adaptively modify the originally planned treatment course. Conclusions: A Bayesian approach allows handling and propagating probabilistic data in a logical and principled manner. Decision networks provide the further ability to provide utility-based trade-offs, reflecting non-medical but practical cost/benefit analysis. The network demonstrated illustrates the basic concept, but many other factors may affect these decisions and work on building better models are being designed and tested. Acknowledgement: Supported by NIH-P01-CA59827

Is probabilistic bias analysis approximately Bayesian?

PubMed Central

MacLehose, Richard F.; Gustafson, Paul

2011-01-01

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

Unsupervised Bayesian linear unmixing of gene expression microarrays.

PubMed

Bazot, Cécile; Dobigeon, Nicolas; Tourneret, Jean-Yves; Zaas, Aimee K; Ginsburg, Geoffrey S; Hero, Alfred O

2013-03-19

This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters. Firstly, the proposed uBLU method is applied to several simulated datasets with known ground truth and compared with previous factor decomposition methods, such as principal component analysis (PCA), non negative matrix factorization (NMF), Bayesian factor regression modeling (BFRM), and the gradient-based algorithm for general matrix factorization (GB-GMF). Secondly, we illustrate the application of uBLU on a real time-evolving gene expression dataset from a recent viral challenge study in which individuals have been inoculated with influenza A/H3N2/Wisconsin. We show that the uBLU method significantly outperforms the other methods on the simulated and real data sets considered here. The results obtained on synthetic and real data illustrate the accuracy of the proposed uBLU method when compared to other factor decomposition methods from the literature (PCA, NMF, BFRM, and GB-GMF). The uBLU method identifies an inflammatory component closely associated with clinical symptom scores collected during the study. Using a constrained model allows recovery of all the inflammatory genes in a single factor.

A Bayesian Method for Evaluating and Discovering Disease Loci Associations

PubMed Central

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

2011-01-01

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

A Bayesian Approach to the Paleomagnetic Conglomerate Test

NASA Astrophysics Data System (ADS)

Heslop, David; Roberts, Andrew P.

2018-02-01

The conglomerate test has served the paleomagnetic community for over 60 years as a means to detect remagnetizations. The test states that if a suite of clasts within a bed have uniformly random paleomagnetic directions, then the conglomerate cannot have experienced a pervasive event that remagnetized the clasts in the same direction. The current form of the conglomerate test is based on null hypothesis testing, which results in a binary "pass" (uniformly random directions) or "fail" (nonrandom directions) outcome. We have recast the conglomerate test in a Bayesian framework with the aim of providing more information concerning the level of support a given data set provides for a hypothesis of uniformly random paleomagnetic directions. Using this approach, we place the conglomerate test in a fully probabilistic framework that allows for inconclusive results when insufficient information is available to draw firm conclusions concerning the randomness or nonrandomness of directions. With our method, sample sets larger than those typically employed in paleomagnetism may be required to achieve strong support for a hypothesis of random directions. Given the potentially detrimental effect of unrecognized remagnetizations on paleomagnetic reconstructions, it is important to provide a means to draw statistically robust data-driven inferences. Our Bayesian analysis provides a means to do this for the conglomerate test.

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

NASA Astrophysics Data System (ADS)

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

2008-04-01

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

A multiscale Bayesian data integration approach for mapping air dose rates around the Fukushima Daiichi Nuclear Power Plant.

PubMed

Wainwright, Haruko M; Seki, Akiyuki; Chen, Jinsong; Saito, Kimiaki

2017-02-01

This paper presents a multiscale data integration method to estimate the spatial distribution of air dose rates in the regional scale around the Fukushima Daiichi Nuclear Power Plant. We integrate various types of datasets, such as ground-based walk and car surveys, and airborne surveys, all of which have different scales, resolutions, spatial coverage, and accuracy. This method is based on geostatistics to represent spatial heterogeneous structures, and also on Bayesian hierarchical models to integrate multiscale, multi-type datasets in a consistent manner. The Bayesian method allows us to quantify the uncertainty in the estimates, and to provide the confidence intervals that are critical for robust decision-making. Although this approach is primarily data-driven, it has great flexibility to include mechanistic models for representing radiation transport or other complex correlations. We demonstrate our approach using three types of datasets collected at the same time over Fukushima City in Japan: (1) coarse-resolution airborne surveys covering the entire area, (2) car surveys along major roads, and (3) walk surveys in multiple neighborhoods. Results show that the method can successfully integrate three types of datasets and create an integrated map (including the confidence intervals) of air dose rates over the domain in high resolution. Moreover, this study provides us with various insights into the characteristics of each dataset, as well as radiocaesium distribution. In particular, the urban areas show high heterogeneity in the contaminant distribution due to human activities as well as large discrepancy among different surveys due to such heterogeneity. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

Estimation of the latent mediated effect with ordinal data using the limited-information and Bayesian full-information approaches.

PubMed

Chen, Jinsong; Zhang, Dake; Choi, Jaehwa

2015-12-01

It is common to encounter latent variables with ordinal data in social or behavioral research. Although a mediated effect of latent variables (latent mediated effect, or LME) with ordinal data may appear to be a straightforward combination of LME with continuous data and latent variables with ordinal data, the methodological challenges to combine the two are not trivial. This research covers model structures as complex as LME and formulates both point and interval estimates of LME for ordinal data using the Bayesian full-information approach. We also combine weighted least squares (WLS) estimation with the bias-corrected bootstrapping (BCB; Efron Journal of the American Statistical Association, 82, 171-185, 1987) method or the traditional delta method as the limited-information approach. We evaluated the viability of these different approaches across various conditions through simulation studies, and provide an empirical example to illustrate the approaches. We found that the Bayesian approach with reasonably informative priors is preferred when both point and interval estimates are of interest and the sample size is 200 or above.

Integrating quantitative PCR and Bayesian statistics in quantifying human adenoviruses in small volumes of source water.

PubMed

Wu, Jianyong; Gronewold, Andrew D; Rodriguez, Roberto A; Stewart, Jill R; Sobsey, Mark D

2014-02-01

Rapid quantification of viral pathogens in drinking and recreational water can help reduce waterborne disease risks. For this purpose, samples in small volume (e.g. 1L) are favored because of the convenience of collection, transportation and processing. However, the results of viral analysis are often subject to uncertainty. To overcome this limitation, we propose an approach that integrates Bayesian statistics, efficient concentration methods, and quantitative PCR (qPCR) to quantify viral pathogens in water. Using this approach, we quantified human adenoviruses (HAdVs) in eighteen samples of source water collected from six drinking water treatment plants. HAdVs were found in seven samples. In the other eleven samples, HAdVs were not detected by qPCR, but might have existed based on Bayesian inference. Our integrated approach that quantifies uncertainty provides a better understanding than conventional assessments of potential risks to public health, particularly in cases when pathogens may present a threat but cannot be detected by traditional methods. © 2013 Elsevier B.V. All rights reserved.

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.

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%.

Statistical modeling for Bayesian extrapolation of adult clinical trial information in pediatric drug evaluation.

PubMed

Gamalo-Siebers, Margaret; Savic, Jasmina; Basu, Cynthia; Zhao, Xin; Gopalakrishnan, Mathangi; Gao, Aijun; Song, Guochen; Baygani, Simin; Thompson, Laura; Xia, H Amy; Price, Karen; Tiwari, Ram; Carlin, Bradley P

2017-07-01

Children represent a large underserved population of "therapeutic orphans," as an estimated 80% of children are treated off-label. However, pediatric drug development often faces substantial challenges, including economic, logistical, technical, and ethical barriers, among others. Among many efforts trying to remove these barriers, increased recent attention has been paid to extrapolation; that is, the leveraging of available data from adults or older age groups to draw conclusions for the pediatric population. The Bayesian statistical paradigm is natural in this setting, as it permits the combining (or "borrowing") of information across disparate sources, such as the adult and pediatric data. In this paper, authored by the pediatric subteam of the Drug Information Association Bayesian Scientific Working Group and Adaptive Design Working Group, we develop, illustrate, and provide suggestions on Bayesian statistical methods that could be used to design improved pediatric development programs that use all available information in the most efficient manner. A variety of relevant Bayesian approaches are described, several of which are illustrated through 2 case studies: extrapolating adult efficacy data to expand the labeling for Remicade to include pediatric ulcerative colitis and extrapolating adult exposure-response information for antiepileptic drugs to pediatrics. Copyright © 2017 John Wiley & Sons, Ltd.

Approximate Bayesian evaluations of measurement uncertainty

NASA Astrophysics Data System (ADS)

Possolo, Antonio; Bodnar, Olha

2018-04-01

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

Estimating Bayesian Phylogenetic Information Content

PubMed Central

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

2016-01-01

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

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.

Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method.

PubMed

Zhang, Guanglei; Liu, Fei; Liu, Jie; Luo, Jianwen; Xie, Yaoqin; Bai, Jing; Xing, Lei

2017-01-01

X-ray luminescence computed tomography (XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. Combining the principles of X-ray excitation of luminescence-based probes and optical signal detection, XLCT naturally fuses functional and anatomical images and provides complementary information for a wide range of applications in biomedical research. In order to improve the data acquisition efficiency of previously developed narrow-beam XLCT, a cone beam XLCT (CB-XLCT) mode is adopted here to take advantage of the useful geometric features of cone beam excitation. Practically, a major hurdle in using cone beam X-ray for XLCT is that the inverse problem here is seriously ill-conditioned, hindering us to achieve good image quality. In this paper, we propose a novel Bayesian method to tackle the bottleneck in CB-XLCT reconstruction. The method utilizes a local regularization strategy based on Gaussian Markov random field to mitigate the ill-conditioness of CB-XLCT. An alternating optimization scheme is then used to automatically calculate all the unknown hyperparameters while an iterative coordinate descent algorithm is adopted to reconstruct the image with a voxel-based closed-form solution. Results of numerical simulations and mouse experiments show that the self-adaptive Bayesian method significantly improves the CB-XLCT image quality as compared with conventional methods.

Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method

PubMed Central

Liu, Fei; Luo, Jianwen; Xie, Yaoqin; Bai, Jing

2017-01-01

X-ray luminescence computed tomography (XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. Combining the principles of X-ray excitation of luminescence-based probes and optical signal detection, XLCT naturally fuses functional and anatomical images and provides complementary information for a wide range of applications in biomedical research. In order to improve the data acquisition efficiency of previously developed narrow-beam XLCT, a cone beam XLCT (CB-XLCT) mode is adopted here to take advantage of the useful geometric features of cone beam excitation. Practically, a major hurdle in using cone beam X-ray for XLCT is that the inverse problem here is seriously ill-conditioned, hindering us to achieve good image quality. In this paper, we propose a novel Bayesian method to tackle the bottleneck in CB-XLCT reconstruction. The method utilizes a local regularization strategy based on Gaussian Markov random field to mitigate the ill-conditioness of CB-XLCT. An alternating optimization scheme is then used to automatically calculate all the unknown hyperparameters while an iterative coordinate descent algorithm is adopted to reconstruct the image with a voxel-based closed-form solution. Results of numerical simulations and mouse experiments show that the self-adaptive Bayesian method significantly improves the CB-XLCT image quality as compared with conventional methods. PMID:27576245

Selection of Polynomial Chaos Bases via Bayesian Model Uncertainty Methods with Applications to Sparse Approximation of PDEs with Stochastic Inputs

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

Karagiannis, Georgios; Lin, Guang

2014-02-15

Generalized polynomial chaos (gPC) expansions allow the representation of the solution of a stochastic system as a series of polynomial terms. The number of gPC terms increases dramatically with the dimension of the random input variables. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs if the evaluations of the system are expensive, the evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solution, both in spacial and random domains, by coupling Bayesianmore » model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spacial points via (1) Bayesian model average or (2) medial probability model, and their construction as functions on the spacial domain via spline interpolation. The former accounts the model uncertainty and provides Bayes-optimal predictions; while the latter, additionally, provides a sparse representation of the solution by evaluating the expansion on a subset of dominating gPC bases when represented as a gPC expansion. Moreover, the method quantifies the importance of the gPC bases through inclusion probabilities. We design an MCMC sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed method is suitable for, but not restricted to, problems whose stochastic solution is sparse at the stochastic level with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the good performance of the proposed method and make comparisons with others on 1D, 14D and 40D in random space elliptic stochastic partial differential equations.« less

Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design

NASA Astrophysics Data System (ADS)

Leube, P. C.; Geiges, A.; Nowak, W.

2012-02-01

Incorporating hydro(geo)logical data, such as head and tracer data, into stochastic models of (subsurface) flow and transport helps to reduce prediction uncertainty. Because of financial limitations for investigation campaigns, information needs toward modeling or prediction goals should be satisfied efficiently and rationally. Optimal design techniques find the best one among a set of investigation strategies. They optimize the expected impact of data on prediction confidence or related objectives prior to data collection. We introduce a new optimal design method, called PreDIA(gnosis) (Preposterior Data Impact Assessor). PreDIA derives the relevant probability distributions and measures of data utility within a fully Bayesian, generalized, flexible, and accurate framework. It extends the bootstrap filter (BF) and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values. PreDIA is a strictly formal information-processing scheme free of linearizations. It works with arbitrary simulation tools, provides full flexibility concerning measurement types (linear, nonlinear, direct, indirect), allows for any desired task-driven formulations, and can account for various sources of uncertainty (e.g., heterogeneity, geostatistical assumptions, boundary conditions, measurement values, model structure uncertainty, a large class of model errors) via Bayesian geostatistics and model averaging. Existing methods fail to simultaneously provide these crucial advantages, which our method buys at relatively higher-computational costs. We demonstrate the applicability and advantages of PreDIA over conventional linearized methods in a synthetic example of subsurface transport. In the example, we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence. Hence, PreDIA will often lead to substantially better sampling designs. Finally, we extend our example to specifically highlight the consideration of conceptual model uncertainty.

Bayesian methods for characterizing unknown parameters of material models

DOE PAGES

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

2016-02-04

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

Bayesian methods for characterizing unknown parameters of material models

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

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

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

Bayesian Hypothesis Testing for Psychologists: A Tutorial on the Savage-Dickey Method

ERIC Educational Resources Information Center

Wagenmakers, Eric-Jan; Lodewyckx, Tom; Kuriyal, Himanshu; Grasman, Raoul

2010-01-01

In the field of cognitive psychology, the "p"-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the "p"-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is…

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.

A novel method for expediting the development of patient-reported outcome measures and an evaluation across several populations

PubMed Central

Garrard, Lili; Price, Larry R.; Bott, Marjorie J.; Gajewski, Byron J.

2016-01-01

Item response theory (IRT) models provide an appropriate alternative to the classical ordinal confirmatory factor analysis (CFA) during the development of patient-reported outcome measures (PROMs). Current literature has identified the assessment of IRT model fit as both challenging and underdeveloped (Sinharay & Johnson, 2003; Sinharay, Johnson, & Stern, 2006). This study evaluates the performance of Ordinal Bayesian Instrument Development (OBID), a Bayesian IRT model with a probit link function approach, through applications in two breast cancer-related instrument development studies. The primary focus is to investigate an appropriate method for comparing Bayesian IRT models in PROMs development. An exact Bayesian leave-one-out cross-validation (LOO-CV) approach (Vehtari & Lampinen, 2002) is implemented to assess prior selection for the item discrimination parameter in the IRT model and subject content experts’ bias (in a statistical sense and not to be confused with psychometric bias as in differential item functioning) toward the estimation of item-to-domain correlations. Results support the utilization of content subject experts’ information in establishing evidence for construct validity when sample size is small. However, the incorporation of subject experts’ content information in the OBID approach can be sensitive to the level of expertise of the recruited experts. More stringent efforts need to be invested in the appropriate selection of subject experts to efficiently use the OBID approach and reduce potential bias during PROMs development. PMID:27667878

A novel method for expediting the development of patient-reported outcome measures and an evaluation across several populations.

PubMed

Garrard, Lili; Price, Larry R; Bott, Marjorie J; Gajewski, Byron J

2016-10-01

Item response theory (IRT) models provide an appropriate alternative to the classical ordinal confirmatory factor analysis (CFA) during the development of patient-reported outcome measures (PROMs). Current literature has identified the assessment of IRT model fit as both challenging and underdeveloped (Sinharay & Johnson, 2003; Sinharay, Johnson, & Stern, 2006). This study evaluates the performance of Ordinal Bayesian Instrument Development (OBID), a Bayesian IRT model with a probit link function approach, through applications in two breast cancer-related instrument development studies. The primary focus is to investigate an appropriate method for comparing Bayesian IRT models in PROMs development. An exact Bayesian leave-one-out cross-validation (LOO-CV) approach (Vehtari & Lampinen, 2002) is implemented to assess prior selection for the item discrimination parameter in the IRT model and subject content experts' bias (in a statistical sense and not to be confused with psychometric bias as in differential item functioning) toward the estimation of item-to-domain correlations. Results support the utilization of content subject experts' information in establishing evidence for construct validity when sample size is small. However, the incorporation of subject experts' content information in the OBID approach can be sensitive to the level of expertise of the recruited experts. More stringent efforts need to be invested in the appropriate selection of subject experts to efficiently use the OBID approach and reduce potential bias during PROMs development.

A parametric interpretation of Bayesian Nonparametric Inference from Gene Genealogies: Linking ecological, population genetics and evolutionary processes.

PubMed

Ponciano, José Miguel

2017-11-22

Using a nonparametric Bayesian approach Palacios and Minin (2013) dramatically improved the accuracy, precision of Bayesian inference of population size trajectories from gene genealogies. These authors proposed an extension of a Gaussian Process (GP) nonparametric inferential method for the intensity function of non-homogeneous Poisson processes. They found that not only the statistical properties of the estimators were improved with their method, but also, that key aspects of the demographic histories were recovered. The authors' work represents the first Bayesian nonparametric solution to this inferential problem because they specify a convenient prior belief without a particular functional form on the population trajectory. Their approach works so well and provides such a profound understanding of the biological process, that the question arises as to how truly "biology-free" their approach really is. Using well-known concepts of stochastic population dynamics, here I demonstrate that in fact, Palacios and Minin's GP model can be cast as a parametric population growth model with density dependence and environmental stochasticity. Making this link between population genetics and stochastic population dynamics modeling provides novel insights into eliciting biologically meaningful priors for the trajectory of the effective population size. The results presented here also bring novel understanding of GP as models for the evolution of a trait. Thus, the ecological principles foundation of Palacios and Minin (2013)'s prior adds to the conceptual and scientific value of these authors' inferential approach. I conclude this note by listing a series of insights brought about by this connection with Ecology. Copyright © 2017 The Author. Published by Elsevier Inc. All rights reserved.

Reducing the Uncertainty in Atlantic Meridional Overturning Circulation Projections Using Bayesian Model Averaging

NASA Astrophysics Data System (ADS)

Olson, R.; An, S. I.

2016-12-01

Atlantic Meridional Overturning Circulation (AMOC) in the ocean might slow down in the future, which can lead to a host of climatic effects in North Atlantic and throughout the world. Despite improvements in climate models and availability of new observations, AMOC projections remain uncertain. Here we constrain CMIP5 multi-model ensemble output with observations of a recently developed AMOC index to provide improved Bayesian predictions of future AMOC. Specifically, we first calculate yearly AMOC index loosely based on Rahmstorf et al. (2015) for years 1880—2004 for both observations, and the CMIP5 models for which relevant output is available. We then assign a weight to each model based on a Bayesian Model Averaging method that accounts for differential model skill in terms of both mean state and variability. We include the temporal autocorrelation in climate model errors, and account for the uncertainty in the parameters of our statistical model. We use the weights to provide future weighted projections of AMOC, and compare them to un-weighted ones. Our projections use bootstrapping to account for uncertainty in internal AMOC variability. We also perform spectral and other statistical analyses to show that AMOC index variability, both in models and in observations, is consistent with red noise. Our results improve on and complement previous work by using a new ensemble of climate models, a different observational metric, and an improved Bayesian weighting method that accounts for differential model skill at reproducing internal variability. Reference: Rahmstorf, S., Box, J. E., Feulner, G., Mann, M. E., Robinson, A., Rutherford, S., & Schaffernicht, E. J. (2015). Exceptional twentieth-century slowdown in atlantic ocean overturning circulation. Nature Climate Change, 5(5), 475-480. doi:10.1038/nclimate2554

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

PubMed

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

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

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

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

Marzouk, Youssef

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

BAYESIAN ESTIMATION OF THERMONUCLEAR REACTION RATES

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

Iliadis, C.; Anderson, K. S.; Coc, A.

