The image recognition based on neural network and Bayesian decision

NASA Astrophysics Data System (ADS)

Wang, Chugege

2018-04-01

The artificial neural network began in 1940, which is an important part of artificial intelligence. At present, it has become a hot topic in the fields of neuroscience, computer science, brain science, mathematics, and psychology. Thomas Bayes firstly reported the Bayesian theory in 1763. After the development in the twentieth century, it has been widespread in all areas of statistics. In recent years, due to the solution of the problem of high-dimensional integral calculation, Bayesian Statistics has been improved theoretically, which solved many problems that cannot be solved by classical statistics and is also applied to the interdisciplinary fields. In this paper, the related concepts and principles of the artificial neural network are introduced. It also summarizes the basic content and principle of Bayesian Statistics, and combines the artificial neural network technology and Bayesian decision theory and implement them in all aspects of image recognition, such as enhanced face detection method based on neural network and Bayesian decision, as well as the image classification based on the Bayesian decision. It can be seen that the combination of artificial intelligence and statistical algorithms has always been the hot research topic.

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

Structure Learning in Bayesian Sensorimotor Integration

PubMed Central

Genewein, Tim; Hez, Eduard; Razzaghpanah, Zeynab; Braun, Daniel A.

2015-01-01

Previous studies have shown that sensorimotor processing can often be described by Bayesian learning, in particular the integration of prior and feedback information depending on its degree of reliability. Here we test the hypothesis that the integration process itself can be tuned to the statistical structure of the environment. We exposed human participants to a reaching task in a three-dimensional virtual reality environment where we could displace the visual feedback of their hand position in a two dimensional plane. When introducing statistical structure between the two dimensions of the displacement, we found that over the course of several days participants adapted their feedback integration process in order to exploit this structure for performance improvement. In control experiments we found that this adaptation process critically depended on performance feedback and could not be induced by verbal instructions. Our results suggest that structural learning is an important meta-learning component of Bayesian sensorimotor integration. PMID:26305797

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…

Technical Topic 3.2.2.d Bayesian and Non-Parametric Statistics: Integration of Neural Networks with Bayesian Networks for Data Fusion and Predictive Modeling

DTIC Science & Technology

2016-05-31

and included explosives such as TATP, HMTD, RDX, RDX, ammonium nitrate , potassium perchlorate, potassium nitrate , sugar, and TNT. The approach...Distribution Unlimited UU UU UU UU 31-05-2016 15-Apr-2014 14-Jan-2015 Final Report: Technical Topic 3.2.2. d Bayesian and Non- parametric Statistics...of Papers published in non peer-reviewed journals: Final Report: Technical Topic 3.2.2. d Bayesian and Non-parametric Statistics: Integration of Neural

Enhancing pediatric clinical trial feasibility through the use of Bayesian statistics.

PubMed

Huff, Robin A; Maca, Jeff D; Puri, Mala; Seltzer, Earl W

2017-11-01

BackgroundPediatric clinical trials commonly experience recruitment challenges including limited number of patients and investigators, inclusion/exclusion criteria that further reduce the patient pool, and a competitive research landscape created by pediatric regulatory commitments. To overcome these challenges, innovative approaches are needed.MethodsThis article explores the use of Bayesian statistics to improve pediatric trial feasibility, using pediatric Type-2 diabetes as an example. Data for six therapies approved for adults were used to perform simulations to determine the impact on pediatric trial size.ResultsWhen the number of adult patients contributing to the simulation was assumed to be the same as the number of patients to be enrolled in the pediatric trial, the pediatric trial size was reduced by 75-78% when compared with a frequentist statistical approach, but was associated with a 34-45% false-positive rate. In subsequent simulations, greater control was exerted over the false-positive rate by decreasing the contribution of the adult data. A 30-33% reduction in trial size was achieved when false-positives were held to less than 10%.ConclusionReducing the trial size through the use of Bayesian statistics would facilitate completion of pediatric trials, enabling drugs to be labeled appropriately for children.

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.

Bayesian performance metrics of binary sensors in homeland security applications

NASA Astrophysics Data System (ADS)

Jannson, Tomasz P.; Forrester, Thomas C.

2008-04-01

Bayesian performance metrics, based on such parameters, as: prior probability, probability of detection (or, accuracy), false alarm rate, and positive predictive value, characterizes the performance of binary sensors; i.e., sensors that have only binary response: true target/false target. Such binary sensors, very common in Homeland Security, produce an alarm that can be true, or false. They include: X-ray airport inspection, IED inspections, product quality control, cancer medical diagnosis, part of ATR, and many others. In this paper, we analyze direct and inverse conditional probabilities in the context of Bayesian inference and binary sensors, using X-ray luggage inspection statistical results as a guideline.

What Is the Probability You Are a Bayesian?