The problem of estimating non-resonant astrophysical S -factors and thermonuclear reaction rates, based on measured nuclear cross sections, is of major interest for nuclear energy generation, neutrino physics, and element synthesis. Many different methods have been applied to this problem in the past, almost all of them based on traditional statistics. Bayesian methods, on the other hand, are now in widespread use in the physical sciences. In astronomy, for example, Bayesian statistics is applied to the observation of extrasolar planets, gravitational waves, and Type Ia supernovae. However, nuclear physics, in particular, has been slow to adopt Bayesian methods. We presentmore » astrophysical S -factors and reaction rates based on Bayesian statistics. We develop a framework that incorporates robust parameter estimation, systematic effects, and non-Gaussian uncertainties in a consistent manner. The method is applied to the reactions d(p, γ ){sup 3}He, {sup 3}He({sup 3}He,2p){sup 4}He, and {sup 3}He( α , γ ){sup 7}Be, important for deuterium burning, solar neutrinos, and Big Bang nucleosynthesis.« less

Statistics provide guidance for indigenous organic carbon detection on Mars missions.

PubMed

Sephton, Mark A; Carter, Jonathan N

2014-08-01

Data from the Viking and Mars Science Laboratory missions indicate the presence of organic compounds that are not definitively martian in origin. Both contamination and confounding mineralogies have been suggested as alternatives to indigenous organic carbon. Intuitive thought suggests that we are repeatedly obtaining data that confirms the same level of uncertainty. Bayesian statistics may suggest otherwise. If an organic detection method has a true positive to false positive ratio greater than one, then repeated organic matter detection progressively increases the probability of indigeneity. Bayesian statistics also reveal that methods with higher ratios of true positives to false positives give higher overall probabilities and that detection of organic matter in a sample with a higher prior probability of indigenous organic carbon produces greater confidence. Bayesian statistics, therefore, provide guidance for the planning and operation of organic carbon detection activities on Mars. Suggestions for future organic carbon detection missions and instruments are as follows: (i) On Earth, instruments should be tested with analog samples of known organic content to determine their true positive to false positive ratios. (ii) On the mission, for an instrument with a true positive to false positive ratio above one, it should be recognized that each positive detection of organic carbon will result in a progressive increase in the probability of indigenous organic carbon being present; repeated measurements, therefore, can overcome some of the deficiencies of a less-than-definitive test. (iii) For a fixed number of analyses, the highest true positive to false positive ratio method or instrument will provide the greatest probability that indigenous organic carbon is present. (iv) On Mars, analyses should concentrate on samples with highest prior probability of indigenous organic carbon; intuitive desires to contrast samples of high prior probability and low prior probability of indigenous organic carbon should be resisted.

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

PubMed Central

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

2016-01-01

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

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

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.

Self-optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification

NASA Astrophysics Data System (ADS)

Swinburne, Thomas D.; Perez, Danny

2018-05-01

A massively parallel method to build large transition rate matrices from temperature-accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state space, providing crucial uncertainty quantification for higher-scale simulation schemes such as kinetic Monte Carlo or cluster dynamics. The estimators are additionally used to optimize where exploration is performed and the degree of temperature acceleration on the fly, giving an autonomous, optimal procedure to explore the state space of complex systems. The method is tested against exactly solvable models and used to explore the dynamics of C15 interstitial defects in iron. Our uncertainty quantification scheme allows for accurate modeling of the evolution of these defects over timescales of several seconds.

Using Bayesian Imputation to Assess Racial and Ethnic Disparities in Pediatric Performance Measures.

PubMed

Brown, David P; Knapp, Caprice; Baker, Kimberly; Kaufmann, Meggen

2016-06-01

To analyze health care disparities in pediatric quality of care measures and determine the impact of data imputation. Five HEDIS measures are calculated based on 2012 administrative data for 145,652 children in two public insurance programs in Florida. The Bayesian Improved Surname and Geocoding (BISG) imputation method is used to impute missing race and ethnicity data for 42 percent of the sample (61,954 children). Models are estimated with and without the imputed race and ethnicity data. Dropping individuals with missing race and ethnicity data biases quality of care measures for minorities downward relative to nonminority children for several measures. These results provide further support for the importance of appropriately accounting for missing race and ethnicity data through imputation methods. © Health Research and Educational Trust.

On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

NASA Astrophysics Data System (ADS)

Hu, Zixi; Yao, Zhewei; Li, Jinglai

2017-03-01

Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

Bayesian averaging over Decision Tree models for trauma severity scoring.

PubMed

Schetinin, V; Jakaite, L; Krzanowski, W

2018-01-01

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

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

Brain white matter fiber estimation and tractography using Q-ball imaging and Bayesian MODEL.

PubMed

Lu, Meng

2015-01-01

Diffusion tensor imaging allows for the non-invasive in vivo mapping of the brain tractography. However, fiber bundles have complex structures such as fiber crossings, fiber branchings and fibers with large curvatures that tensor imaging (DTI) cannot accurately handle. This study presents a novel brain white matter tractography method using Q-ball imaging as the data source instead of DTI, because QBI can provide accurate information about multiple fiber crossings and branchings in a single voxel using an orientation distribution function (ODF). The presented method also uses graph theory to construct the Bayesian model-based graph, so that the fiber tracking between two voxels can be represented as the shortest path in a graph. Our experiment showed that our new method can accurately handle brain white matter fiber crossings and branchings, and reconstruct brain tractograhpy both in phantom data and real brain data.

Iterative Bayesian Estimation of Travel Times on Urban Arterials: Fusing Loop Detector and Probe Vehicle Data.

PubMed

Liu, Kai; Cui, Meng-Ying; Cao, Peng; Wang, Jiang-Bo

2016-01-01

On urban arterials, travel time estimation is challenging especially from various data sources. Typically, fusing loop detector data and probe vehicle data to estimate travel time is a troublesome issue while considering the data issue of uncertain, imprecise and even conflicting. In this paper, we propose an improved data fusing methodology for link travel time estimation. Link travel times are simultaneously pre-estimated using loop detector data and probe vehicle data, based on which Bayesian fusion is then applied to fuse the estimated travel times. Next, Iterative Bayesian estimation is proposed to improve Bayesian fusion by incorporating two strategies: 1) substitution strategy which replaces the lower accurate travel time estimation from one sensor with the current fused travel time; and 2) specially-designed conditions for convergence which restrict the estimated travel time in a reasonable range. The estimation results show that, the proposed method outperforms probe vehicle data based method, loop detector based method and single Bayesian fusion, and the mean absolute percentage error is reduced to 4.8%. Additionally, iterative Bayesian estimation performs better for lighter traffic flows when the variability of travel time is practically higher than other periods.

Iterative Bayesian Estimation of Travel Times on Urban Arterials: Fusing Loop Detector and Probe Vehicle Data

PubMed Central

Cui, Meng-Ying; Cao, Peng; Wang, Jiang-Bo

2016-01-01

On urban arterials, travel time estimation is challenging especially from various data sources. Typically, fusing loop detector data and probe vehicle data to estimate travel time is a troublesome issue while considering the data issue of uncertain, imprecise and even conflicting. In this paper, we propose an improved data fusing methodology for link travel time estimation. Link travel times are simultaneously pre-estimated using loop detector data and probe vehicle data, based on which Bayesian fusion is then applied to fuse the estimated travel times. Next, Iterative Bayesian estimation is proposed to improve Bayesian fusion by incorporating two strategies: 1) substitution strategy which replaces the lower accurate travel time estimation from one sensor with the current fused travel time; and 2) specially-designed conditions for convergence which restrict the estimated travel time in a reasonable range. The estimation results show that, the proposed method outperforms probe vehicle data based method, loop detector based method and single Bayesian fusion, and the mean absolute percentage error is reduced to 4.8%. Additionally, iterative Bayesian estimation performs better for lighter traffic flows when the variability of travel time is practically higher than other periods. PMID:27362654

Bayesian calibration for forensic age estimation.

PubMed

Ferrante, Luigi; Skrami, Edlira; Gesuita, Rosaria; Cameriere, Roberto

2015-05-10

Forensic medicine is increasingly called upon to assess the age of individuals. Forensic age estimation is mostly required in relation to illegal immigration and identification of bodies or skeletal remains. A variety of age estimation methods are based on dental samples and use of regression models, where the age of an individual is predicted by morphological tooth changes that take place over time. From the medico-legal point of view, regression models, with age as the dependent random variable entail that age tends to be overestimated in the young and underestimated in the old. To overcome this bias, we describe a new full Bayesian calibration method (asymmetric Laplace Bayesian calibration) for forensic age estimation that uses asymmetric Laplace distribution as the probability model. The method was compared with three existing approaches (two Bayesian and a classical method) using simulated data. Although its accuracy was comparable with that of the other methods, the asymmetric Laplace Bayesian calibration appears to be significantly more reliable and robust in case of misspecification of the probability model. The proposed method was also applied to a real dataset of values of the pulp chamber of the right lower premolar measured on x-ray scans of individuals of known age. Copyright © 2015 John Wiley & Sons, Ltd.

On Bayesian methods of exploring qualitative interactions for targeted treatment.

PubMed

Chen, Wei; Ghosh, Debashis; Raghunathan, Trivellore E; Norkin, Maxim; Sargent, Daniel J; Bepler, Gerold

2012-12-10

Providing personalized treatments designed to maximize benefits and minimizing harms is of tremendous current medical interest. One problem in this area is the evaluation of the interaction between the treatment and other predictor variables. Treatment effects in subgroups having the same direction but different magnitudes are called quantitative interactions, whereas those having opposite directions in subgroups are called qualitative interactions (QIs). Identifying QIs is challenging because they are rare and usually unknown among many potential biomarkers. Meanwhile, subgroup analysis reduces the power of hypothesis testing and multiple subgroup analyses inflate the type I error rate. We propose a new Bayesian approach to search for QI in a multiple regression setting with adaptive decision rules. We consider various regression models for the outcome. We illustrate this method in two examples of phase III clinical trials. The algorithm is straightforward and easy to implement using existing software packages. We provide a sample code in Appendix A. Copyright © 2012 John Wiley & Sons, Ltd.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

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

2014-01-01

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

Bayesian Statistics for Biological Data: Pedigree Analysis

ERIC Educational Resources Information Center

Stanfield, William D.; Carlton, Matthew A.

2004-01-01

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

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

PubMed

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

2018-05-31

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

Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

Epistemic-based investigation of the probability of hazard scenarios using Bayesian network for the lifting operation of floating objects

NASA Astrophysics Data System (ADS)

Toroody, Ahmad Bahoo; Abaiee, Mohammad Mahdi; Gholamnia, Reza; Ketabdari, Mohammad Javad

2016-09-01

Owing to the increase in unprecedented accidents with new root causes in almost all operational areas, the importance of risk management has dramatically risen. Risk assessment, one of the most significant aspects of risk management, has a substantial impact on the system-safety level of organizations, industries, and operations. If the causes of all kinds of failure and the interactions between them are considered, effective risk assessment can be highly accurate. A combination of traditional risk assessment approaches and modern scientific probability methods can help in realizing better quantitative risk assessment methods. Most researchers face the problem of minimal field data with respect to the probability and frequency of each failure. Because of this limitation in the availability of epistemic knowledge, it is important to conduct epistemic estimations by applying the Bayesian theory for identifying plausible outcomes. In this paper, we propose an algorithm and demonstrate its application in a case study for a light-weight lifting operation in the Persian Gulf of Iran. First, we identify potential accident scenarios and present them in an event tree format. Next, excluding human error, we use the event tree to roughly estimate the prior probability of other hazard-promoting factors using a minimal amount of field data. We then use the Success Likelihood Index Method (SLIM) to calculate the probability of human error. On the basis of the proposed event tree, we use the Bayesian network of the provided scenarios to compensate for the lack of data. Finally, we determine the resulting probability of each event based on its evidence in the epistemic estimation format by building on two Bayesian network types: the probability of hazard promotion factors and the Bayesian theory. The study results indicate that despite the lack of available information on the operation of floating objects, a satisfactory result can be achieved using epistemic data.

An NCME Instructional Module on Estimating Item Response Theory Models Using Markov Chain Monte Carlo Methods

ERIC Educational Resources Information Center

Kim, Jee-Seon; Bolt, Daniel M.

2007-01-01

The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…

Application of Turchin's method of statistical regularization

NASA Astrophysics Data System (ADS)

Zelenyi, Mikhail; Poliakova, Mariia; Nozik, Alexander; Khudyakov, Alexey

2018-04-01

During analysis of experimental data, one usually needs to restore a signal after it has been convoluted with some kind of apparatus function. According to Hadamard's definition this problem is ill-posed and requires regularization to provide sensible results. In this article we describe an implementation of the Turchin's method of statistical regularization based on the Bayesian approach to the regularization strategy.

Bayesian identification of acoustic impedance in treated ducts.

PubMed

Buot de l'Épine, Y; Chazot, J-D; Ville, J-M

2015-07-01

The noise reduction of a liner placed in the nacelle of a turbofan engine is still difficult to predict due to the lack of knowledge of its acoustic impedance that depends on grazing flow profile, mode order, and sound pressure level. An eduction method, based on a Bayesian approach, is presented here to adjust an impedance model of the liner from sound pressures measured in a rectangular treated duct under multimodal propagation and flow. The cost function is regularized with prior information provided by Guess's [J. Sound Vib. 40, 119-137 (1975)] impedance of a perforated plate. The multi-parameter optimization is achieved with an Evolutionary-Markov-Chain-Monte-Carlo algorithm.

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.

Doctor, what does my positive test mean? From Bayesian textbook tasks to personalized risk communication

PubMed Central

Navarrete, Gorka; Correia, Rut; Sirota, Miroslav; Juanchich, Marie; Huepe, David

2015-01-01

Most of the research on Bayesian reasoning aims to answer theoretical questions about the extent to which people are able to update their beliefs according to Bayes' Theorem, about the evolutionary nature of Bayesian inference, or about the role of cognitive abilities in Bayesian inference. Few studies aim to answer practical, mainly health-related questions, such as, “What does it mean to have a positive test in a context of cancer screening?” or “What is the best way to communicate a medical test result so a patient will understand it?”. This type of research aims to translate empirical findings into effective ways of providing risk information. In addition, the applied research often adopts the paradigms and methods of the theoretically-motivated research. But sometimes it works the other way around, and the theoretical research borrows the importance of the practical question in the medical context. The study of Bayesian reasoning is relevant to risk communication in that, to be as useful as possible, applied research should employ specifically tailored methods and contexts specific to the recipients of the risk information. In this paper, we concentrate on the communication of the result of medical tests and outline the epidemiological and test parameters that affect the predictive power of a test—whether it is correct or not. Building on this, we draw up recommendations for better practice to convey the results of medical tests that could inform health policy makers (What are the drawbacks of mass screenings?), be used by health practitioners and, in turn, help patients to make better and more informed decisions. PMID:26441711

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.

Advances in Bayesian Modeling in Educational Research

ERIC Educational Resources Information Center

Levy, Roy

2016-01-01

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

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

EPA Science Inventory

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

Methods for fitting a parametric probability distribution to most probable number data.

PubMed

Williams, Michael S; Ebel, Eric D

2012-07-02

Every year hundreds of thousands, if not millions, of samples are collected and analyzed to assess microbial contamination in food and water. The concentration of pathogenic organisms at the end of the production process is low for most commodities, so a highly sensitive screening test is used to determine whether the organism of interest is present in a sample. In some applications, samples that test positive are subjected to quantitation. The most probable number (MPN) technique is a common method to quantify the level of contamination in a sample because it is able to provide estimates at low concentrations. This technique uses a series of dilution count experiments to derive estimates of the concentration of the microorganism of interest. An application for these data is food-safety risk assessment, where the MPN concentration estimates can be fitted to a parametric distribution to summarize the range of potential exposures to the contaminant. Many different methods (e.g., substitution methods, maximum likelihood and regression on order statistics) have been proposed to fit microbial contamination data to a distribution, but the development of these methods rarely considers how the MPN technique influences the choice of distribution function and fitting method. An often overlooked aspect when applying these methods is whether the data represent actual measurements of the average concentration of microorganism per milliliter or the data are real-valued estimates of the average concentration, as is the case with MPN data. In this study, we propose two methods for fitting MPN data to a probability distribution. The first method uses a maximum likelihood estimator that takes average concentration values as the data inputs. The second is a Bayesian latent variable method that uses the counts of the number of positive tubes at each dilution to estimate the parameters of the contamination distribution. The performance of the two fitting methods is compared for two data sets that represent Salmonella and Campylobacter concentrations on chicken carcasses. The results demonstrate a bias in the maximum likelihood estimator that increases with reductions in average concentration. The Bayesian method provided unbiased estimates of the concentration distribution parameters for all data sets. We provide computer code for the Bayesian fitting method. Published by Elsevier B.V.

A novel Bayesian respiratory motion model to estimate and resolve uncertainty in image-guided cardiac interventions.

PubMed

Peressutti, Devis; Penney, Graeme P; Housden, R James; Kolbitsch, Christoph; Gomez, Alberto; Rijkhorst, Erik-Jan; Barratt, Dean C; Rhode, Kawal S; King, Andrew P

2013-05-01

In image-guided cardiac interventions, respiratory motion causes misalignments between the pre-procedure roadmap of the heart used for guidance and the intra-procedure position of the heart, reducing the accuracy of the guidance information and leading to potentially dangerous consequences. We propose a novel technique for motion-correcting the pre-procedural information that combines a probabilistic MRI-derived affine motion model with intra-procedure real-time 3D echocardiography (echo) images in a Bayesian framework. The probabilistic model incorporates a measure of confidence in its motion estimates which enables resolution of the potentially conflicting information supplied by the model and the echo data. Unlike models proposed so far, our method allows the final motion estimate to deviate from the model-produced estimate according to the information provided by the echo images, so adapting to the complex variability of respiratory motion. The proposed method is evaluated using gold-standard MRI-derived motion fields and simulated 3D echo data for nine volunteers and real 3D live echo images for four volunteers. The Bayesian method is compared to 5 other motion estimation techniques and results show mean/max improvements in estimation accuracy of 10.6%/18.9% for simulated echo images and 20.8%/41.5% for real 3D live echo data, over the best comparative estimation method. Copyright © 2013 Elsevier B.V. All rights reserved.

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.

PubMed

Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J

2010-12-01

Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies conservation planning. Journal compilation © 2010 Society for Conservation Biology. No claim to original US government works.

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.

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

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

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

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

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.

The evolution of autodigestion in the mushroom family Psathyrellaceae (Agaricales) inferred from Maximum Likelihood and Bayesian methods.

PubMed

Nagy, László G; Urban, Alexander; Orstadius, Leif; Papp, Tamás; Larsson, Ellen; Vágvölgyi, Csaba

2010-12-01

Recently developed comparative phylogenetic methods offer a wide spectrum of applications in evolutionary biology, although it is generally accepted that their statistical properties are incompletely known. Here, we examine and compare the statistical power of the ML and Bayesian methods with regard to selection of best-fit models of fruiting-body evolution and hypothesis testing of ancestral states on a real-life data set of a physiological trait (autodigestion) in the family Psathyrellaceae. Our phylogenies are based on the first multigene data set generated for the family. Two different coding regimes (binary and multistate) and two data sets differing in taxon sampling density are examined. The Bayesian method outperformed Maximum Likelihood with regard to statistical power in all analyses. This is particularly evident if the signal in the data is weak, i.e. in cases when the ML approach does not provide support to choose among competing hypotheses. Results based on binary and multistate coding differed only modestly, although it was evident that multistate analyses were less conclusive in all cases. It seems that increased taxon sampling density has favourable effects on inference of ancestral states, while model parameters are influenced to a smaller extent. The model best fitting our data implies that the rate of losses of deliquescence equals zero, although model selection in ML does not provide proper support to reject three of the four candidate models. The results also support the hypothesis that non-deliquescence (lack of autodigestion) has been ancestral in Psathyrellaceae, and that deliquescent fruiting bodies represent the preferred state, having evolved independently several times during evolution. Copyright © 2010 Elsevier Inc. All rights reserved.

Suspected pulmonary embolism and lung scan interpretation: Trial of a Bayesian reporting method

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

Becker, D.M.; Philbrick, J.T.; Schoonover, F.W.

The objective of this research is to determine whether a Bayesian method of lung scan (LS) reporting could influence the management of patients with suspected pulmonary embolism (PE). The study is performed by the following: (1) A descriptive study of the diagnostic process for suspected PE using the new reporting method; (2) a non-experimental evaluation of the reporting method comparing prospective patients and historical controls; and (3) a survey of physicians' reactions to the reporting innovation. Of 148 consecutive patients enrolled at the time of LS, 129 were completely evaluated; 75 patients scanned the previous year served as controls. Themore » LS results of patients with suspected PE were reported as posttest probabilities of PE calculated from physician-provided pretest probabilities and the likelihood ratios for PE of LS interpretations. Despite the Bayesian intervention, the confirmation or exclusion of PE was often based on inconclusive evidence. PE was considered by the clinician to be ruled out in 98% of patients with posttest probabilities less than 25% and ruled in for 95% of patients with posttest probabilities greater than 75%. Prospective patients and historical controls were similar in terms of tests ordered after the LS (e.g., pulmonary angiography). Patients with intermediate or indeterminate lung scan results had the highest proportion of subsequent testing. Most physicians (80%) found the reporting innovation to be helpful, either because it confirmed clinical judgement (94 cases) or because it led to additional testing (7 cases). Despite the probabilistic guidance provided by the study, the diagnosis of PE was often neither clearly established nor excluded. While physicians appreciated the innovation and were not confused by the terminology, their clinical decision making was not clearly enhanced.« less

Analysis of phase II methodologies for single-arm clinical trials with multiple endpoints in rare cancers: An example in Ewing's sarcoma.

PubMed

Dutton, P; Love, S B; Billingham, L; Hassan, A B

2018-05-01

Trials run in either rare diseases, such as rare cancers, or rare sub-populations of common diseases are challenging in terms of identifying, recruiting and treating sufficient patients in a sensible period. Treatments for rare diseases are often designed for other disease areas and then later proposed as possible treatments for the rare disease after initial phase I testing is complete. To ensure the trial is in the best interests of the patient participants, frequent interim analyses are needed to force the trial to stop promptly if the treatment is futile or toxic. These non-definitive phase II trials should also be stopped for efficacy to accelerate research progress if the treatment proves to be particularly promising. In this paper, we review frequentist and Bayesian methods that have been adapted to incorporate two binary endpoints and frequent interim analyses. The Eurosarc Trial of Linsitinib in advanced Ewing Sarcoma (LINES) is used as a motivating example and provides a suitable platform to compare these approaches. The Bayesian approach provides greater design flexibility, but does not provide additional value over the frequentist approaches in a single trial setting when the prior is non-informative. However, Bayesian designs are able to borrow from any previous experience, using prior information to improve efficiency.

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

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.

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.

Using Bayesian belief networks in adaptive management.

Treesearch

J.B. Nyberg; B.G. Marcot; R. Sulyma

2006-01-01

Bayesian belief and decision networks are relatively new modeling methods that are especially well suited to adaptive-management applications, but they appear not to have been widely used in adaptive management to date. Bayesian belief networks (BBNs) can serve many purposes for practioners of adaptive management, from illustrating system relations conceptually to...

The Application of Bayesian Analysis to Issues in Developmental Research

ERIC Educational Resources Information Center

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

2007-01-01

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

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

NASA Astrophysics Data System (ADS)

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33TC.

Bayesian approach to spectral function reconstruction for Euclidean quantum field theories.

PubMed

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33T(C).

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.

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.

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

UNIFORMLY MOST POWERFUL BAYESIAN TESTS

PubMed Central

Johnson, Valen E.

2014-01-01

Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternative hypothesis, exceeds a specified threshold. Like their classical counterpart, uniformly most powerful Bayesian tests are most easily defined in one-parameter exponential family models, although extensions outside of this class are possible. The connection between uniformly most powerful tests and uniformly most powerful Bayesian tests can be used to provide an approximate calibration between p-values and Bayes factors. Finally, issues regarding the strong dependence of resulting Bayes factors and p-values on sample size are discussed. PMID:24659829

A Tutorial in Bayesian Potential Outcomes Mediation Analysis.

PubMed

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

2018-01-01

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

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.

Kernel-imbedded Gaussian processes for disease classification using microarray gene expression data

PubMed Central

Zhao, Xin; Cheung, Leo Wang-Kit

2007-01-01

Background Designing appropriate machine learning methods for identifying genes that have a significant discriminating power for disease outcomes has become more and more important for our understanding of diseases at genomic level. Although many machine learning methods have been developed and applied to the area of microarray gene expression data analysis, the majority of them are based on linear models, which however are not necessarily appropriate for the underlying connection between the target disease and its associated explanatory genes. Linear model based methods usually also bring in false positive significant features more easily. Furthermore, linear model based algorithms often involve calculating the inverse of a matrix that is possibly singular when the number of potentially important genes is relatively large. This leads to problems of numerical instability. To overcome these limitations, a few non-linear methods have recently been introduced to the area. Many of the existing non-linear methods have a couple of critical problems, the model selection problem and the model parameter tuning problem, that remain unsolved or even untouched. In general, a unified framework that allows model parameters of both linear and non-linear models to be easily tuned is always preferred in real-world applications. Kernel-induced learning methods form a class of approaches that show promising potentials to achieve this goal. Results A hierarchical statistical model named kernel-imbedded Gaussian process (KIGP) is developed under a unified Bayesian framework for binary disease classification problems using microarray gene expression data. In particular, based on a probit regression setting, an adaptive algorithm with a cascading structure is designed to find the appropriate kernel, to discover the potentially significant genes, and to make the optimal class prediction accordingly. A Gibbs sampler is built as the core of the algorithm to make Bayesian inferences. Simulation studies showed that, even without any knowledge of the underlying generative model, the KIGP performed very close to the theoretical Bayesian bound not only in the case with a linear Bayesian classifier but also in the case with a very non-linear Bayesian classifier. This sheds light on its broader usability to microarray data analysis problems, especially to those that linear methods work awkwardly. The KIGP was also applied to four published microarray datasets, and the results showed that the KIGP performed better than or at least as well as any of the referred state-of-the-art methods did in all of these cases. Conclusion Mathematically built on the kernel-induced feature space concept under a Bayesian framework, the KIGP method presented in this paper provides a unified machine learning approach to explore both the linear and the possibly non-linear underlying relationship between the target features of a given binary disease classification problem and the related explanatory gene expression data. More importantly, it incorporates the model parameter tuning into the framework. The model selection problem is addressed in the form of selecting a proper kernel type. The KIGP method also gives Bayesian probabilistic predictions for disease classification. These properties and features are beneficial to most real-world applications. The algorithm is naturally robust in numerical computation. The simulation studies and the published data studies demonstrated that the proposed KIGP performs satisfactorily and consistently. PMID:17328811

Impact of censoring on learning Bayesian networks in survival modelling.

PubMed

Stajduhar, Ivan; Dalbelo-Basić, Bojana; Bogunović, Nikola

2009-11-01

Bayesian networks are commonly used for presenting uncertainty and covariate interactions in an easily interpretable way. Because of their efficient inference and ability to represent causal relationships, they are an excellent choice for medical decision support systems in diagnosis, treatment, and prognosis. Although good procedures for learning Bayesian networks from data have been defined, their performance in learning from censored survival data has not been widely studied. In this paper, we explore how to use these procedures to learn about possible interactions between prognostic factors and their influence on the variate of interest. We study how censoring affects the probability of learning correct Bayesian network structures. Additionally, we analyse the potential usefulness of the learnt models for predicting the time-independent probability of an event of interest. We analysed the influence of censoring with a simulation on synthetic data sampled from randomly generated Bayesian networks. We used two well-known methods for learning Bayesian networks from data: a constraint-based method and a score-based method. We compared the performance of each method under different levels of censoring to those of the naive Bayes classifier and the proportional hazards model. We did additional experiments on several datasets from real-world medical domains. The machine-learning methods treated censored cases in the data as event-free. We report and compare results for several commonly used model evaluation metrics. On average, the proportional hazards method outperformed other methods in most censoring setups. As part of the simulation study, we also analysed structural similarities of the learnt networks. Heavy censoring, as opposed to no censoring, produces up to a 5% surplus and up to 10% missing total arcs. It also produces up to 50% missing arcs that should originally be connected to the variate of interest. Presented methods for learning Bayesian networks from data can be used to learn from censored survival data in the presence of light censoring (up to 20%) by treating censored cases as event-free. Given intermediate or heavy censoring, the learnt models become tuned to the majority class and would thus require a different approach.

An application of Bayesian statistics to the extragalactic Cepheid distance scale

NASA Astrophysics Data System (ADS)

Barnes, Thomas G., III; Moffett, Thomas J.; Jefferys, W. H.; Forestell, Amy D.

2004-05-01

We have determined quasi-geometric distances to the Magellanic Clouds, M31 and M33. Our analysis uses a Bayesian statistical method to provide mathematically rigorous and objective solutions for individual Cepheids. We combine the individual distances with a hierarchial Bayesian model to determine the galactic distances. We obtain distance moduli 18.87 ± 0.07 mag (LMC, 12 stars), 19.14 ± 0.10 (SMC, 8 stars), 23.83 ± 0.35 mag (M33, 1 star) and 25.2 ± 0.6 mag (M31, 1 star) - all uncorrected for metallicity. The M31 and M33 distances are very preliminary. If the Pl relations of the LMC, SMC, and Galaxy are identical, our results exclude the metallicity effect in the V, (V - R) surface brightness method predicted by Hindsley and Bell (1989) at the 5σ level. Alternately, if Hindsley & Bell's prediction is adopted as true, we find a metallicity effect intrinsic to the Cepheid PL relation requiring a correction Δ(V - Mv) = (0.36 ± 0.07)Δ[A/H] mag. The latter has the opposite sign to other observational estimates of the Cepheid metallicity effect.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Bayesian nonparametric adaptive control using Gaussian processes.

PubMed

Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A

2015-03-01

Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.

Bayesian operational modal analysis with asynchronous data, part I: Most probable value

NASA Astrophysics Data System (ADS)

Zhu, Yi-Chen; Au, Siu-Kui

2018-01-01

In vibration tests, multiple sensors are used to obtain detailed mode shape information about the tested structure. Time synchronisation among data channels is required in conventional modal identification approaches. Modal identification can be more flexibly conducted if this is not required. Motivated by the potential gain in feasibility and economy, this work proposes a Bayesian frequency domain method for modal identification using asynchronous 'output-only' ambient data, i.e. 'operational modal analysis'. It provides a rigorous means for identifying the global mode shape taking into account the quality of the measured data and their asynchronous nature. This paper (Part I) proposes an efficient algorithm for determining the most probable values of modal properties. The method is validated using synthetic and laboratory data. The companion paper (Part II) investigates identification uncertainty and challenges in applications to field vibration data.

The discounting model selector: Statistical software for delay discounting applications.

PubMed

Gilroy, Shawn P; Franck, Christopher T; Hantula, Donald A

2017-05-01

Original, open-source computer software was developed and validated against established delay discounting methods in the literature. The software executed approximate Bayesian model selection methods from user-supplied temporal discounting data and computed the effective delay 50 (ED50) from the best performing model. Software was custom-designed to enable behavior analysts to conveniently apply recent statistical methods to temporal discounting data with the aid of a graphical user interface (GUI). The results of independent validation of the approximate Bayesian model selection methods indicated that the program provided results identical to that of the original source paper and its methods. Monte Carlo simulation (n = 50,000) confirmed that true model was selected most often in each setting. Simulation code and data for this study were posted to an online repository for use by other researchers. The model selection approach was applied to three existing delay discounting data sets from the literature in addition to the data from the source paper. Comparisons of model selected ED50 were consistent with traditional indices of discounting. Conceptual issues related to the development and use of computer software by behavior analysts and the opportunities afforded by free and open-sourced software are discussed and a review of possible expansions of this software are provided. © 2017 Society for the Experimental Analysis of Behavior.

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…

Using Bayesian neural networks to classify forest scenes

NASA Astrophysics Data System (ADS)

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

1998-10-01

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

Bayesian-MCMC-based parameter estimation of stealth aircraft RCS models

NASA Astrophysics Data System (ADS)

Xia, Wei; Dai, Xiao-Xia; Feng, Yuan

2015-12-01

When modeling a stealth aircraft with low RCS (Radar Cross Section), conventional parameter estimation methods may cause a deviation from the actual distribution, owing to the fact that the characteristic parameters are estimated via directly calculating the statistics of RCS. The Bayesian-Markov Chain Monte Carlo (Bayesian-MCMC) method is introduced herein to estimate the parameters so as to improve the fitting accuracies of fluctuation models. The parameter estimations of the lognormal and the Legendre polynomial models are reformulated in the Bayesian framework. The MCMC algorithm is then adopted to calculate the parameter estimates. Numerical results show that the distribution curves obtained by the proposed method exhibit improved consistence with the actual ones, compared with those fitted by the conventional method. The fitting accuracy could be improved by no less than 25% for both fluctuation models, which implies that the Bayesian-MCMC method might be a good candidate among the optimal parameter estimation methods for stealth aircraft RCS models. Project supported by the National Natural Science Foundation of China (Grant No. 61101173), the National Basic Research Program of China (Grant No. 613206), the National High Technology Research and Development Program of China (Grant No. 2012AA01A308), the State Scholarship Fund by the China Scholarship Council (CSC), and the Oversea Academic Training Funds, and University of Electronic Science and Technology of China (UESTC).

A fuzzy Bayesian approach to flood frequency estimation with imprecise historical information

PubMed Central

Kiss, Andrea; Viglione, Alberto; Viertl, Reinhard; Blöschl, Günter

2016-01-01

Abstract This paper presents a novel framework that links imprecision (through a fuzzy approach) and stochastic uncertainty (through a Bayesian approach) in estimating flood probabilities from historical flood information and systematic flood discharge data. The method exploits the linguistic characteristics of historical source material to construct membership functions, which may be wider or narrower, depending on the vagueness of the statements. The membership functions are either included in the prior distribution or the likelihood function to obtain a fuzzy version of the flood frequency curve. The viability of the approach is demonstrated by three case studies that differ in terms of their hydromorphological conditions (from an Alpine river with bedrock profile to a flat lowland river with extensive flood plains) and historical source material (including narratives, town and county meeting protocols, flood marks and damage accounts). The case studies are presented in order of increasing fuzziness (the Rhine at Basel, Switzerland; the Werra at Meiningen, Germany; and the Tisza at Szeged, Hungary). Incorporating imprecise historical information is found to reduce the range between the 5% and 95% Bayesian credibility bounds of the 100 year floods by 45% and 61% for the Rhine and Werra case studies, respectively. The strengths and limitations of the framework are discussed relative to alternative (non‐fuzzy) methods. The fuzzy Bayesian inference framework provides a flexible methodology that fits the imprecise nature of linguistic information on historical floods as available in historical written documentation. PMID:27840456

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 fuzzy Bayesian approach to flood frequency estimation with imprecise historical information

NASA Astrophysics Data System (ADS)

Salinas, José Luis; Kiss, Andrea; Viglione, Alberto; Viertl, Reinhard; Blöschl, Günter

2016-09-01

This paper presents a novel framework that links imprecision (through a fuzzy approach) and stochastic uncertainty (through a Bayesian approach) in estimating flood probabilities from historical flood information and systematic flood discharge data. The method exploits the linguistic characteristics of historical source material to construct membership functions, which may be wider or narrower, depending on the vagueness of the statements. The membership functions are either included in the prior distribution or the likelihood function to obtain a fuzzy version of the flood frequency curve. The viability of the approach is demonstrated by three case studies that differ in terms of their hydromorphological conditions (from an Alpine river with bedrock profile to a flat lowland river with extensive flood plains) and historical source material (including narratives, town and county meeting protocols, flood marks and damage accounts). The case studies are presented in order of increasing fuzziness (the Rhine at Basel, Switzerland; the Werra at Meiningen, Germany; and the Tisza at Szeged, Hungary). Incorporating imprecise historical information is found to reduce the range between the 5% and 95% Bayesian credibility bounds of the 100 year floods by 45% and 61% for the Rhine and Werra case studies, respectively. The strengths and limitations of the framework are discussed relative to alternative (non-fuzzy) methods. The fuzzy Bayesian inference framework provides a flexible methodology that fits the imprecise nature of linguistic information on historical floods as available in historical written documentation.

A fuzzy Bayesian approach to flood frequency estimation with imprecise historical information.

PubMed

Salinas, José Luis; Kiss, Andrea; Viglione, Alberto; Viertl, Reinhard; Blöschl, Günter

2016-09-01

This paper presents a novel framework that links imprecision (through a fuzzy approach) and stochastic uncertainty (through a Bayesian approach) in estimating flood probabilities from historical flood information and systematic flood discharge data. The method exploits the linguistic characteristics of historical source material to construct membership functions, which may be wider or narrower, depending on the vagueness of the statements. The membership functions are either included in the prior distribution or the likelihood function to obtain a fuzzy version of the flood frequency curve. The viability of the approach is demonstrated by three case studies that differ in terms of their hydromorphological conditions (from an Alpine river with bedrock profile to a flat lowland river with extensive flood plains) and historical source material (including narratives, town and county meeting protocols, flood marks and damage accounts). The case studies are presented in order of increasing fuzziness (the Rhine at Basel, Switzerland; the Werra at Meiningen, Germany; and the Tisza at Szeged, Hungary). Incorporating imprecise historical information is found to reduce the range between the 5% and 95% Bayesian credibility bounds of the 100 year floods by 45% and 61% for the Rhine and Werra case studies, respectively. The strengths and limitations of the framework are discussed relative to alternative (non-fuzzy) methods. The fuzzy Bayesian inference framework provides a flexible methodology that fits the imprecise nature of linguistic information on historical floods as available in historical written documentation.

Bayesian Methods and Confidence Intervals for Automatic Target Recognition of SAR Canonical Shapes

DTIC Science & Technology

2014-03-27

and DirectX [22]. The CUDA platform was developed by the NVIDIA Corporation to allow programmers access to the computational capabilities of the...were used for the intense repetitive computations. Developing CUDA software requires writing code for specialized compilers provided by NVIDIA and

Computer Aided Evaluation of Higher Education Tutors' Performance

ERIC Educational Resources Information Center

Xenos, Michalis; Papadopoulos, Thanos

2007-01-01

This article presents a method for computer-aided tutor evaluation: Bayesian Networks are used for organizing the collected data about tutors and for enabling accurate estimations and predictions about future tutor behavior. The model provides indications about each tutor's strengths and weaknesses, which enables the evaluator to exploit strengths…

Specifying and Refining a Complex Measurement Model.

ERIC Educational Resources Information Center

Levy, Roy; Mislevy, Robert J.

This paper aims to describe a Bayesian approach to modeling and estimating cognitive models both in terms of statistical machinery and actual instrument development. Such a method taps the knowledge of experts to provide initial estimates for the probabilistic relationships among the variables in a multivariate latent variable model and refines…

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

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

2015-08-01

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

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.

Evaluation of the procedure 1A component of the 1980 US/Canada wheat and barley exploratory experiment

NASA Technical Reports Server (NTRS)

Chapman, G. M. (Principal Investigator); Carnes, J. G.