ERIC Educational Resources Information Center

Wulff, Shaun S.; Robinson, Timothy J.

2014-01-01

Bayesian methodology continues to be widely used in statistical applications. As a result, it is increasingly important to introduce students to Bayesian thinking at early stages in their mathematics and statistics education. While many students in upper level probability courses can recite the differences in the Frequentist and Bayesian…

Bayesian Posterior Odds Ratios: Statistical Tools for Collaborative Evaluations

ERIC Educational Resources Information Center

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

2018-01-01

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

[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.

Characterization of a Saccharomyces cerevisiae fermentation process for production of a therapeutic recombinant protein using a multivariate Bayesian approach.

PubMed

Fu, Zhibiao; Baker, Daniel; Cheng, Aili; Leighton, Julie; Appelbaum, Edward; Aon, Juan

2016-05-01

The principle of quality by design (QbD) has been widely applied to biopharmaceutical manufacturing processes. Process characterization is an essential step to implement the QbD concept to establish the design space and to define the proven acceptable ranges (PAR) for critical process parameters (CPPs). In this study, we present characterization of a Saccharomyces cerevisiae fermentation process using risk assessment analysis, statistical design of experiments (DoE), and the multivariate Bayesian predictive approach. The critical quality attributes (CQAs) and CPPs were identified with a risk assessment. The statistical model for each attribute was established using the results from the DoE study with consideration given to interactions between CPPs. Both the conventional overlapping contour plot and the multivariate Bayesian predictive approaches were used to establish the region of process operating conditions where all attributes met their specifications simultaneously. The quantitative Bayesian predictive approach was chosen to define the PARs for the CPPs, which apply to the manufacturing control strategy. Experience from the 10,000 L manufacturing scale process validation, including 64 continued process verification batches, indicates that the CPPs remain under a state of control and within the established PARs. The end product quality attributes were within their drug substance specifications. The probability generated with the Bayesian approach was also used as a tool to assess CPP deviations. This approach can be extended to develop other production process characterization and quantify a reliable operating region. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:799-812, 2016. © 2016 American Institute of Chemical Engineers.

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.

Teaching Bayesian Statistics to Undergraduate Students through Debates

ERIC Educational Resources Information Center

Stewart, Sepideh; Stewart, Wayne

2014-01-01

This paper describes a lecturer's approach to teaching Bayesian statistics to students who were only exposed to the classical paradigm. The study shows how the lecturer extended himself by making use of ventriloquist dolls to grab hold of students' attention and embed important ideas in revealing the differences between the Bayesian and classical…

A critique of statistical hypothesis testing in clinical research

PubMed Central

Raha, Somik

2011-01-01

Many have documented the difficulty of using the current paradigm of Randomized Controlled Trials (RCTs) to test and validate the effectiveness of alternative medical systems such as Ayurveda. This paper critiques the applicability of RCTs for all clinical knowledge-seeking endeavors, of which Ayurveda research is a part. This is done by examining statistical hypothesis testing, the underlying foundation of RCTs, from a practical and philosophical perspective. In the philosophical critique, the two main worldviews of probability are that of the Bayesian and the frequentist. The frequentist worldview is a special case of the Bayesian worldview requiring the unrealistic assumptions of knowing nothing about the universe and believing that all observations are unrelated to each other. Many have claimed that the first belief is necessary for science, and this claim is debunked by comparing variations in learning with different prior beliefs. Moving beyond the Bayesian and frequentist worldviews, the notion of hypothesis testing itself is challenged on the grounds that a hypothesis is an unclear distinction, and assigning a probability on an unclear distinction is an exercise that does not lead to clarity of action. This critique is of the theory itself and not any particular application of statistical hypothesis testing. A decision-making frame is proposed as a way of both addressing this critique and transcending ideological debates on probability. An example of a Bayesian decision-making approach is shown as an alternative to statistical hypothesis testing, utilizing data from a past clinical trial that studied the effect of Aspirin on heart attacks in a sample population of doctors. As a big reason for the prevalence of RCTs in academia is legislation requiring it, the ethics of legislating the use of statistical methods for clinical research is also examined. PMID:22022152

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

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.

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.

Bayes in biological anthropology.