1981-01-01

Several techniques which use clusters generated by a new clustering algorithm, CLASSY, are proposed as alternatives to random sampling to obtain greater precision in crop proportion estimation: (1) Proportional Allocation/relative count estimator (PA/RCE) uses proportional allocation of dots to clusters on the basis of cluster size and a relative count cluster level estimate; (2) Proportional Allocation/Bayes Estimator (PA/BE) uses proportional allocation of dots to clusters and a Bayesian cluster-level estimate; and (3) Bayes Sequential Allocation/Bayesian Estimator (BSA/BE) uses sequential allocation of dots to clusters and a Bayesian cluster level estimate. Clustering in an effective method in making proportion estimates. It is estimated that, to obtain the same precision with random sampling as obtained by the proportional sampling of 50 dots with an unbiased estimator, samples of 85 or 166 would need to be taken if dot sets with AI labels (integrated procedure) or ground truth labels, respectively were input. Dot reallocation provides dot sets that are unbiased. It is recommended that these proportion estimation techniques are maintained, particularly the PA/BE because it provides the greatest precision.

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

Applying a Bayesian Approach to Identification of Orthotropic Elastic Constants from Full Field Displacement Measurements

NASA Astrophysics Data System (ADS)

Gogu, C.; Yin, W.; Haftka, R.; Ifju, P.; Molimard, J.; Le Riche, R.; Vautrin, A.

2010-06-01

A major challenge in the identification of material properties is handling different sources of uncertainty in the experiment and the modelling of the experiment for estimating the resulting uncertainty in the identified properties. Numerous improvements in identification methods have provided increasingly accurate estimates of various material properties. However, characterizing the uncertainty in the identified properties is still relatively crude. Different material properties obtained from a single test are not obtained with the same confidence. Typically the highest uncertainty is associated with respect to properties to which the experiment is the most insensitive. In addition, the uncertainty in different properties can be strongly correlated, so that obtaining only variance estimates may be misleading. A possible approach for handling the different sources of uncertainty and estimating the uncertainty in the identified properties is the Bayesian method. This method was introduced in the late 1970s in the context of identification [1] and has been applied since to different problems, notably identification of elastic constants from plate vibration experiments [2]-[4]. The applications of the method to these classical pointwise tests involved only a small number of measurements (typically ten natural frequencies in the previously cited vibration test) which facilitated the application of the Bayesian approach. For identifying elastic constants, full field strain or displacement measurements provide a high number of measured quantities (one measurement per image pixel) and hence a promise of smaller uncertainties in the properties. However, the high number of measurements represents also a major computational challenge in applying the Bayesian approach to full field measurements. To address this challenge we propose an approach based on the proper orthogonal decomposition (POD) of the full fields in order to drastically reduce their dimensionality. POD is based on projecting the full field images on a modal basis, constructed from sample simulations, and which can account for the variations of the full field as the elastic constants and other parameters of interest are varied. The fidelity of the decomposition depends on the number of basis vectors used. Typically even complex fields can be accurately represented with no more than a few dozen modes and for our problem we showed that only four or five modes are sufficient [5]. To further reduce the computational cost of the Bayesian approach we use response surface approximations of the POD coefficients of the fields. We show that 3rd degree polynomial response surface approximations provide a satisfying accuracy. The combination of POD decomposition and response surface methodology allows to bring down the computational time of the Bayesian identification to a few days. The proposed approach is applied to Moiré interferometry full field displacement measurements from a traction experiment on a plate with a hole. The laminate with a layup of [45,- 45,0]s is made out of a Toray® T800/3631 graphite/epoxy prepreg. The measured displacement maps are provided in Figure 1. The mean values of the identified properties joint probability density function are in agreement with previous identifications carried out on the same material. Furthermore the probability density function also provides the coefficient of variation with which the properties are identified as well as the correlations between the various properties. We find that while the longitudinal Young’s modulus is identified with good accuracy (low standard deviation), the Poisson’s ration is identified with much higher uncertainty. Several of the properties are also found to be correlated. The identified uncertainty structure of the elastic constants (i.e. variance co-variance matrix) has potential benefits to reliability analyses, by allowing a more accurate description of the input uncertainty. An additional advantage of the Bayesian approach is that it provides a natural way (in the form of the prior probability density function) for accounting for prior information that may be available on the material properties thought. This is of great interest for reducing the uncertainty on properties that can only be determined with low confidence from the plate with a hole experiment, such as Poisson’s ratio or transverse Young’s modulus in our case.

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.

A Bayesian nonparametric method for prediction in EST analysis

PubMed Central

Lijoi, Antonio; Mena, Ramsés H; Prünster, Igor

2007-01-01

Background Expressed sequence tags (ESTs) analyses are a fundamental tool for gene identification in organisms. Given a preliminary EST sample from a certain library, several statistical prediction problems arise. In particular, it is of interest to estimate how many new genes can be detected in a future EST sample of given size and also to determine the gene discovery rate: these estimates represent the basis for deciding whether to proceed sequencing the library and, in case of a positive decision, a guideline for selecting the size of the new sample. Such information is also useful for establishing sequencing efficiency in experimental design and for measuring the degree of redundancy of an EST library. Results In this work we propose a Bayesian nonparametric approach for tackling statistical problems related to EST surveys. In particular, we provide estimates for: a) the coverage, defined as the proportion of unique genes in the library represented in the given sample of reads; b) the number of new unique genes to be observed in a future sample; c) the discovery rate of new genes as a function of the future sample size. The Bayesian nonparametric model we adopt conveys, in a statistically rigorous way, the available information into prediction. Our proposal has appealing properties over frequentist nonparametric methods, which become unstable when prediction is required for large future samples. EST libraries, previously studied with frequentist methods, are analyzed in detail. Conclusion The Bayesian nonparametric approach we undertake yields valuable tools for gene capture and prediction in EST libraries. The estimators we obtain do not feature the kind of drawbacks associated with frequentist estimators and are reliable for any size of the additional sample. PMID:17868445

A sub-space greedy search method for efficient Bayesian Network inference.

PubMed

Zhang, Qing; Cao, Yong; Li, Yong; Zhu, Yanming; Sun, Samuel S M; Guo, Dianjing

2011-09-01

Bayesian network (BN) has been successfully used to infer the regulatory relationships of genes from microarray dataset. However, one major limitation of BN approach is the computational cost because the calculation time grows more than exponentially with the dimension of the dataset. In this paper, we propose a sub-space greedy search method for efficient Bayesian Network inference. Particularly, this method limits the greedy search space by only selecting gene pairs with higher partial correlation coefficients. Using both synthetic and real data, we demonstrate that the proposed method achieved comparable results with standard greedy search method yet saved ∼50% of the computational time. We believe that sub-space search method can be widely used for efficient BN inference in systems biology. Copyright © 2011 Elsevier Ltd. All rights reserved.

Bayesian-information-gap decision theory with an application to CO 2 sequestration

DOE PAGES

O'Malley, D.; Vesselinov, V. V.

2015-09-04

Decisions related to subsurface engineering problems such as groundwater management, fossil fuel production, and geologic carbon sequestration are frequently challenging because of an overabundance of uncertainties (related to conceptualizations, parameters, observations, etc.). Because of the importance of these problems to agriculture, energy, and the climate (respectively), good decisions that are scientifically defensible must be made despite the uncertainties. We describe a general approach to making decisions for challenging problems such as these in the presence of severe uncertainties that combines probabilistic and non-probabilistic methods. The approach uses Bayesian sampling to assess parametric uncertainty and Information-Gap Decision Theory (IGDT) to addressmore » model inadequacy. The combined approach also resolves an issue that frequently arises when applying Bayesian methods to real-world engineering problems related to the enumeration of possible outcomes. In the case of zero non-probabilistic uncertainty, the method reduces to a Bayesian method. Lastly, to illustrate the approach, we apply it to a site-selection decision for geologic CO 2 sequestration.« less

An Intuitive Dashboard for Bayesian Network Inference

NASA Astrophysics Data System (ADS)

Reddy, Vikas; Charisse Farr, Anna; Wu, Paul; Mengersen, Kerrie; Yarlagadda, Prasad K. D. V.

2014-03-01

Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++.

A Bayesian approach to tracking patients having changing pharmacokinetic parameters

NASA Technical Reports Server (NTRS)

Bayard, David S.; Jelliffe, Roger W.

2004-01-01

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

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2016-08-01

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

Bayesian X-ray computed tomography using a three-level hierarchical prior model

NASA Astrophysics Data System (ADS)

Wang, Li; Mohammad-Djafari, Ali; Gac, Nicolas

2017-06-01

In recent decades X-ray Computed Tomography (CT) image reconstruction has been largely developed in both medical and industrial domain. In this paper, we propose using the Bayesian inference approach with a new hierarchical prior model. In the proposed model, a generalised Student-t distribution is used to enforce the Haar transformation of images to be sparse. Comparisons with some state of the art methods are presented. It is shown that by using the proposed model, the sparsity of sparse representation of images is enforced, so that edges of images are preserved. Simulation results are also provided to demonstrate the effectiveness of the new hierarchical model for reconstruction with fewer projections.

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.

New applications of maximum likelihood and Bayesian statistics in macromolecular crystallography.

PubMed

McCoy, Airlie J

2002-10-01

Maximum likelihood methods are well known to macromolecular crystallographers as the methods of choice for isomorphous phasing and structure refinement. Recently, the use of maximum likelihood and Bayesian statistics has extended to the areas of molecular replacement and density modification, placing these methods on a stronger statistical foundation and making them more accurate and effective.

A Bayesian estimate of the concordance correlation coefficient with skewed data.

PubMed

Feng, Dai; Baumgartner, Richard; Svetnik, Vladimir

2015-01-01

Concordance correlation coefficient (CCC) is one of the most popular scaled indices used to evaluate agreement. Most commonly, it is used under the assumption that data is normally distributed. This assumption, however, does not apply to skewed data sets. While methods for the estimation of the CCC of skewed data sets have been introduced and studied, the Bayesian approach and its comparison with the previous methods has been lacking. In this study, we propose a Bayesian method for the estimation of the CCC of skewed data sets and compare it with the best method previously investigated. The proposed method has certain advantages. It tends to outperform the best method studied before when the variation of the data is mainly from the random subject effect instead of error. Furthermore, it allows for greater flexibility in application by enabling incorporation of missing data, confounding covariates, and replications, which was not considered previously. The superiority of this new approach is demonstrated using simulation as well as real-life biomarker data sets used in an electroencephalography clinical study. The implementation of the Bayesian method is accessible through the Comprehensive R Archive Network. Copyright © 2015 John Wiley & Sons, Ltd.

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

PubMed

Qian, Song S; Lyons, Regan E

2006-10-01

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

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.

Robust nonlinear system identification: Bayesian mixture of experts using the t-distribution

NASA Astrophysics Data System (ADS)

Baldacchino, Tara; Worden, Keith; Rowson, Jennifer

2017-02-01

A novel variational Bayesian mixture of experts model for robust regression of bifurcating and piece-wise continuous processes is introduced. The mixture of experts model is a powerful model which probabilistically splits the input space allowing different models to operate in the separate regions. However, current methods have no fail-safe against outliers. In this paper, a robust mixture of experts model is proposed which consists of Student-t mixture models at the gates and Student-t distributed experts, trained via Bayesian inference. The Student-t distribution has heavier tails than the Gaussian distribution, and so it is more robust to outliers, noise and non-normality in the data. Using both simulated data and real data obtained from the Z24 bridge this robust mixture of experts performs better than its Gaussian counterpart when outliers are present. In particular, it provides robustness to outliers in two forms: unbiased parameter regression models, and robustness to overfitting/complex models.

Comparing Families of Dynamic Causal Models

PubMed Central

Penny, Will D.; Stephan, Klaas E.; Daunizeau, Jean; Rosa, Maria J.; Friston, Karl J.; Schofield, Thomas M.; Leff, Alex P.

2010-01-01

Mathematical models of scientific data can be formally compared using Bayesian model evidence. Previous applications in the biological sciences have mainly focussed on model selection in which one first selects the model with the highest evidence and then makes inferences based on the parameters of that model. This “best model” approach is very useful but can become brittle if there are a large number of models to compare, and if different subjects use different models. To overcome this shortcoming we propose the combination of two further approaches: (i) family level inference and (ii) Bayesian model averaging within families. Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest. For example: What are the inputs to the system? Is processing serial or parallel? Is it linear or nonlinear? Is it mediated by a single, crucial connection? We apply Bayesian model averaging within families to provide inferences about parameters that are independent of further assumptions about model structure. We illustrate the methods using Dynamic Causal Models of brain imaging data. PMID:20300649

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

BAYESIAN LARGE-SCALE MULTIPLE REGRESSION WITH SUMMARY STATISTICS FROM GENOME-WIDE ASSOCIATION STUDIES1

PubMed Central

Zhu, Xiang; Stephens, Matthew

2017-01-01

Bayesian methods for large-scale multiple regression provide attractive approaches to the analysis of genome-wide association studies (GWAS). For example, they can estimate heritability of complex traits, allowing for both polygenic and sparse models; and by incorporating external genomic data into the priors, they can increase power and yield new biological insights. However, these methods require access to individual genotypes and phenotypes, which are often not easily available. Here we provide a framework for performing these analyses without individual-level data. Specifically, we introduce a “Regression with Summary Statistics” (RSS) likelihood, which relates the multiple regression coefficients to univariate regression results that are often easily available. The RSS likelihood requires estimates of correlations among covariates (SNPs), which also can be obtained from public databases. We perform Bayesian multiple regression analysis by combining the RSS likelihood with previously proposed prior distributions, sampling posteriors by Markov chain Monte Carlo. In a wide range of simulations RSS performs similarly to analyses using the individual data, both for estimating heritability and detecting associations. We apply RSS to a GWAS of human height that contains 253,288 individuals typed at 1.06 million SNPs, for which analyses of individual-level data are practically impossible. Estimates of heritability (52%) are consistent with, but more precise, than previous results using subsets of these data. We also identify many previously unreported loci that show evidence for association with height in our analyses. Software is available at https://github.com/stephenslab/rss. PMID:29399241

Hamiltonian Monte Carlo acceleration using surrogate functions with random bases.

PubMed

Zhang, Cheng; Shahbaba, Babak; Zhao, Hongkai

2017-11-01

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov chain Monte Carlo methods, namely, Hamiltonian Monte Carlo. The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the-art methods.

Beyond maximum entropy: Fractal pixon-based image reconstruction

NASA Technical Reports Server (NTRS)

Puetter, R. C.; Pina, R. K.

1994-01-01

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other methods, including Goodness-of-Fit (e.g. Least-Squares and Lucy-Richardson) and Maximum Entropy (ME). Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME.

Bayesian methodology for the design and interpretation of clinical trials in critical care medicine: a primer for clinicians.

PubMed

Kalil, Andre C; Sun, Junfeng

2014-10-01

To review Bayesian methodology and its utility to clinical decision making and research in the critical care field. Clinical, epidemiological, and biostatistical studies on Bayesian methods in PubMed and Embase from their inception to December 2013. Bayesian methods have been extensively used by a wide range of scientific fields, including astronomy, engineering, chemistry, genetics, physics, geology, paleontology, climatology, cryptography, linguistics, ecology, and computational sciences. The application of medical knowledge in clinical research is analogous to the application of medical knowledge in clinical practice. Bedside physicians have to make most diagnostic and treatment decisions on critically ill patients every day without clear-cut evidence-based medicine (more subjective than objective evidence). Similarly, clinical researchers have to make most decisions about trial design with limited available data. Bayesian methodology allows both subjective and objective aspects of knowledge to be formally measured and transparently incorporated into the design, execution, and interpretation of clinical trials. In addition, various degrees of knowledge and several hypotheses can be tested at the same time in a single clinical trial without the risk of multiplicity. Notably, the Bayesian technology is naturally suited for the interpretation of clinical trial findings for the individualized care of critically ill patients and for the optimization of public health policies. We propose that the application of the versatile Bayesian methodology in conjunction with the conventional statistical methods is not only ripe for actual use in critical care clinical research but it is also a necessary step to maximize the performance of clinical trials and its translation to the practice of critical care medicine.

Inference of reactive transport model parameters using a Bayesian multivariate approach

NASA Astrophysics Data System (ADS)

Carniato, Luca; Schoups, Gerrit; van de Giesen, Nick

2014-08-01

Parameter estimation of subsurface transport models from multispecies data requires the definition of an objective function that includes different types of measurements. Common approaches are weighted least squares (WLS), where weights are specified a priori for each measurement, and weighted least squares with weight estimation (WLS(we)) where weights are estimated from the data together with the parameters. In this study, we formulate the parameter estimation task as a multivariate Bayesian inference problem. The WLS and WLS(we) methods are special cases in this framework, corresponding to specific prior assumptions about the residual covariance matrix. The Bayesian perspective allows for generalizations to cases where residual correlation is important and for efficient inference by analytically integrating out the variances (weights) and selected covariances from the joint posterior. Specifically, the WLS and WLS(we) methods are compared to a multivariate (MV) approach that accounts for specific residual correlations without the need for explicit estimation of the error parameters. When applied to inference of reactive transport model parameters from column-scale data on dissolved species concentrations, the following results were obtained: (1) accounting for residual correlation between species provides more accurate parameter estimation for high residual correlation levels whereas its influence for predictive uncertainty is negligible, (2) integrating out the (co)variances leads to an efficient estimation of the full joint posterior with a reduced computational effort compared to the WLS(we) method, and (3) in the presence of model structural errors, none of the methods is able to identify the correct parameter values.

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

PubMed

Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

2015-09-01

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

Decision-Tree Program

NASA Technical Reports Server (NTRS)

Buntine, Wray

1994-01-01

IND computer program introduces Bayesian and Markov/maximum-likelihood (MML) methods and more-sophisticated methods of searching in growing trees. Produces more-accurate class-probability estimates important in applications like diagnosis. Provides range of features and styles with convenience for casual user, fine-tuning for advanced user or for those interested in research. Consists of four basic kinds of routines: data-manipulation, tree-generation, tree-testing, and tree-display. Written in C language.

Hepatitis disease detection using Bayesian theory

NASA Astrophysics Data System (ADS)

Maseleno, Andino; Hidayati, Rohmah Zahroh

2017-02-01

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

Fitting Residual Error Structures for Growth Models in SAS PROC MCMC

ERIC Educational Resources Information Center

McNeish, Daniel

2017-01-01

In behavioral sciences broadly, estimating growth models with Bayesian methods is becoming increasingly common, especially to combat small samples common with longitudinal data. Although Mplus is becoming an increasingly common program for applied research employing Bayesian methods, the limited selection of prior distributions for the elements of…

Bayesian and Frequentist Methods for Estimating Joint Uncertainty of Freundlich Adsorption Isotherm Fitting Parameters

EPA Science Inventory

In this paper, we present methods for estimating Freundlich isotherm fitting parameters (K and N) and their joint uncertainty, which have been implemented into the freeware software platforms R and WinBUGS. These estimates were determined by both Frequentist and Bayesian analyse...

Comments: Causal Interpretations of Mediation Effects

ERIC Educational Resources Information Center

Jo, Booil; Stuart, Elizabeth A.

2012-01-01

The authors thank Dr. Lindsay Page for providing a nice illustration of the use of the principal stratification framework to define causal effects, and a Bayesian model for effect estimation. They hope that her well-written article will help expose education researchers to these concepts and methods, and move the field of mediation analysis in…

Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques

NASA Technical Reports Server (NTRS)

Saha, Bhaskar; Goebel, kai

2007-01-01

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

Modeling error distributions of growth curve models through Bayesian methods.

PubMed

Zhang, Zhiyong

2016-06-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided.

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

PubMed

Yu, Rongjie; Abdel-Aty, Mohamed

2013-07-01

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

Application of Bayesian methods to habitat selection modeling of the northern spotted owl in California: new statistical methods for wildlife research

Treesearch

Howard B. Stauffer; Cynthia J. Zabel; Jeffrey R. Dunk

2005-01-01

We compared a set of competing logistic regression habitat selection models for Northern Spotted Owls (Strix occidentalis caurina) in California. The habitat selection models were estimated, compared, evaluated, and tested using multiple sample datasets collected on federal forestlands in northern California. We used Bayesian methods in interpreting...

Bayesian updating in a fault tree model for shipwreck risk assessment.

PubMed

Landquist, H; Rosén, L; Lindhe, A; Norberg, T; Hassellöv, I-M

2017-07-15

Shipwrecks containing oil and other hazardous substances have been deteriorating on the seabeds of the world for many years and are threatening to pollute the marine environment. The status of the wrecks and the potential volume of harmful substances present in the wrecks are affected by a multitude of uncertainties. Each shipwreck poses a unique threat, the nature of which is determined by the structural status of the wreck and possible damage resulting from hazardous activities that could potentially cause a discharge. Decision support is required to ensure the efficiency of the prioritisation process and the allocation of resources required to carry out risk mitigation measures. Whilst risk assessments can provide the requisite decision support, comprehensive methods that take into account key uncertainties related to shipwrecks are limited. The aim of this paper was to develop a method for estimating the probability of discharge of hazardous substances from shipwrecks. The method is based on Bayesian updating of generic information on the hazards posed by different activities in the surroundings of the wreck, with information on site-specific and wreck-specific conditions in a fault tree model. Bayesian updating is performed using Monte Carlo simulations for estimating the probability of a discharge of hazardous substances and formal handling of intrinsic uncertainties. An example application involving two wrecks located off the Swedish coast is presented. Results show the estimated probability of opening, discharge and volume of the discharge for the two wrecks and illustrate the capability of the model to provide decision support. Together with consequence estimations of a discharge of hazardous substances, the suggested model enables comprehensive and probabilistic risk assessments of shipwrecks to be made. Copyright © 2017 Elsevier B.V. All rights reserved.

Comparison of Bayesian clustering and edge detection methods for inferring boundaries in landscape genetics

USGS Publications Warehouse

Safner, T.; Miller, M.P.; McRae, B.H.; Fortin, M.-J.; Manel, S.

2011-01-01

Recently, techniques available for identifying clusters of individuals or boundaries between clusters using genetic data from natural populations have expanded rapidly. Consequently, there is a need to evaluate these different techniques. We used spatially-explicit simulation models to compare three spatial Bayesian clustering programs and two edge detection methods. Spatially-structured populations were simulated where a continuous population was subdivided by barriers. We evaluated the ability of each method to correctly identify boundary locations while varying: (i) time after divergence, (ii) strength of isolation by distance, (iii) level of genetic diversity, and (iv) amount of gene flow across barriers. To further evaluate the methods' effectiveness to detect genetic clusters in natural populations, we used previously published data on North American pumas and a European shrub. Our results show that with simulated and empirical data, the Bayesian spatial clustering algorithms outperformed direct edge detection methods. All methods incorrectly detected boundaries in the presence of strong patterns of isolation by distance. Based on this finding, we support the application of Bayesian spatial clustering algorithms for boundary detection in empirical datasets, with necessary tests for the influence of isolation by distance. ?? 2011 by the authors; licensee MDPI, Basel, Switzerland.

Analysis of phase II methodologies for single-arm clinical trials with multiple endpoints in rare cancers: An example in Ewing’s sarcoma

PubMed Central

Dutton, P; Love, SB; Billingham, L; Hassan, AB

2016-01-01

Trials run in either rare diseases, such as rare cancers, or rare sub-populations of common diseases are challenging in terms of identifying, recruiting and treating sufficient patients in a sensible period. Treatments for rare diseases are often designed for other disease areas and then later proposed as possible treatments for the rare disease after initial phase I testing is complete. To ensure the trial is in the best interests of the patient participants, frequent interim analyses are needed to force the trial to stop promptly if the treatment is futile or toxic. These non-definitive phase II trials should also be stopped for efficacy to accelerate research progress if the treatment proves to be particularly promising. In this paper, we review frequentist and Bayesian methods that have been adapted to incorporate two binary endpoints and frequent interim analyses. The Eurosarc Trial of Linsitinib in advanced Ewing Sarcoma (LINES) is used as a motivating example and provides a suitable platform to compare these approaches. The Bayesian approach provides greater design flexibility, but does not provide additional value over the frequentist approaches in a single trial setting when the prior is non-informative. However, Bayesian designs are able to borrow from any previous experience, using prior information to improve efficiency. PMID:27587590

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Evidence and Clinical Trials.

NASA Astrophysics Data System (ADS)

Goodman, Steven N.

1989-11-01

This dissertation explores the use of a mathematical measure of statistical evidence, the log likelihood ratio, in clinical trials. The methods and thinking behind the use of an evidential measure are contrasted with traditional methods of analyzing data, which depend primarily on a p-value as an estimate of the statistical strength of an observed data pattern. It is contended that neither the behavioral dictates of Neyman-Pearson hypothesis testing methods, nor the coherency dictates of Bayesian methods are realistic models on which to base inference. The use of the likelihood alone is applied to four aspects of trial design or conduct: the calculation of sample size, the monitoring of data, testing for the equivalence of two treatments, and meta-analysis--the combining of results from different trials. Finally, a more general model of statistical inference, using belief functions, is used to see if it is possible to separate the assessment of evidence from our background knowledge. It is shown that traditional and Bayesian methods can be modeled as two ends of a continuum of structured background knowledge, methods which summarize evidence at the point of maximum likelihood assuming no structure, and Bayesian methods assuming complete knowledge. Both schools are seen to be missing a concept of ignorance- -uncommitted belief. This concept provides the key to understanding the problem of sampling to a foregone conclusion and the role of frequency properties in statistical inference. The conclusion is that statistical evidence cannot be defined independently of background knowledge, and that frequency properties of an estimator are an indirect measure of uncommitted belief. Several likelihood summaries need to be used in clinical trials, with the quantitative disparity between summaries being an indirect measure of our ignorance. This conclusion is linked with parallel ideas in the philosophy of science and cognitive psychology.

Smartphone technologies and Bayesian networks to assess shorebird habitat selection

USGS Publications Warehouse

Zeigler, Sara; Thieler, E. Robert; Gutierrez, Ben; Plant, Nathaniel G.; Hines, Megan K.; Fraser, James D.; Catlin, Daniel H.; Karpanty, Sarah M.

2017-01-01

Understanding patterns of habitat selection across a species’ geographic distribution can be critical for adequately managing populations and planning for habitat loss and related threats. However, studies of habitat selection can be time consuming and expensive over broad spatial scales, and a lack of standardized monitoring targets or methods can impede the generalization of site-based studies. Our objective was to collaborate with natural resource managers to define available nesting habitat for piping plovers (Charadrius melodus) throughout their U.S. Atlantic coast distribution from Maine to North Carolina, with a goal of providing science that could inform habitat management in response to sea-level rise. We characterized a data collection and analysis approach as being effective if it provided low-cost collection of standardized habitat-selection data across the species’ breeding range within 1–2 nesting seasons and accurate nesting location predictions. In the method developed, >30 managers and conservation practitioners from government agencies and private organizations used a smartphone application, “iPlover,” to collect data on landcover characteristics at piping plover nest locations and random points on 83 beaches and barrier islands in 2014 and 2015. We analyzed these data with a Bayesian network that predicted the probability a specific combination of landcover variables would be associated with a nesting site. Although we focused on a shorebird, our approach can be modified for other taxa. Results showed that the Bayesian network performed well in predicting habitat availability and confirmed predicted habitat preferences across the Atlantic coast breeding range of the piping plover. We used the Bayesian network to map areas with a high probability of containing nesting habitat on the Rockaway Peninsula in New York, USA, as an example application. Our approach facilitated the collation of evidence-based information on habitat selection from many locations and sources, which can be used in management and decision-making applications.

Bayesian Regression with Network Prior: Optimal Bayesian Filtering Perspective

PubMed Central

Qian, Xiaoning; Dougherty, Edward R.

2017-01-01

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

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.

Python Environment for Bayesian Learning: Inferring the Structure of Bayesian Networks from Knowledge and Data

PubMed Central

Shah, Abhik; Woolf, Peter

2009-01-01

Summary In this paper, we introduce pebl, a Python library and application for learning Bayesian network structure from data and prior knowledge that provides features unmatched by alternative software packages: the ability to use interventional data, flexible specification of structural priors, modeling with hidden variables and exploitation of parallel processing. PMID:20161541

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

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…

Modeling of Academic Achievement of Primary School Students in Ethiopia Using Bayesian Multilevel Approach

ERIC Educational Resources Information Center

Sebro, Negusse Yohannes; Goshu, Ayele Taye

2017-01-01

This study aims to explore Bayesian multilevel modeling to investigate variations of average academic achievement of grade eight school students. A sample of 636 students is randomly selected from 26 private and government schools by a two-stage stratified sampling design. Bayesian method is used to estimate the fixed and random effects. Input and…

A Simulation Study Comparison of Bayesian Estimation with Conventional Methods for Estimating Unknown Change Points

ERIC Educational Resources Information Center

Wang, Lijuan; McArdle, John J.

2008-01-01

The main purpose of this research is to evaluate the performance of a Bayesian approach for estimating unknown change points using Monte Carlo simulations. The univariate and bivariate unknown change point mixed models were presented and the basic idea of the Bayesian approach for estimating the models was discussed. The performance of Bayesian…

Improving statistical inference on pathogen densities estimated by quantitative molecular methods: malaria gametocytaemia as a case study.

PubMed

Walker, Martin; Basáñez, María-Gloria; Ouédraogo, André Lin; Hermsen, Cornelus; Bousema, Teun; Churcher, Thomas S

2015-01-16

Quantitative molecular methods (QMMs) such as quantitative real-time polymerase chain reaction (q-PCR), reverse-transcriptase PCR (qRT-PCR) and quantitative nucleic acid sequence-based amplification (QT-NASBA) are increasingly used to estimate pathogen density in a variety of clinical and epidemiological contexts. These methods are often classified as semi-quantitative, yet estimates of reliability or sensitivity are seldom reported. Here, a statistical framework is developed for assessing the reliability (uncertainty) of pathogen densities estimated using QMMs and the associated diagnostic sensitivity. The method is illustrated with quantification of Plasmodium falciparum gametocytaemia by QT-NASBA. The reliability of pathogen (e.g. gametocyte) densities, and the accompanying diagnostic sensitivity, estimated by two contrasting statistical calibration techniques, are compared; a traditional method and a mixed model Bayesian approach. The latter accounts for statistical dependence of QMM assays run under identical laboratory protocols and permits structural modelling of experimental measurements, allowing precision to vary with pathogen density. Traditional calibration cannot account for inter-assay variability arising from imperfect QMMs and generates estimates of pathogen density that have poor reliability, are variable among assays and inaccurately reflect diagnostic sensitivity. The Bayesian mixed model approach assimilates information from replica QMM assays, improving reliability and inter-assay homogeneity, providing an accurate appraisal of quantitative and diagnostic performance. Bayesian mixed model statistical calibration supersedes traditional techniques in the context of QMM-derived estimates of pathogen density, offering the potential to improve substantially the depth and quality of clinical and epidemiological inference for a wide variety of pathogens.

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%.

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.

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.

Review of Reliability-Based Design Optimization Approach and Its Integration with Bayesian Method

NASA Astrophysics Data System (ADS)

Zhang, Xiangnan

2018-03-01

A lot of uncertain factors lie in practical engineering, such as external load environment, material property, geometrical shape, initial condition, boundary condition, etc. Reliability method measures the structural safety condition and determine the optimal design parameter combination based on the probabilistic theory. Reliability-based design optimization (RBDO) is the most commonly used approach to minimize the structural cost or other performance under uncertainty variables which combines the reliability theory and optimization. However, it cannot handle the various incomplete information. The Bayesian approach is utilized to incorporate this kind of incomplete information in its uncertainty quantification. In this paper, the RBDO approach and its integration with Bayesian method are introduced.

Detection and Classification of Transformer Winding Mechanical Faults Using UWB Sensors and Bayesian Classifier

NASA Astrophysics Data System (ADS)

Alehosseini, Ali; A. Hejazi, Maryam; Mokhtari, Ghassem; B. Gharehpetian, Gevork; Mohammadi, Mohammad

2015-06-01

In this paper, the Bayesian classifier is used to detect and classify the radial deformation and axial displacement of transformer windings. The proposed method is tested on a model of transformer for different volumes of radial deformation and axial displacement. In this method, ultra-wideband (UWB) signal is sent to the simplified model of the transformer winding. The received signal from the winding model is recorded and used for training and testing of Bayesian classifier in different axial displacement and radial deformation states of the winding. It is shown that the proposed method has a good accuracy to detect and classify the axial displacement and radial deformation of the winding.

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.

2016-01-01

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

With or without you: predictive coding and Bayesian inference in the brain

PubMed Central

Aitchison, Laurence; Lengyel, Máté

2018-01-01

Two theoretical ideas have emerged recently with the ambition to provide a unifying functional explanation of neural population coding and dynamics: predictive coding and Bayesian inference. Here, we describe the two theories and their combination into a single framework: Bayesian predictive coding. We clarify how the two theories can be distinguished, despite sharing core computational concepts and addressing an overlapping set of empirical phenomena. We argue that predictive coding is an algorithmic / representational motif that can serve several different computational goals of which Bayesian inference is but one. Conversely, while Bayesian inference can utilize predictive coding, it can also be realized by a variety of other representations. We critically evaluate the experimental evidence supporting Bayesian predictive coding and discuss how to test it more directly. PMID:28942084

Spatial distribution of psychotic disorders in an urban area of France: an ecological study.

PubMed

Pignon, Baptiste; Schürhoff, Franck; Baudin, Grégoire; Ferchiou, Aziz; Richard, Jean-Romain; Saba, Ghassen; Leboyer, Marion; Kirkbride, James B; Szöke, Andrei

2016-05-18

Previous analyses of neighbourhood variations of non-affective psychotic disorders (NAPD) have focused mainly on incidence. However, prevalence studies provide important insights on factors associated with disease evolution as well as for healthcare resource allocation. This study aimed to investigate the distribution of prevalent NAPD cases in an urban area in France. The number of cases in each neighbourhood was modelled as a function of potential confounders and ecological variables, namely: migrant density, economic deprivation and social fragmentation. This was modelled using statistical models of increasing complexity: frequentist models (using Poisson and negative binomial regressions), and several Bayesian models. For each model, assumptions validity were checked and compared as to how this fitted to the data, in order to test for possible spatial variation in prevalence. Data showed significant overdispersion (invalidating the Poisson regression model) and residual autocorrelation (suggesting the need to use Bayesian models). The best Bayesian model was Leroux's model (i.e. a model with both strong correlation between neighbouring areas and weaker correlation between areas further apart), with economic deprivation as an explanatory variable (OR = 1.13, 95% CI [1.02-1.25]). In comparison with frequentist methods, the Bayesian model showed a better fit. The number of cases showed non-random spatial distribution and was linked to economic deprivation.

A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites

NASA Astrophysics Data System (ADS)

Wang, Q. J.; Robertson, D. E.; Chiew, F. H. S.

2009-05-01

Seasonal forecasting of streamflows can be highly valuable for water resources management. In this paper, a Bayesian joint probability (BJP) modeling approach for seasonal forecasting of streamflows at multiple sites is presented. A Box-Cox transformed multivariate normal distribution is proposed to model the joint distribution of future streamflows and their predictors such as antecedent streamflows and El Niño-Southern Oscillation indices and other climate indicators. Bayesian inference of model parameters and uncertainties is implemented using Markov chain Monte Carlo sampling, leading to joint probabilistic forecasts of streamflows at multiple sites. The model provides a parametric structure for quantifying relationships between variables, including intersite correlations. The Box-Cox transformed multivariate normal distribution has considerable flexibility for modeling a wide range of predictors and predictands. The Bayesian inference formulated allows the use of data that contain nonconcurrent and missing records. The model flexibility and data-handling ability means that the BJP modeling approach is potentially of wide practical application. The paper also presents a number of statistical measures and graphical methods for verification of probabilistic forecasts of continuous variables. Results for streamflows at three river gauges in the Murrumbidgee River catchment in southeast Australia show that the BJP modeling approach has good forecast quality and that the fitted model is consistent with observed data.

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

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

Zhang, Jiangjiang; Li, Weixuan; Zeng, Lingzao

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

Lead isotope ratios for bullets, forensic evaluation in a Bayesian paradigm.

PubMed

Sjåstad, Knut-Endre; Lucy, David; Andersen, Tom

2016-01-01

Forensic science is a discipline concerned with collection, examination and evaluation of physical evidence related to criminal cases. The results from the activities of the forensic scientist may ultimately be presented to the court in such a way that the triers of fact understand the implications of the data. Forensic science has been, and still is, driven by development of new technology, and in the last two decades evaluation of evidence based on logical reasoning and Bayesian statistic has reached some level of general acceptance within the forensic community. Tracing of lead fragments of unknown origin to a given source of ammunition is a task that might be of interest for the Court. Use of data from lead isotope ratios analysis interpreted within a Bayesian framework has shown to be suitable method to guide the Court to draw their conclusion for such task. In this work we have used isotopic composition of lead from small arms projectiles (cal. .22) and developed an approach based on Bayesian statistics and likelihood ratio calculation. The likelihood ratio is a single quantity that provides a measure of the value of evidence that can be used in the deliberation of the court. Copyright © 2015 Elsevier B.V. All rights reserved.

Bayesian adaptive phase II screening design for combination trials

PubMed Central

Cai, Chunyan; Yuan, Ying; Johnson, Valen E

2013-01-01

Background Trials of combination therapies for the treatment of cancer are playing an increasingly important role in the battle against this disease. To more efficiently handle the large number of combination therapies that must be tested, we propose a novel Bayesian phase II adaptive screening design to simultaneously select among possible treatment combinations involving multiple agents. Methods Our design is based on formulating the selection procedure as a Bayesian hypothesis testing problem in which the superiority of each treatment combination is equated to a single hypothesis. During the trial conduct, we use the current values of the posterior probabilities of all hypotheses to adaptively allocate patients to treatment combinations. Results Simulation studies show that the proposed design substantially outperforms the conventional multiarm balanced factorial trial design. The proposed design yields a significantly higher probability for selecting the best treatment while allocating substantially more patients to efficacious treatments. Limitations The proposed design is most appropriate for the trials combining multiple agents and screening out the efficacious combination to be further investigated. Conclusions The proposed Bayesian adaptive phase II screening design substantially outperformed the conventional complete factorial design. Our design allocates more patients to better treatments while providing higher power to identify the best treatment at the end of the trial. PMID:23359875

Bayesian approach for assessing non-inferiority in a three-arm trial with pre-specified margin.

PubMed

Ghosh, Samiran; Ghosh, Santu; Tiwari, Ram C

2016-02-28

Non-inferiority trials are becoming increasingly popular for comparative effectiveness research. However, inclusion of the placebo arm, whenever possible, gives rise to a three-arm trial which has lesser burdensome assumptions than a standard two-arm non-inferiority trial. Most of the past developments in a three-arm trial consider defining a pre-specified fraction of unknown effect size of reference drug, that is, without directly specifying a fixed non-inferiority margin. However, in some recent developments, a more direct approach is being considered with pre-specified fixed margin albeit in the frequentist setup. Bayesian paradigm provides a natural path to integrate historical and current trials' information via sequential learning. In this paper, we propose a Bayesian approach for simultaneous testing of non-inferiority and assay sensitivity in a three-arm trial with normal responses. For the experimental arm, in absence of historical information, non-informative priors are assumed under two situations, namely when (i) variance is known and (ii) variance is unknown. A Bayesian decision criteria is derived and compared with the frequentist method using simulation studies. Finally, several published clinical trial examples are reanalyzed to demonstrate the benefit of the proposed procedure. Copyright © 2015 John Wiley & Sons, Ltd.

A Hierarchical Bayesian Model for Calibrating Estimates of Species Divergence Times

PubMed Central

Heath, Tracy A.

2012-01-01

In Bayesian divergence time estimation methods, incorporating calibrating information from the fossil record is commonly done by assigning prior densities to ancestral nodes in the tree. Calibration prior densities are typically parametric distributions offset by minimum age estimates provided by the fossil record. Specification of the parameters of calibration densities requires the user to quantify his or her prior knowledge of the age of the ancestral node relative to the age of its calibrating fossil. The values of these parameters can, potentially, result in biased estimates of node ages if they lead to overly informative prior distributions. Accordingly, determining parameter values that lead to adequate prior densities is not straightforward. In this study, I present a hierarchical Bayesian model for calibrating divergence time analyses with multiple fossil age constraints. This approach applies a Dirichlet process prior as a hyperprior on the parameters of calibration prior densities. Specifically, this model assumes that the rate parameters of exponential prior distributions on calibrated nodes are distributed according to a Dirichlet process, whereby the rate parameters are clustered into distinct parameter categories. Both simulated and biological data are analyzed to evaluate the performance of the Dirichlet process hyperprior. Compared with fixed exponential prior densities, the hierarchical Bayesian approach results in more accurate and precise estimates of internal node ages. When this hyperprior is applied using Markov chain Monte Carlo methods, the ages of calibrated nodes are sampled from mixtures of exponential distributions and uncertainty in the values of calibration density parameters is taken into account. PMID:22334343

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

NASA Astrophysics Data System (ADS)

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

2014-02-01

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

The Impact of the Tree Prior on Molecular Dating of Data Sets Containing a Mixture of Inter- and Intraspecies Sampling.