PubMed

Konigsberg, Lyle W; Frankenberg, Susan R

2013-12-01

In this article, we both contend and illustrate that biological anthropologists, particularly in the Americas, often think like Bayesians but act like frequentists when it comes to analyzing a wide variety of data. In other words, while our research goals and perspectives are rooted in probabilistic thinking and rest on prior knowledge, we often proceed to use statistical hypothesis tests and confidence interval methods unrelated (or tenuously related) to the research questions of interest. We advocate for applying Bayesian analyses to a number of different bioanthropological questions, especially since many of the programming and computational challenges to doing so have been overcome in the past two decades. To facilitate such applications, this article explains Bayesian principles and concepts, and provides concrete examples of Bayesian computer simulations and statistics that address questions relevant to biological anthropology, focusing particularly on bioarchaeology and forensic anthropology. It also simultaneously reviews the use of Bayesian methods and inference within the discipline to date. This article is intended to act as primer to Bayesian methods and inference in biological anthropology, explaining the relationships of various methods to likelihoods or probabilities and to classical statistical models. Our contention is not that traditional frequentist statistics should be rejected outright, but that there are many situations where biological anthropology is better served by taking a Bayesian approach. To this end it is hoped that the examples provided in this article will assist researchers in choosing from among the broad array of statistical methods currently available. Copyright © 2013 Wiley Periodicals, Inc.

Bayesian statistics in radionuclide metrology: measurement of a decaying source

NASA Astrophysics Data System (ADS)

Bochud, François O.; Bailat, Claude J.; Laedermann, Jean-Pascal

2007-08-01

The most intuitive way of defining a probability is perhaps through the frequency at which it appears when a large number of trials are realized in identical conditions. The probability derived from the obtained histogram characterizes the so-called frequentist or conventional statistical approach. In this sense, probability is defined as a physical property of the observed system. By contrast, in Bayesian statistics, a probability is not a physical property or a directly observable quantity, but a degree of belief or an element of inference. The goal of this paper is to show how Bayesian statistics can be used in radionuclide metrology and what its advantages and disadvantages are compared with conventional statistics. This is performed through the example of an yttrium-90 source typically encountered in environmental surveillance measurement. Because of the very low activity of this kind of source and the small half-life of the radionuclide, this measurement takes several days, during which the source decays significantly. Several methods are proposed to compute simultaneously the number of unstable nuclei at a given reference time, the decay constant and the background. Asymptotically, all approaches give the same result. However, Bayesian statistics produces coherent estimates and confidence intervals in a much smaller number of measurements. Apart from the conceptual understanding of statistics, the main difficulty that could deter radionuclide metrologists from using Bayesian statistics is the complexity of the computation.

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

PubMed Central

Puig, X; Ginebra, J; Graffelman, J

2017-01-01

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

Statistical Surrogate Modeling of Atmospheric Dispersion Events Using Bayesian Adaptive Splines

NASA Astrophysics Data System (ADS)

Francom, D.; Sansó, B.; Bulaevskaya, V.; Lucas, D. D.

2016-12-01

Uncertainty in the inputs of complex computer models, including atmospheric dispersion and transport codes, is often assessed via statistical surrogate models. Surrogate models are computationally efficient statistical approximations of expensive computer models that enable uncertainty analysis. We introduce Bayesian adaptive spline methods for producing surrogate models that capture the major spatiotemporal patterns of the parent model, while satisfying all the necessities of flexibility, accuracy and computational feasibility. We present novel methodological and computational approaches motivated by a controlled atmospheric tracer release experiment conducted at the Diablo Canyon nuclear power plant in California. Traditional methods for building statistical surrogate models often do not scale well to experiments with large amounts of data. Our approach is well suited to experiments involving large numbers of model inputs, large numbers of simulations, and functional output for each simulation. Our approach allows us to perform global sensitivity analysis with ease. We also present an approach to calibration of simulators using field data.

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

PubMed Central

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

2012-01-01

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

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

ERIC Educational Resources Information Center

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

2014-01-01

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

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

PubMed

Bartlett, Jonathan W; Keogh, Ruth H

2018-06-01

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

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.

Statistical estimation via convex optimization for trending and performance monitoring

NASA Astrophysics Data System (ADS)

Samar, Sikandar

This thesis presents an optimization-based statistical estimation approach to find unknown trends in noisy data. A Bayesian framework is used to explicitly take into account prior information about the trends via trend models and constraints. The main focus is on convex formulation of the Bayesian estimation problem, which allows efficient computation of (globally) optimal estimates. There are two main parts of this thesis. The first part formulates trend estimation in systems described by known detailed models as a convex optimization problem. Statistically optimal estimates are then obtained by maximizing a concave log-likelihood function subject to convex constraints. We consider the problem of increasing problem dimension as more measurements become available, and introduce a moving horizon framework to enable recursive estimation of the unknown trend by solving a fixed size convex optimization problem at each horizon. We also present a distributed estimation framework, based on the dual decomposition method, for a system formed by a network of complex sensors with local (convex) estimation. Two specific applications of the convex optimization-based Bayesian estimation approach are described in the second part of the thesis. Batch estimation for parametric diagnostics in a flight control simulation of a space launch vehicle is shown to detect incipient fault trends despite the natural masking properties of feedback in the guidance and control loops. Moving horizon approach is used to estimate time varying fault parameters in a detailed nonlinear simulation model of an unmanned aerial vehicle. An excellent performance is demonstrated in the presence of winds and turbulence.