PubMed

Ritchie, Andrew M; Lo, Nathan; Ho, Simon Y W

2017-05-01

In Bayesian phylogenetic analyses of genetic data, prior probability distributions need to be specified for the model parameters, including the tree. When Bayesian methods are used for molecular dating, available tree priors include those designed for species-level data, such as the pure-birth and birth-death priors, and coalescent-based priors designed for population-level data. However, molecular dating methods are frequently applied to data sets that include multiple individuals across multiple species. Such data sets violate the assumptions of both the speciation and coalescent-based tree priors, making it unclear which should be chosen and whether this choice can affect the estimation of node times. To investigate this problem, we used a simulation approach to produce data sets with different proportions of within- and between-species sampling under the multispecies coalescent model. These data sets were then analyzed under pure-birth, birth-death, constant-size coalescent, and skyline coalescent tree priors. We also explored the ability of Bayesian model testing to select the best-performing priors. We confirmed the applicability of our results to empirical data sets from cetaceans, phocids, and coregonid whitefish. Estimates of node times were generally robust to the choice of tree prior, but some combinations of tree priors and sampling schemes led to large differences in the age estimates. In particular, the pure-birth tree prior frequently led to inaccurate estimates for data sets containing a mixture of inter- and intraspecific sampling, whereas the birth-death and skyline coalescent priors produced stable results across all scenarios. Model testing provided an adequate means of rejecting inappropriate tree priors. Our results suggest that tree priors do not strongly affect Bayesian molecular dating results in most cases, even when severely misspecified. However, the choice of tree prior can be significant for the accuracy of dating results in the case of data sets with mixed inter- and intraspecies sampling. [Bayesian phylogenetic methods; model testing; molecular dating; node time; tree prior.]. © The authors 2016. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

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.

Explaining Inference on a Population of Independent Agents Using Bayesian Networks

ERIC Educational Resources Information Center

Sutovsky, Peter

2013-01-01

The main goal of this research is to design, implement, and evaluate a novel explanation method, the hierarchical explanation method (HEM), for explaining Bayesian network (BN) inference when the network is modeling a population of conditionally independent agents, each of which is modeled as a subnetwork. For example, consider disease-outbreak…

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. ...

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

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

2014-06-01

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

Exact posterior computation in non-conjugate Gaussian location-scale parameters models

NASA Astrophysics Data System (ADS)

Andrade, J. A. A.; Rathie, P. N.

2017-12-01

In Bayesian analysis the class of conjugate models allows to obtain exact posterior distributions, however this class quite restrictive in the sense that it involves only a few distributions. In fact, most of the practical applications involves non-conjugate models, thus approximate methods, such as the MCMC algorithms, are required. Although these methods can deal with quite complex structures, some practical problems can make their applications quite time demanding, for example, when we use heavy-tailed distributions, convergence may be difficult, also the Metropolis-Hastings algorithm can become very slow, in addition to the extra work inevitably required on choosing efficient candidate generator distributions. In this work, we draw attention to the special functions as a tools for Bayesian computation, we propose an alternative method for obtaining the posterior distribution in Gaussian non-conjugate models in an exact form. We use complex integration methods based on the H-function in order to obtain the posterior distribution and some of its posterior quantities in an explicit computable form. Two examples are provided in order to illustrate the theory.

A New Method for Predicting Patient Survivorship Using Efficient Bayesian Network Learning

PubMed Central

Jiang, Xia; Xue, Diyang; Brufsky, Adam; Khan, Seema; Neapolitan, Richard

2014-01-01

The purpose of this investigation is to develop and evaluate a new Bayesian network (BN)-based patient survivorship prediction method. The central hypothesis is that the method predicts patient survivorship well, while having the capability to handle high-dimensional data and be incorporated into a clinical decision support system (CDSS). We have developed EBMC_Survivorship (EBMC_S), which predicts survivorship for each year individually. EBMC_S is based on the EBMC BN algorithm, which has been shown to handle high-dimensional data. BNs have excellent architecture for decision support systems. In this study, we evaluate EBMC_S using the Molecular Taxonomy of Breast Cancer International Consortium (METABRIC) dataset, which concerns breast tumors. A 5-fold cross-validation study indicates that EMBC_S performs better than the Cox proportional hazard model and is comparable to the random survival forest method. We show that EBMC_S provides additional information such as sensitivity analyses, which covariates predict each year, and yearly areas under the ROC curve (AUROCs). We conclude that our investigation supports the central hypothesis. PMID:24558297

A new method for predicting patient survivorship using efficient bayesian network learning.

PubMed

Jiang, Xia; Xue, Diyang; Brufsky, Adam; Khan, Seema; Neapolitan, Richard

2014-01-01

The purpose of this investigation is to develop and evaluate a new Bayesian network (BN)-based patient survivorship prediction method. The central hypothesis is that the method predicts patient survivorship well, while having the capability to handle high-dimensional data and be incorporated into a clinical decision support system (CDSS). We have developed EBMC_Survivorship (EBMC_S), which predicts survivorship for each year individually. EBMC_S is based on the EBMC BN algorithm, which has been shown to handle high-dimensional data. BNs have excellent architecture for decision support systems. In this study, we evaluate EBMC_S using the Molecular Taxonomy of Breast Cancer International Consortium (METABRIC) dataset, which concerns breast tumors. A 5-fold cross-validation study indicates that EMBC_S performs better than the Cox proportional hazard model and is comparable to the random survival forest method. We show that EBMC_S provides additional information such as sensitivity analyses, which covariates predict each year, and yearly areas under the ROC curve (AUROCs). We conclude that our investigation supports the central hypothesis.

Bayesian additive decision trees of biomarker by treatment interactions for predictive biomarker detection and subgroup identification.

PubMed

Zhao, Yang; Zheng, Wei; Zhuo, Daisy Y; Lu, Yuefeng; Ma, Xiwen; Liu, Hengchang; Zeng, Zhen; Laird, Glen

2017-10-11

Personalized medicine, or tailored therapy, has been an active and important topic in recent medical research. Many methods have been proposed in the literature for predictive biomarker detection and subgroup identification. In this article, we propose a novel decision tree-based approach applicable in randomized clinical trials. We model the prognostic effects of the biomarkers using additive regression trees and the biomarker-by-treatment effect using a single regression tree. Bayesian approach is utilized to periodically revise the split variables and the split rules of the decision trees, which provides a better overall fitting. Gibbs sampler is implemented in the MCMC procedure, which updates the prognostic trees and the interaction tree separately. We use the posterior distribution of the interaction tree to construct the predictive scores of the biomarkers and to identify the subgroup where the treatment is superior to the control. Numerical simulations show that our proposed method performs well under various settings comparing to existing methods. We also demonstrate an application of our method in a real clinical trial.

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

NASA Astrophysics Data System (ADS)

Chen, T.; Luo, H.

2013-12-01

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

Bayesian analysis of multimodal data and brain imaging

NASA Astrophysics Data System (ADS)

Assadi, Amir H.; Eghbalnia, Hamid; Backonja, Miroslav; Wakai, Ronald T.; Rutecki, Paul; Haughton, Victor

2000-06-01

It is often the case that information about a process can be obtained using a variety of methods. Each method is employed because of specific advantages over the competing alternatives. An example in medical neuro-imaging is the choice between fMRI and MEG modes where fMRI can provide high spatial resolution in comparison to the superior temporal resolution of MEG. The combination of data from varying modes provides the opportunity to infer results that may not be possible by means of any one mode alone. We discuss a Bayesian and learning theoretic framework for enhanced feature extraction that is particularly suited to multi-modal investigations of massive data sets from multiple experiments. In the following Bayesian approach, acquired knowledge (information) regarding various aspects of the process are all directly incorporated into the formulation. This information can come from a variety of sources. In our case, it represents statistical information obtained from other modes of data collection. The information is used to train a learning machine to estimate a probability distribution, which is used in turn by a second machine as a prior, in order to produce a more refined estimation of the distribution of events. The computational demand of the algorithm is handled by proposing a distributed parallel implementation on a cluster of workstations that can be scaled to address real-time needs if required. We provide a simulation of these methods on a set of synthetically generated MEG and EEG data. We show how spatial and temporal resolutions improve by using prior distributions. The method on fMRI signals permits one to construct the probability distribution of the non-linear hemodynamics of the human brain (real data). These computational results are in agreement with biologically based measurements of other labs, as reported to us by researchers from UK. We also provide preliminary analysis involving multi-electrode cortical recording that accompanies behavioral data in pain experiments on freely moving mice subjected to moderate heat delivered by an electric bulb. Summary of new or breakthrough ideas: (1) A new method to estimate probability distribution for measurement of nonlinear hemodynamics of brain from a multi- modal neuronal data. This is the first time that such an idea is tried, to our knowledge. (2) Breakthrough in improvement of time resolution of fMRI signals using (1) above.

Bayesian refinement of protein structures and ensembles against SAXS data using molecular dynamics

PubMed Central

Shevchuk, Roman; Hub, Jochen S.

2017-01-01

Small-angle X-ray scattering is an increasingly popular technique used to detect protein structures and ensembles in solution. However, the refinement of structures and ensembles against SAXS data is often ambiguous due to the low information content of SAXS data, unknown systematic errors, and unknown scattering contributions from the solvent. We offer a solution to such problems by combining Bayesian inference with all-atom molecular dynamics simulations and explicit-solvent SAXS calculations. The Bayesian formulation correctly weights the SAXS data versus prior physical knowledge, it quantifies the precision or ambiguity of fitted structures and ensembles, and it accounts for unknown systematic errors due to poor buffer matching. The method further provides a probabilistic criterion for identifying the number of states required to explain the SAXS data. The method is validated by refining ensembles of a periplasmic binding protein against calculated SAXS curves. Subsequently, we derive the solution ensembles of the eukaryotic chaperone heat shock protein 90 (Hsp90) against experimental SAXS data. We find that the SAXS data of the apo state of Hsp90 is compatible with a single wide-open conformation, whereas the SAXS data of Hsp90 bound to ATP or to an ATP-analogue strongly suggest heterogenous ensembles of a closed and a wide-open state. PMID:29045407

Quantum-Like Bayesian Networks for Modeling Decision Making

PubMed Central

Moreira, Catarina; Wichert, Andreas

2016-01-01

In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios. PMID:26858669

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.

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.

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

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

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

2016-07-01

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

Bayesian models for comparative analysis integrating phylogenetic uncertainty

PubMed Central

2012-01-01

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

Bayesian 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.

Identification of transmissivity fields using a Bayesian strategy and perturbative approach

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

A Tutorial Introduction to Bayesian Models of Cognitive Development

ERIC Educational Resources Information Center

Perfors, Amy; Tenenbaum, Joshua B.; Griffiths, Thomas L.; Xu, Fei

2011-01-01

We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. Our goal is to provide an intuitive and accessible guide to the "what", the "how", and the "why" of the Bayesian approach: what sorts of problems and data the framework is most relevant for, and how and why it may be useful for…

Bayesian Inference: with ecological applications

USGS Publications Warehouse

Link, William A.; Barker, Richard J.

2010-01-01

This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.

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.

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.…

Probability-Based Recognition Framework for Underwater Landmarks Using Sonar Images †.

PubMed

Lee, Yeongjun; Choi, Jinwoo; Ko, Nak Yong; Choi, Hyun-Taek

2017-08-24

This paper proposes a probability-based framework for recognizing underwater landmarks using sonar images. Current recognition methods use a single image, which does not provide reliable results because of weaknesses of the sonar image such as unstable acoustic source, many speckle noises, low resolution images, single channel image, and so on. However, using consecutive sonar images, if the status-i.e., the existence and identity (or name)-of an object is continuously evaluated by a stochastic method, the result of the recognition method is available for calculating the uncertainty, and it is more suitable for various applications. Our proposed framework consists of three steps: (1) candidate selection, (2) continuity evaluation, and (3) Bayesian feature estimation. Two probability methods-particle filtering and Bayesian feature estimation-are used to repeatedly estimate the continuity and feature of objects in consecutive images. Thus, the status of the object is repeatedly predicted and updated by a stochastic method. Furthermore, we develop an artificial landmark to increase detectability by an imaging sonar, which we apply to the characteristics of acoustic waves, such as instability and reflection depending on the roughness of the reflector surface. The proposed method is verified by conducting basin experiments, and the results are presented.

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

Probabilistic Space Weather Forecasting: a Bayesian Perspective

NASA Astrophysics Data System (ADS)

Camporeale, E.; Chandorkar, M.; Borovsky, J.; Care', A.

2017-12-01

Most of the Space Weather forecasts, both at operational and research level, are not probabilistic in nature. Unfortunately, a prediction that does not provide a confidence level is not very useful in a decision-making scenario. Nowadays, forecast models range from purely data-driven, machine learning algorithms, to physics-based approximation of first-principle equations (and everything that sits in between). Uncertainties pervade all such models, at every level: from the raw data to finite-precision implementation of numerical methods. The most rigorous way of quantifying the propagation of uncertainties is by embracing a Bayesian probabilistic approach. One of the simplest and most robust machine learning technique in the Bayesian framework is Gaussian Process regression and classification. Here, we present the application of Gaussian Processes to the problems of the DST geomagnetic index forecast, the solar wind type classification, and the estimation of diffusion parameters in radiation belt modeling. In each of these very diverse problems, the GP approach rigorously provide forecasts in the form of predictive distributions. In turn, these distributions can be used as input for ensemble simulations in order to quantify the amplification of uncertainties. We show that we have achieved excellent results in all of the standard metrics to evaluate our models, with very modest computational cost.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

IZI: INFERRING THE GAS PHASE METALLICITY (Z) AND IONIZATION PARAMETER (q) OF IONIZED NEBULAE USING BAYESIAN STATISTICS

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

Blanc, Guillermo A.; Kewley, Lisa; Vogt, Frédéric P. A.

2015-01-10

We present a new method for inferring the metallicity (Z) and ionization parameter (q) of H II regions and star-forming galaxies using strong nebular emission lines (SELs). We use Bayesian inference to derive the joint and marginalized posterior probability density functions for Z and q given a set of observed line fluxes and an input photoionization model. Our approach allows the use of arbitrary sets of SELs and the inclusion of flux upper limits. The method provides a self-consistent way of determining the physical conditions of ionized nebulae that is not tied to the arbitrary choice of a particular SELmore » diagnostic and uses all the available information. Unlike theoretically calibrated SEL diagnostics, the method is flexible and not tied to a particular photoionization model. We describe our algorithm, validate it against other methods, and present a tool that implements it called IZI. Using a sample of nearby extragalactic H II regions, we assess the performance of commonly used SEL abundance diagnostics. We also use a sample of 22 local H II regions having both direct and recombination line (RL) oxygen abundance measurements in the literature to study discrepancies in the abundance scale between different methods. We find that oxygen abundances derived through Bayesian inference using currently available photoionization models in the literature can be in good (∼30%) agreement with RL abundances, although some models perform significantly better than others. We also confirm that abundances measured using the direct method are typically ∼0.2 dex lower than both RL and photoionization-model-based abundances.« less

Evaluating Bayesian spatial methods for modelling species distributions with clumped and restricted occurrence data.

PubMed

Redding, David W; Lucas, Tim C D; Blackburn, Tim M; Jones, Kate E

2017-01-01

Statistical approaches for inferring the spatial distribution of taxa (Species Distribution Models, SDMs) commonly rely on available occurrence data, which is often clumped and geographically restricted. Although available SDM methods address some of these factors, they could be more directly and accurately modelled using a spatially-explicit approach. Software to fit models with spatial autocorrelation parameters in SDMs are now widely available, but whether such approaches for inferring SDMs aid predictions compared to other methodologies is unknown. Here, within a simulated environment using 1000 generated species' ranges, we compared the performance of two commonly used non-spatial SDM methods (Maximum Entropy Modelling, MAXENT and boosted regression trees, BRT), to a spatial Bayesian SDM method (fitted using R-INLA), when the underlying data exhibit varying combinations of clumping and geographic restriction. Finally, we tested how any recommended methodological settings designed to account for spatially non-random patterns in the data impact inference. Spatial Bayesian SDM method was the most consistently accurate method, being in the top 2 most accurate methods in 7 out of 8 data sampling scenarios. Within high-coverage sample datasets, all methods performed fairly similarly. When sampling points were randomly spread, BRT had a 1-3% greater accuracy over the other methods and when samples were clumped, the spatial Bayesian SDM method had a 4%-8% better AUC score. Alternatively, when sampling points were restricted to a small section of the true range all methods were on average 10-12% less accurate, with greater variation among the methods. Model inference under the recommended settings to account for autocorrelation was not impacted by clumping or restriction of data, except for the complexity of the spatial regression term in the spatial Bayesian model. Methods, such as those made available by R-INLA, can be successfully used to account for spatial autocorrelation in an SDM context and, by taking account of random effects, produce outputs that can better elucidate the role of covariates in predicting species occurrence. Given that it is often unclear what the drivers are behind data clumping in an empirical occurrence dataset, or indeed how geographically restricted these data are, spatially-explicit Bayesian SDMs may be the better choice when modelling the spatial distribution of target species.

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.

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2017-06-07

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

Fundamentals and Recent Developments in Approximate Bayesian Computation

PubMed Central

Lintusaari, Jarno; Gutmann, Michael U.; Dutta, Ritabrata; Kaski, Samuel; Corander, Jukka

2017-01-01

Abstract Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.] PMID:28175922

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 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.

Bayesian inference of Calibration curves: application to archaeomagnetism

NASA Astrophysics Data System (ADS)

Lanos, P.

2003-04-01

The range of errors that occur at different stages of the archaeomagnetic calibration process are modelled using a Bayesian hierarchical model. The archaeomagnetic data obtained from archaeological structures such as hearths, kilns or sets of bricks and tiles, exhibit considerable experimental errors and are typically more or less well dated by archaeological context, history or chronometric methods (14C, TL, dendrochronology, etc.). They can also be associated with stratigraphic observations which provide prior relative chronological information. The modelling we describe in this paper allows all these observations, on materials from a given period, to be linked together, and the use of penalized maximum likelihood for smoothing univariate, spherical or three-dimensional time series data allows representation of the secular variation of the geomagnetic field over time. The smooth curve we obtain (which takes the form of a penalized natural cubic spline) provides an adaptation to the effects of variability in the density of reference points over time. Since our model takes account of all the known errors in the archaeomagnetic calibration process, we are able to obtain a functional highest-posterior-density envelope on the new curve. With this new posterior estimate of the curve available to us, the Bayesian statistical framework then allows us to estimate the calendar dates of undated archaeological features (such as kilns) based on one, two or three geomagnetic parameters (inclination, declination and/or intensity). Date estimates are presented in much the same way as those that arise from radiocarbon dating. In order to illustrate the model and inference methods used, we will present results based on German archaeomagnetic data recently published by a German team.

Bayes and empirical Bayes estimators of abundance and density from spatial capture-recapture data

USGS Publications Warehouse

Dorazio, Robert M.

2013-01-01

In capture-recapture and mark-resight surveys, movements of individuals both within and between sampling periods can alter the susceptibility of individuals to detection over the region of sampling. In these circumstances spatially explicit capture-recapture (SECR) models, which incorporate the observed locations of individuals, allow population density and abundance to be estimated while accounting for differences in detectability of individuals. In this paper I propose two Bayesian SECR models, one for the analysis of recaptures observed in trapping arrays and another for the analysis of recaptures observed in area searches. In formulating these models I used distinct submodels to specify the distribution of individual home-range centers and the observable recaptures associated with these individuals. This separation of ecological and observational processes allowed me to derive a formal connection between Bayes and empirical Bayes estimators of population abundance that has not been established previously. I showed that this connection applies to every Poisson point-process model of SECR data and provides theoretical support for a previously proposed estimator of abundance based on recaptures in trapping arrays. To illustrate results of both classical and Bayesian methods of analysis, I compared Bayes and empirical Bayes esimates of abundance and density using recaptures from simulated and real populations of animals. Real populations included two iconic datasets: recaptures of tigers detected in camera-trap surveys and recaptures of lizards detected in area-search surveys. In the datasets I analyzed, classical and Bayesian methods provided similar – and often identical – inferences, which is not surprising given the sample sizes and the noninformative priors used in the analyses.

Bayesian model selection validates a biokinetic model for zirconium processing in humans

PubMed Central

2012-01-01

Background In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection. Results We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler. Conclusions In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology. PMID:22863152

Spatial Guilds in the Serengeti Food Web Revealed by a Bayesian Group Model

PubMed Central

Baskerville, Edward B.; Dobson, Andy P.; Bedford, Trevor; Allesina, Stefano; Anderson, T. Michael; Pascual, Mercedes

2011-01-01

Food webs, networks of feeding relationships in an ecosystem, provide fundamental insights into mechanisms that determine ecosystem stability and persistence. A standard approach in food-web analysis, and network analysis in general, has been to identify compartments, or modules, defined by many links within compartments and few links between them. This approach can identify large habitat boundaries in the network but may fail to identify other important structures. Empirical analyses of food webs have been further limited by low-resolution data for primary producers. In this paper, we present a Bayesian computational method for identifying group structure using a flexible definition that can describe both functional trophic roles and standard compartments. We apply this method to a newly compiled plant-mammal food web from the Serengeti ecosystem that includes high taxonomic resolution at the plant level, allowing a simultaneous examination of the signature of both habitat and trophic roles in network structure. We find that groups at the plant level reflect habitat structure, coupled at higher trophic levels by groups of herbivores, which are in turn coupled by carnivore groups. Thus the group structure of the Serengeti web represents a mixture of trophic guild structure and spatial pattern, in contrast to the standard compartments typically identified. The network topology supports recent ideas on spatial coupling and energy channels in ecosystems that have been proposed as important for persistence. Furthermore, our Bayesian approach provides a powerful, flexible framework for the study of network structure, and we believe it will prove instrumental in a variety of biological contexts. PMID:22219719

Bayes and empirical Bayes estimators of abundance and density from spatial capture-recapture data.

PubMed

Dorazio, Robert M

2013-01-01

In capture-recapture and mark-resight surveys, movements of individuals both within and between sampling periods can alter the susceptibility of individuals to detection over the region of sampling. In these circumstances spatially explicit capture-recapture (SECR) models, which incorporate the observed locations of individuals, allow population density and abundance to be estimated while accounting for differences in detectability of individuals. In this paper I propose two Bayesian SECR models, one for the analysis of recaptures observed in trapping arrays and another for the analysis of recaptures observed in area searches. In formulating these models I used distinct submodels to specify the distribution of individual home-range centers and the observable recaptures associated with these individuals. This separation of ecological and observational processes allowed me to derive a formal connection between Bayes and empirical Bayes estimators of population abundance that has not been established previously. I showed that this connection applies to every Poisson point-process model of SECR data and provides theoretical support for a previously proposed estimator of abundance based on recaptures in trapping arrays. To illustrate results of both classical and Bayesian methods of analysis, I compared Bayes and empirical Bayes esimates of abundance and density using recaptures from simulated and real populations of animals. Real populations included two iconic datasets: recaptures of tigers detected in camera-trap surveys and recaptures of lizards detected in area-search surveys. In the datasets I analyzed, classical and Bayesian methods provided similar - and often identical - inferences, which is not surprising given the sample sizes and the noninformative priors used in the analyses.

Faculty Development for Fostering Clinical Reasoning Skills in Early Medical Students Using a Modified Bayesian Approach.

PubMed

Addy, Tracie Marcella; Hafler, Janet; Galerneau, France

2016-01-01

Clinical reasoning is a necessary skill for medical students to acquire in the course of their education, and there is evidence that they can start this process at the undergraduate level. However, physician educators who are experts in their given fields may have difficulty conveying their complex thought processes to students. Providing faculty development that equips educators with tools to teach clinical reasoning may support skill development in early medical students. We provided faculty development on a modified Bayesian method of teaching clinical reasoning to clinician educators who facilitated small-group, case-based workshops with 2nd-year medical students. We interviewed them before and after the module regarding their perceptions on teaching clinical reasoning. We solicited feedback from the students about the effectiveness of the method in developing their clinical reasoning skills. We carried out this project during an institutional curriculum rebuild where clinical reasoning was a defined goal. At the time of the intervention, there was also increased involvement of the Teaching and Learning Center in elevating the status of teaching and learning. There was high overall satisfaction with the faculty development program. Both the faculty and the students described the modified Bayesian approach as effective in fostering the development of clinical reasoning skills. Through this work, we learned how to form a beneficial partnership between a clinician educator and Teaching and Learning Center to promote faculty development on a clinical reasoning teaching method for early medical students. We uncovered challenges faced by both faculty and early learners in this study. We observed that our faculty chose to utilize the method of teaching clinical reasoning in a variety of manners in the classroom. Despite obstacles and differing approaches utilized, we believe that this model can be emulated at other institutions to foster the development of clinical reasoning skills in preclerkship students.

A BAYESIAN METHOD OF ESTIMATING KINETIC PARAMETERS FOR THE INACTIVATION OF CRYPTOSPORIDIUM PARVUM OOCYSTS WITH CHLORINE DIOXIDE AND OZONE

EPA Science Inventory

The main objective of this paper is to use Bayesian methods to estimate the kinetic parameters for the inactivation kinetics of Cryptosporidium parvum oocysts with chlorine dioxide or ozone which are characterized by the delayed Chick-Watson model, i.e., a lag phase or shoulder f...

A General and Flexible Approach to Estimating the Social Relations Model Using Bayesian Methods

ERIC Educational Resources Information Center

Ludtke, Oliver; Robitzsch, Alexander; Kenny, David A.; Trautwein, Ulrich

2013-01-01

The social relations model (SRM) is a conceptual, methodological, and analytical approach that is widely used to examine dyadic behaviors and interpersonal perception within groups. This article introduces a general and flexible approach to estimating the parameters of the SRM that is based on Bayesian methods using Markov chain Monte Carlo…

Rejoinder to MacCallum, Edwards, and Cai (2012) and Rindskopf (2012): Mastering a New Method

ERIC Educational Resources Information Center

Muthen, Bengt; Asparouhov, Tihomir

2012-01-01

This rejoinder discusses the general comments on how to use Bayesian structural equation modeling (BSEM) wisely and how to get more people better trained in using Bayesian methods. Responses to specific comments cover how to handle sign switching, nonconvergence and nonidentification, and prior choices in latent variable models. Two new…

Bayesian learning

NASA Technical Reports Server (NTRS)

Denning, Peter J.

1989-01-01

In 1983 and 1984, the Infrared Astronomical Satellite (IRAS) detected 5,425 stellar objects and measured their infrared spectra. In 1987 a program called AUTOCLASS used Bayesian inference methods to discover the classes present in these data and determine the most probable class of each object, revealing unknown phenomena in astronomy. AUTOCLASS has rekindled the old debate on the suitability of Bayesian methods, which are computationally intensive, interpret probabilities as plausibility measures rather than frequencies, and appear to depend on a subjective assessment of the probability of a hypothesis before the data were collected. Modern statistical methods have, however, recently been shown to also depend on subjective elements. These debates bring into question the whole tradition of scientific objectivity and offer scientists a new way to take responsibility for their findings and conclusions.

A default Bayesian hypothesis test for mediation.

PubMed

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

2015-03-01

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

A functional-dependencies-based Bayesian networks learning method and its application in a mobile commerce system.

PubMed

Liao, Stephen Shaoyi; Wang, Huai Qing; Li, Qiu Dan; Liu, Wei Yi

2006-06-01

This paper presents a new method for learning Bayesian networks from functional dependencies (FD) and third normal form (3NF) tables in relational databases. The method sets up a linkage between the theory of relational databases and probabilistic reasoning models, which is interesting and useful especially when data are incomplete and inaccurate. The effectiveness and practicability of the proposed method is demonstrated by its implementation in a mobile commerce system.

Comparing methods of measuring geographic patterns in temporal trends: an application to county-level heart disease mortality in the United States, 1973 to 2010.

PubMed

Vaughan, Adam S; Kramer, Michael R; Waller, Lance A; Schieb, Linda J; Greer, Sophia; Casper, Michele

2015-05-01

To demonstrate the implications of choosing analytical methods for quantifying spatiotemporal trends, we compare the assumptions, implementation, and outcomes of popular methods using county-level heart disease mortality in the United States between 1973 and 2010. We applied four regression-based approaches (joinpoint regression, both aspatial and spatial generalized linear mixed models, and Bayesian space-time model) and compared resulting inferences for geographic patterns of local estimates of annual percent change and associated uncertainty. The average local percent change in heart disease mortality from each method was -4.5%, with the Bayesian model having the smallest range of values. The associated uncertainty in percent change differed markedly across the methods, with the Bayesian space-time model producing the narrowest range of variance (0.0-0.8). The geographic pattern of percent change was consistent across methods with smaller declines in the South Central United States and larger declines in the Northeast and Midwest. However, the geographic patterns of uncertainty differed markedly between methods. The similarity of results, including geographic patterns, for magnitude of percent change across these methods validates the underlying spatial pattern of declines in heart disease mortality. However, marked differences in degree of uncertainty indicate that Bayesian modeling offers substantially more precise estimates. Copyright © 2015 Elsevier Inc. All rights reserved.

Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics

PubMed Central

Chen, Wenan; Larrabee, Beth R.; Ovsyannikova, Inna G.; Kennedy, Richard B.; Haralambieva, Iana H.; Poland, Gregory A.; Schaid, Daniel J.

2015-01-01

Two recently developed fine-mapping methods, CAVIAR and PAINTOR, demonstrate better performance over other fine-mapping methods. They also have the advantage of using only the marginal test statistics and the correlation among SNPs. Both methods leverage the fact that the marginal test statistics asymptotically follow a multivariate normal distribution and are likelihood based. However, their relationship with Bayesian fine mapping, such as BIMBAM, is not clear. In this study, we first show that CAVIAR and BIMBAM are actually approximately equivalent to each other. This leads to a fine-mapping method using marginal test statistics in the Bayesian framework, which we call CAVIAR Bayes factor (CAVIARBF). Another advantage of the Bayesian framework is that it can answer both association and fine-mapping questions. We also used simulations to compare CAVIARBF with other methods under different numbers of causal variants. The results showed that both CAVIARBF and BIMBAM have better performance than PAINTOR and other methods. Compared to BIMBAM, CAVIARBF has the advantage of using only marginal test statistics and takes about one-quarter to one-fifth of the running time. We applied different methods on two independent cohorts of the same phenotype. Results showed that CAVIARBF, BIMBAM, and PAINTOR selected the same top 3 SNPs; however, CAVIARBF and BIMBAM had better consistency in selecting the top 10 ranked SNPs between the two cohorts. Software is available at https://bitbucket.org/Wenan/caviarbf. PMID:25948564

[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.

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 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

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.

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

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.

Monte Carlo Bayesian Inference on a Statistical Model of Sub-gridcolumn Moisture Variability Using High-resolution Cloud Observations . Part II; Sensitivity Tests and Results

NASA Technical Reports Server (NTRS)

da Silva, Arlindo M.; Norris, Peter M.

2013-01-01

Part I presented a Monte Carlo Bayesian method for constraining a complex statistical model of GCM sub-gridcolumn moisture variability using high-resolution MODIS cloud data, thereby permitting large-scale model parameter estimation and cloud data assimilation. This part performs some basic testing of this new approach, verifying that it does indeed significantly reduce mean and standard deviation biases with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud top pressure, and that it also improves the simulated rotational-Ramman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the OMI instrument. Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows finite jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast where the background state has a clear swath. This paper also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in the cloud observables on cloud vertical structure, beyond cloud top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification due to Riishojgaard (1998) provides some help in this respect, by better honoring inversion structures in the background state.

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

NASA Astrophysics Data System (ADS)

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

2013-08-01

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

Assessment of phylogenetic sensitivity for reconstructing HIV-1 epidemiological relationships.

PubMed

Beloukas, Apostolos; Magiorkinis, Emmanouil; Magiorkinis, Gkikas; Zavitsanou, Asimina; Karamitros, Timokratis; Hatzakis, Angelos; Paraskevis, Dimitrios

2012-06-01

Phylogenetic analysis has been extensively used as a tool for the reconstruction of epidemiological relations for research or for forensic purposes. It was our objective to assess the sensitivity of different phylogenetic methods and various phylogenetic programs to reconstruct epidemiological links among HIV-1 infected patients that is the probability to reveal a true transmission relationship. Multiple datasets (90) were prepared consisting of HIV-1 sequences in protease (PR) and partial reverse transcriptase (RT) sampled from patients with documented epidemiological relationship (target population), and from unrelated individuals (control population) belonging to the same HIV-1 subtype as the target population. Each dataset varied regarding the number, the geographic origin and the transmission risk groups of the sequences among the control population. Phylogenetic trees were inferred by neighbor-joining (NJ), maximum likelihood heuristics (hML) and Bayesian methods. All clusters of sequences belonging to the target population were correctly reconstructed by NJ and Bayesian methods receiving high bootstrap and posterior probability (PP) support, respectively. On the other hand, TreePuzzle failed to reconstruct or provide significant support for several clusters; high puzzling step support was associated with the inclusion of control sequences from the same geographic area as the target population. In contrary, all clusters were correctly reconstructed by hML as implemented in PhyML 3.0 receiving high bootstrap support. We report that under the conditions of our study, hML using PhyML, NJ and Bayesian methods were the most sensitive for the reconstruction of epidemiological links mostly from sexually infected individuals. Copyright © 2012 Elsevier B.V. All rights reserved.

A computer program for uncertainty analysis integrating regression and Bayesian methods

USGS Publications Warehouse

Lu, Dan; Ye, Ming; Hill, Mary C.; Poeter, Eileen P.; Curtis, Gary

2014-01-01

This work develops a new functionality in UCODE_2014 to evaluate Bayesian credible intervals using the Markov Chain Monte Carlo (MCMC) method. The MCMC capability in UCODE_2014 is based on the FORTRAN version of the differential evolution adaptive Metropolis (DREAM) algorithm of Vrugt et al. (2009), which estimates the posterior probability density function of model parameters in high-dimensional and multimodal sampling problems. The UCODE MCMC capability provides eleven prior probability distributions and three ways to initialize the sampling process. It evaluates parametric and predictive uncertainties and it has parallel computing capability based on multiple chains to accelerate the sampling process. This paper tests and demonstrates the MCMC capability using a 10-dimensional multimodal mathematical function, a 100-dimensional Gaussian function, and a groundwater reactive transport model. The use of the MCMC capability is made straightforward and flexible by adopting the JUPITER API protocol. With the new MCMC capability, UCODE_2014 can be used to calculate three types of uncertainty intervals, which all can account for prior information: (1) linear confidence intervals which require linearity and Gaussian error assumptions and typically 10s–100s of highly parallelizable model runs after optimization, (2) nonlinear confidence intervals which require a smooth objective function surface and Gaussian observation error assumptions and typically 100s–1,000s of partially parallelizable model runs after optimization, and (3) MCMC Bayesian credible intervals which require few assumptions and commonly 10,000s–100,000s or more partially parallelizable model runs. Ready access allows users to select methods best suited to their work, and to compare methods in many circumstances.

Functional Multi-Locus QTL Mapping of Temporal Trends in Scots Pine Wood Traits

PubMed Central

Li, Zitong; Hallingbäck, Henrik R.; Abrahamsson, Sara; Fries, Anders; Gull, Bengt Andersson; Sillanpää, Mikko J.; García-Gil, M. Rosario

2014-01-01

Quantitative trait loci (QTL) mapping of wood properties in conifer species has focused on single time point measurements or on trait means based on heterogeneous wood samples (e.g., increment cores), thus ignoring systematic within-tree trends. In this study, functional QTL mapping was performed for a set of important wood properties in increment cores from a 17-yr-old Scots pine (Pinus sylvestris L.) full-sib family with the aim of detecting wood trait QTL for general intercepts (means) and for linear slopes by increasing cambial age. Two multi-locus functional QTL analysis approaches were proposed and their performances were compared on trait datasets comprising 2 to 9 time points, 91 to 455 individual tree measurements and genotype datasets of amplified length polymorphisms (AFLP), and single nucleotide polymorphism (SNP) markers. The first method was a multilevel LASSO analysis whereby trend parameter estimation and QTL mapping were conducted consecutively; the second method was our Bayesian linear mixed model whereby trends and underlying genetic effects were estimated simultaneously. We also compared several different hypothesis testing methods under either the LASSO or the Bayesian framework to perform QTL inference. In total, five and four significant QTL were observed for the intercepts and slopes, respectively, across wood traits such as earlywood percentage, wood density, radial fiberwidth, and spiral grain angle. Four of these QTL were represented by candidate gene SNPs, thus providing promising targets for future research in QTL mapping and molecular function. Bayesian and LASSO methods both detected similar sets of QTL given datasets that comprised large numbers of individuals. PMID:25305041

Functional multi-locus QTL mapping of temporal trends in Scots pine wood traits.

PubMed

Li, Zitong; Hallingbäck, Henrik R; Abrahamsson, Sara; Fries, Anders; Gull, Bengt Andersson; Sillanpää, Mikko J; García-Gil, M Rosario

2014-10-09

Quantitative trait loci (QTL) mapping of wood properties in conifer species has focused on single time point measurements or on trait means based on heterogeneous wood samples (e.g., increment cores), thus ignoring systematic within-tree trends. In this study, functional QTL mapping was performed for a set of important wood properties in increment cores from a 17-yr-old Scots pine (Pinus sylvestris L.) full-sib family with the aim of detecting wood trait QTL for general intercepts (means) and for linear slopes by increasing cambial age. Two multi-locus functional QTL analysis approaches were proposed and their performances were compared on trait datasets comprising 2 to 9 time points, 91 to 455 individual tree measurements and genotype datasets of amplified length polymorphisms (AFLP), and single nucleotide polymorphism (SNP) markers. The first method was a multilevel LASSO analysis whereby trend parameter estimation and QTL mapping were conducted consecutively; the second method was our Bayesian linear mixed model whereby trends and underlying genetic effects were estimated simultaneously. We also compared several different hypothesis testing methods under either the LASSO or the Bayesian framework to perform QTL inference. In total, five and four significant QTL were observed for the intercepts and slopes, respectively, across wood traits such as earlywood percentage, wood density, radial fiberwidth, and spiral grain angle. Four of these QTL were represented by candidate gene SNPs, thus providing promising targets for future research in QTL mapping and molecular function. Bayesian and LASSO methods both detected similar sets of QTL given datasets that comprised large numbers of individuals. Copyright © 2014 Li et al.

Internal Medicine residents use heuristics to estimate disease probability

PubMed Central

Phang, Sen Han; Ravani, Pietro; Schaefer, Jeffrey; Wright, Bruce; McLaughlin, Kevin

2015-01-01

Background Training in Bayesian reasoning may have limited impact on accuracy of probability estimates. In this study, our goal was to explore whether residents previously exposed to Bayesian reasoning use heuristics rather than Bayesian reasoning to estimate disease probabilities. We predicted that if residents use heuristics then post-test probability estimates would be increased by non-discriminating clinical features or a high anchor for a target condition. Method We randomized 55 Internal Medicine residents to different versions of four clinical vignettes and asked them to estimate probabilities of target conditions. We manipulated the clinical data for each vignette to be consistent with either 1) using a representative heuristic, by adding non-discriminating prototypical clinical features of the target condition, or 2) using anchoring with adjustment heuristic, by providing a high or low anchor for the target condition. Results When presented with additional non-discriminating data the odds of diagnosing the target condition were increased (odds ratio (OR) 2.83, 95% confidence interval [1.30, 6.15], p = 0.009). Similarly, the odds of diagnosing the target condition were increased when a high anchor preceded the vignette (OR 2.04, [1.09, 3.81], p = 0.025). Conclusions Our findings suggest that despite previous exposure to the use of Bayesian reasoning, residents use heuristics, such as the representative heuristic and anchoring with adjustment, to estimate probabilities. Potential reasons for attribute substitution include the relative cognitive ease of heuristics vs. Bayesian reasoning or perhaps residents in their clinical practice use gist traces rather than precise probability estimates when diagnosing. PMID:27004080

Improving Bayesian credibility intervals for classifier error rates using maximum entropy empirical priors.

PubMed

Gustafsson, Mats G; Wallman, Mikael; Wickenberg Bolin, Ulrika; Göransson, Hanna; Fryknäs, M; Andersson, Claes R; Isaksson, Anders

2010-06-01

Successful use of classifiers that learn to make decisions from a set of patient examples require robust methods for performance estimation. Recently many promising approaches for determination of an upper bound for the error rate of a single classifier have been reported but the Bayesian credibility interval (CI) obtained from a conventional holdout test still delivers one of the tightest bounds. The conventional Bayesian CI becomes unacceptably large in real world applications where the test set sizes are less than a few hundred. The source of this problem is that fact that the CI is determined exclusively by the result on the test examples. In other words, there is no information at all provided by the uniform prior density distribution employed which reflects complete lack of prior knowledge about the unknown error rate. Therefore, the aim of the study reported here was to study a maximum entropy (ME) based approach to improved prior knowledge and Bayesian CIs, demonstrating its relevance for biomedical research and clinical practice. It is demonstrated how a refined non-uniform prior density distribution can be obtained by means of the ME principle using empirical results from a few designs and tests using non-overlapping sets of examples. Experimental results show that ME based priors improve the CIs when employed to four quite different simulated and two real world data sets. An empirically derived ME prior seems promising for improving the Bayesian CI for the unknown error rate of a designed classifier. Copyright 2010 Elsevier B.V. All rights reserved.

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

PubMed

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

2008-05-01

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

Accuracy of dengue clinical diagnosis with and without NS1 antigen rapid test: Comparison between human and Bayesian network model decision.

PubMed

Sa-Ngamuang, Chaitawat; Haddawy, Peter; Luvira, Viravarn; Piyaphanee, Watcharapong; Iamsirithaworn, Sopon; Lawpoolsri, Saranath

2018-06-18

Differentiating dengue patients from other acute febrile illness patients is a great challenge among physicians. Several dengue diagnosis methods are recommended by WHO. The application of specific laboratory tests is still limited due to high cost, lack of equipment, and uncertain validity. Therefore, clinical diagnosis remains a common practice especially in resource limited settings. Bayesian networks have been shown to be a useful tool for diagnostic decision support. This study aimed to construct Bayesian network models using basic demographic, clinical, and laboratory profiles of acute febrile illness patients to diagnose dengue. Data of 397 acute undifferentiated febrile illness patients who visited the fever clinic of the Bangkok Hospital for Tropical Diseases, Thailand, were used for model construction and validation. The two best final models were selected: one with and one without NS1 rapid test result. The diagnostic accuracy of the models was compared with that of physicians on the same set of patients. The Bayesian network models provided good diagnostic accuracy of dengue infection, with ROC AUC of 0.80 and 0.75 for models with and without NS1 rapid test result, respectively. The models had approximately 80% specificity and 70% sensitivity, similar to the diagnostic accuracy of the hospital's fellows in infectious disease. Including information on NS1 rapid test improved the specificity, but reduced the sensitivity, both in model and physician diagnoses. The Bayesian network model developed in this study could be useful to assist physicians in diagnosing dengue, particularly in regions where experienced physicians and laboratory confirmation tests are limited.

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/.

Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

Histogram equalization with Bayesian estimation for noise robust speech recognition.

PubMed

Suh, Youngjoo; Kim, Hoirin

2018-02-01

The histogram equalization approach is an efficient feature normalization technique for noise robust automatic speech recognition. However, it suffers from performance degradation when some fundamental conditions are not satisfied in the test environment. To remedy these limitations of the original histogram equalization methods, class-based histogram equalization approach has been proposed. Although this approach showed substantial performance improvement under noise environments, it still suffers from performance degradation due to the overfitting problem when test data are insufficient. To address this issue, the proposed histogram equalization technique employs the Bayesian estimation method in the test cumulative distribution function estimation. It was reported in a previous study conducted on the Aurora-4 task that the proposed approach provided substantial performance gains in speech recognition systems based on the acoustic modeling of the Gaussian mixture model-hidden Markov model. In this work, the proposed approach was examined in speech recognition systems with deep neural network-hidden Markov model (DNN-HMM), the current mainstream speech recognition approach where it also showed meaningful performance improvement over the conventional maximum likelihood estimation-based method. The fusion of the proposed features with the mel-frequency cepstral coefficients provided additional performance gains in DNN-HMM systems, which otherwise suffer from performance degradation in the clean test condition.

Dynamical Bayesian inference of time-evolving interactions: from a pair of coupled oscillators to networks of oscillators.

PubMed

Duggento, Andrea; Stankovski, Tomislav; McClintock, Peter V E; Stefanovska, Aneta

2012-12-01

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. [Phys. Rev. Lett. 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.

An Automatic Multidocument Text Summarization Approach Based on Naïve Bayesian Classifier Using Timestamp Strategy

PubMed Central

Ramanujam, Nedunchelian; Kaliappan, Manivannan

2016-01-01

Nowadays, automatic multidocument text summarization systems can successfully retrieve the summary sentences from the input documents. But, it has many limitations such as inaccurate extraction to essential sentences, low coverage, poor coherence among the sentences, and redundancy. This paper introduces a new concept of timestamp approach with Naïve Bayesian Classification approach for multidocument text summarization. The timestamp provides the summary an ordered look, which achieves the coherent looking summary. It extracts the more relevant information from the multiple documents. Here, scoring strategy is also used to calculate the score for the words to obtain the word frequency. The higher linguistic quality is estimated in terms of readability and comprehensibility. In order to show the efficiency of the proposed method, this paper presents the comparison between the proposed methods with the existing MEAD algorithm. The timestamp procedure is also applied on the MEAD algorithm and the results are examined with the proposed method. The results show that the proposed method results in lesser time than the existing MEAD algorithm to execute the summarization process. Moreover, the proposed method results in better precision, recall, and F-score than the existing clustering with lexical chaining approach. PMID:27034971

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

Efficient Posterior Probability Mapping Using Savage-Dickey Ratios

PubMed Central

Penny, William D.; Ridgway, Gerard R.

2013-01-01

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

Bayesian inference for disease prevalence using negative binomial group testing

PubMed Central

Pritchard, Nicholas A.; Tebbs, Joshua M.

2011-01-01

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

Defining Probability in Sex Offender Risk Assessment.

PubMed

Elwood, Richard W

2016-12-01

There is ongoing debate and confusion over using actuarial scales to predict individuals' risk of sexual recidivism. Much of the debate comes from not distinguishing Frequentist from Bayesian definitions of probability. Much of the confusion comes from applying Frequentist probability to individuals' risk. By definition, only Bayesian probability can be applied to the single case. The Bayesian concept of probability resolves most of the confusion and much of the debate in sex offender risk assessment. Although Bayesian probability is well accepted in risk assessment generally, it has not been widely used to assess the risk of sex offenders. I review the two concepts of probability and show how the Bayesian view alone provides a coherent scheme to conceptualize individuals' risk of sexual recidivism.

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.

Bayesian least squares deconvolution

NASA Astrophysics Data System (ADS)

Asensio Ramos, A.; Petit, P.

2015-11-01

Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.

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.

Kernel and divergence techniques in high energy physics separations

NASA Astrophysics Data System (ADS)

Bouř, Petr; Kůs, Václav; Franc, Jiří

2017-10-01

Binary decision trees under the Bayesian decision technique are used for supervised classification of high-dimensional data. We present a great potential of adaptive kernel density estimation as the nested separation method of the supervised binary divergence decision tree. Also, we provide a proof of alternative computing approach for kernel estimates utilizing Fourier transform. Further, we apply our method to Monte Carlo data set from the particle accelerator Tevatron at DØ experiment in Fermilab and provide final top-antitop signal separation results. We have achieved up to 82 % AUC while using the restricted feature selection entering the signal separation procedure.

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

Practical differences among probabilities, possibilities, and credibilities

NASA Astrophysics Data System (ADS)

Grandin, Jean-Francois; Moulin, Caroline

2002-03-01

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

Predicting individual brain functional connectivity using a Bayesian hierarchical model.

PubMed

Dai, Tian; Guo, Ying

2017-02-15

Network-oriented analysis of functional magnetic resonance imaging (fMRI), especially resting-state fMRI, has revealed important association between abnormal connectivity and brain disorders such as schizophrenia, major depression and Alzheimer's disease. Imaging-based brain connectivity measures have become a useful tool for investigating the pathophysiology, progression and treatment response of psychiatric disorders and neurodegenerative diseases. Recent studies have started to explore the possibility of using functional neuroimaging to help predict disease progression and guide treatment selection for individual patients. These studies provide the impetus to develop statistical methodology that would help provide predictive information on disease progression-related or treatment-related changes in neural connectivity. To this end, we propose a prediction method based on Bayesian hierarchical model that uses individual's baseline fMRI scans, coupled with relevant subject characteristics, to predict the individual's future functional connectivity. A key advantage of the proposed method is that it can improve the accuracy of individualized prediction of connectivity by combining information from both group-level connectivity patterns that are common to subjects with similar characteristics as well as individual-level connectivity features that are particular to the specific subject. Furthermore, our method also offers statistical inference tools such as predictive intervals that help quantify the uncertainty or variability of the predicted outcomes. The proposed prediction method could be a useful approach to predict the changes in individual patient's brain connectivity with the progression of a disease. It can also be used to predict a patient's post-treatment brain connectivity after a specified treatment regimen. Another utility of the proposed method is that it can be applied to test-retest imaging data to develop a more reliable estimator for individual functional connectivity. We show there exists a nice connection between our proposed estimator and a recently developed shrinkage estimator of connectivity measures in the neuroimaging community. We develop an expectation-maximization (EM) algorithm for estimation of the proposed Bayesian hierarchical model. Simulations studies are performed to evaluate the accuracy of our proposed prediction methods. We illustrate the application of the methods with two data examples: the longitudinal resting-state fMRI from ADNI2 study and the test-retest fMRI data from Kirby21 study. In both the simulation studies and the fMRI data applications, we demonstrate that the proposed methods provide more accurate prediction and more reliable estimation of individual functional connectivity as compared with alternative methods. Copyright © 2017 Elsevier Inc. All rights reserved.

Bayesian methods for outliers detection in GNSS time series

NASA Astrophysics Data System (ADS)

Qianqian, Zhang; Qingming, Gui

2013-07-01

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

A simulation study on Bayesian Ridge regression models for several collinearity levels

NASA Astrophysics Data System (ADS)

Efendi, Achmad; Effrihan

2017-12-01

When analyzing data with multiple regression model if there are collinearities, then one or several predictor variables are usually omitted from the model. However, there sometimes some reasons, for instance medical or economic reasons, the predictors are all important and should be included in the model. Ridge regression model is not uncommon in some researches to use to cope with collinearity. Through this modeling, weights for predictor variables are used for estimating parameters. The next estimation process could follow the concept of likelihood. Furthermore, for the estimation nowadays the Bayesian version could be an alternative. This estimation method does not match likelihood one in terms of popularity due to some difficulties; computation and so forth. Nevertheless, with the growing improvement of computational methodology recently, this caveat should not at the moment become a problem. This paper discusses about simulation process for evaluating the characteristic of Bayesian Ridge regression parameter estimates. There are several simulation settings based on variety of collinearity levels and sample sizes. The results show that Bayesian method gives better performance for relatively small sample sizes, and for other settings the method does perform relatively similar to the likelihood method.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

A Bayesian Approach to the Overlap Analysis of Epidemiologically Linked Traits.

PubMed

Asimit, Jennifer L; Panoutsopoulou, Kalliope; Wheeler, Eleanor; Berndt, Sonja I; Cordell, Heather J; Morris, Andrew P; Zeggini, Eleftheria; Barroso, Inês

2015-12-01

Diseases often cooccur in individuals more often than expected by chance, and may be explained by shared underlying genetic etiology. A common approach to genetic overlap analyses is to use summary genome-wide association study data to identify single-nucleotide polymorphisms (SNPs) that are associated with multiple traits at a selected P-value threshold. However, P-values do not account for differences in power, whereas Bayes' factors (BFs) do, and may be approximated using summary statistics. We use simulation studies to compare the power of frequentist and Bayesian approaches with overlap analyses, and to decide on appropriate thresholds for comparison between the two methods. It is empirically illustrated that BFs have the advantage over P-values of a decreasing type I error rate as study size increases for single-disease associations. Consequently, the overlap analysis of traits from different-sized studies encounters issues in fair P-value threshold selection, whereas BFs are adjusted automatically. Extensive simulations show that Bayesian overlap analyses tend to have higher power than those that assess association strength with P-values, particularly in low-power scenarios. Calibration tables between BFs and P-values are provided for a range of sample sizes, as well as an approximation approach for sample sizes that are not in the calibration table. Although P-values are sometimes thought more intuitive, these tables assist in removing the opaqueness of Bayesian thresholds and may also be used in the selection of a BF threshold to meet a certain type I error rate. An application of our methods is used to identify variants associated with both obesity and osteoarthritis. © 2015 The Authors. *Genetic Epidemiology published by Wiley Periodicals, Inc.

Population-level differences in disease transmission: A Bayesian analysis of multiple smallpox epidemics

PubMed Central

Elderd, Bret D.; Dwyer, Greg; Dukic, Vanja

2013-01-01

Estimates of a disease’s basic reproductive rate R0 play a central role in understanding outbreaks and planning intervention strategies. In many calculations of R0, a simplifying assumption is that different host populations have effectively identical transmission rates. This assumption can lead to an underestimate of the overall uncertainty associated with R0, which, due to the non-linearity of epidemic processes, may result in a mis-estimate of epidemic intensity and miscalculated expenditures associated with public-health interventions. In this paper, we utilize a Bayesian method for quantifying the overall uncertainty arising from differences in population-specific basic reproductive rates. Using this method, we fit spatial and non-spatial susceptible-exposed-infected-recovered (SEIR) models to a series of 13 smallpox outbreaks. Five outbreaks occurred in populations that had been previously exposed to smallpox, while the remaining eight occurred in Native-American populations that were naïve to the disease at the time. The Native-American outbreaks were close in a spatial and temporal sense. Using Bayesian Information Criterion (BIC), we show that the best model includes population-specific R0 values. These differences in R0 values may, in part, be due to differences in genetic background, social structure, or food and water availability. As a result of these inter-population differences, the overall uncertainty associated with the “population average” value of smallpox R0 is larger, a finding that can have important consequences for controlling epidemics. In general, Bayesian hierarchical models are able to properly account for the uncertainty associated with multiple epidemics, provide a clearer understanding of variability in epidemic dynamics, and yield a better assessment of the range of potential risks and consequences that decision makers face. PMID:24021521

Bayesian Inference for Signal-Based Seismic Monitoring

NASA Astrophysics Data System (ADS)

Moore, D.

2015-12-01

Traditional seismic monitoring systems rely on discrete detections produced by station processing software, discarding significant information present in the original recorded signal. SIG-VISA (Signal-based Vertically Integrated Seismic Analysis) is a system for global seismic monitoring through Bayesian inference on seismic signals. By modeling signals directly, our forward model is able to incorporate a rich representation of the physics underlying the signal generation process, including source mechanisms, wave propagation, and station response. This allows inference in the model to recover the qualitative behavior of recent geophysical methods including waveform matching and double-differencing, all as part of a unified Bayesian monitoring system that simultaneously detects and locates events from a global network of stations. We demonstrate recent progress in scaling up SIG-VISA to efficiently process the data stream of global signals recorded by the International Monitoring System (IMS), including comparisons against existing processing methods that show increased sensitivity from our signal-based model and in particular the ability to locate events (including aftershock sequences that can tax analyst processing) precisely from waveform correlation effects. We also provide a Bayesian analysis of an alleged low-magnitude event near the DPRK test site in May 2010 [1] [2], investigating whether such an event could plausibly be detected through automated processing in a signal-based monitoring system. [1] Zhang, Miao and Wen, Lianxing. "Seismological Evidence for a Low-Yield Nuclear Test on 12 May 2010 in North Korea". Seismological Research Letters, January/February 2015. [2] Richards, Paul. "A Seismic Event in North Korea on 12 May 2010". CTBTO SnT 2015 oral presentation, video at https://video-archive.ctbto.org/index.php/kmc/preview/partner_id/103/uiconf_id/4421629/entry_id/0_ymmtpps0/delivery/http

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

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

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

2012-06-01

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

Sparse Event Modeling with Hierarchical Bayesian Kernel Methods

DTIC Science & Technology

2016-01-05

SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model , is able to model the rate of occurrence of...which adds specificity to the model and can make nonlinear data more manageable. Early results show that the 1. REPORT DATE (DD-MM-YYYY) 4. TITLE

A Fault Diagnosis Methodology for Gear Pump Based on EEMD and Bayesian Network

PubMed Central

Liu, Zengkai; Liu, Yonghong; Shan, Hongkai; Cai, Baoping; Huang, Qing

2015-01-01

This paper proposes a fault diagnosis methodology for a gear pump based on the ensemble empirical mode decomposition (EEMD) method and the Bayesian network. Essentially, the presented scheme is a multi-source information fusion based methodology. Compared with the conventional fault diagnosis with only EEMD, the proposed method is able to take advantage of all useful information besides sensor signals. The presented diagnostic Bayesian network consists of a fault layer, a fault feature layer and a multi-source information layer. Vibration signals from sensor measurement are decomposed by the EEMD method and the energy of intrinsic mode functions (IMFs) are calculated as fault features. These features are added into the fault feature layer in the Bayesian network. The other sources of useful information are added to the information layer. The generalized three-layer Bayesian network can be developed by fully incorporating faults and fault symptoms as well as other useful information such as naked eye inspection and maintenance records. Therefore, diagnostic accuracy and capacity can be improved. The proposed methodology is applied to the fault diagnosis of a gear pump and the structure and parameters of the Bayesian network is established. Compared with artificial neural network and support vector machine classification algorithms, the proposed model has the best diagnostic performance when sensor data is used only. A case study has demonstrated that some information from human observation or system repair records is very helpful to the fault diagnosis. It is effective and efficient in diagnosing faults based on uncertain, incomplete information. PMID:25938760

A Fault Diagnosis Methodology for Gear Pump Based on EEMD and Bayesian Network.

PubMed

Liu, Zengkai; Liu, Yonghong; Shan, Hongkai; Cai, Baoping; Huang, Qing

2015-01-01

This paper proposes a fault diagnosis methodology for a gear pump based on the ensemble empirical mode decomposition (EEMD) method and the Bayesian network. Essentially, the presented scheme is a multi-source information fusion based methodology. Compared with the conventional fault diagnosis with only EEMD, the proposed method is able to take advantage of all useful information besides sensor signals. The presented diagnostic Bayesian network consists of a fault layer, a fault feature layer and a multi-source information layer. Vibration signals from sensor measurement are decomposed by the EEMD method and the energy of intrinsic mode functions (IMFs) are calculated as fault features. These features are added into the fault feature layer in the Bayesian network. The other sources of useful information are added to the information layer. The generalized three-layer Bayesian network can be developed by fully incorporating faults and fault symptoms as well as other useful information such as naked eye inspection and maintenance records. Therefore, diagnostic accuracy and capacity can be improved. The proposed methodology is applied to the fault diagnosis of a gear pump and the structure and parameters of the Bayesian network is established. Compared with artificial neural network and support vector machine classification algorithms, the proposed model has the best diagnostic performance when sensor data is used only. A case study has demonstrated that some information from human observation or system repair records is very helpful to the fault diagnosis. It is effective and efficient in diagnosing faults based on uncertain, incomplete information.