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.

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

PubMed Central

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

2017-01-01

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

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

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.

Beyond P Values and Hypothesis Testing: Using the Minimum Bayes Factor to Teach Statistical Inference in Undergraduate Introductory Statistics Courses

ERIC Educational Resources Information Center

Page, Robert; Satake, Eiki

2017-01-01

While interest in Bayesian statistics has been growing in statistics education, the treatment of the topic is still inadequate in both textbooks and the classroom. Because so many fields of study lead to careers that involve a decision-making process requiring an understanding of Bayesian methods, it is becoming increasingly clear that Bayesian…

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.

Fisher, Neyman, and Bayes at FDA.

PubMed

Rubin, Donald B

2016-01-01

The wise use of statistical ideas in practice essentially requires some Bayesian thinking, in contrast to the classical rigid frequentist dogma. This dogma too often has seemed to influence the applications of statistics, even at agencies like the FDA. Greg Campbell was one of the most important advocates there for more nuanced modes of thought, especially Bayesian statistics. Because two brilliant statisticians, Ronald Fisher and Jerzy Neyman, are often credited with instilling the traditional frequentist approach in current practice, I argue that both men were actually seeking very Bayesian answers, and neither would have endorsed the rigid application of their ideas.

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.

Applications of Bayesian Statistics to Problems in Gamma-Ray Bursts

NASA Technical Reports Server (NTRS)

Meegan, Charles A.

1997-01-01

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

Bayesian selective response-adaptive design using the historical control.

PubMed

Kim, Mi-Ok; Harun, Nusrat; Liu, Chunyan; Khoury, Jane C; Broderick, Joseph P

2018-06-13

High quality historical control data, if incorporated, may reduce sample size, trial cost, and duration. A too optimistic use of the data, however, may result in bias under prior-data conflict. Motivated by well-publicized two-arm comparative trials in stroke, we propose a Bayesian design that both adaptively incorporates historical control data and selectively adapt the treatment allocation ratios within an ongoing trial responsively to the relative treatment effects. The proposed design differs from existing designs that borrow from historical controls. As opposed to reducing the number of subjects assigned to the control arm blindly, this design does so adaptively to the relative treatment effects only if evaluation of cumulated current trial data combined with the historical control suggests the superiority of the intervention arm. We used the effective historical sample size approach to quantify borrowed information on the control arm and modified the treatment allocation rules of the doubly adaptive biased coin design to incorporate the quantity. The modified allocation rules were then implemented under the Bayesian framework with commensurate priors addressing prior-data conflict. Trials were also more frequently concluded earlier in line with the underlying truth, reducing trial cost, and duration and yielded parameter estimates with smaller standard errors. © 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons, Ltd.

A study of finite mixture model: Bayesian approach on financial time series data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Yen; Ismail, Mohd Tahir

2014-07-01

Recently, statistician have emphasized on the fitting finite mixture model by using Bayesian method. Finite mixture model is a mixture of distributions in modeling a statistical distribution meanwhile Bayesian method is a statistical method that use to fit the mixture model. Bayesian method is being used widely because it has asymptotic properties which provide remarkable result. In addition, Bayesian method also shows consistency characteristic which means the parameter estimates are close to the predictive distributions. In the present paper, the number of components for mixture model is studied by using Bayesian Information Criterion. Identify the number of component is important because it may lead to an invalid result. Later, the Bayesian method is utilized to fit the k-component mixture model in order to explore the relationship between rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia. Lastly, the results showed that there is a negative effect among rubber price and stock market price for all selected countries.

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

PubMed

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

2018-02-01

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

Editorial: Bayesian benefits for child psychology and psychiatry researchers.

PubMed

Oldehinkel, Albertine J

2016-09-01

For many scientists, performing statistical tests has become an almost automated routine. However, p-values are frequently used and interpreted incorrectly; and even when used appropriately, p-values tend to provide answers that do not match researchers' questions and hypotheses well. Bayesian statistics present an elegant and often more suitable alternative. The Bayesian approach has rarely been applied in child psychology and psychiatry research so far, but the development of user-friendly software packages and tutorials has placed it well within reach now. Because Bayesian analyses require a more refined definition of hypothesized probabilities of possible outcomes than the classical approach, going Bayesian may offer the additional benefit of sparkling the development and refinement of theoretical models in our field. © 2016 Association for Child and Adolescent Mental Health.

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

PubMed

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

2016-01-01

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

A BAYESIAN STATISTICAL APPROACH FOR THE EVALUATION OF CMAQ

EPA Science Inventory

Bayesian statistical methods are used to evaluate Community Multiscale Air Quality (CMAQ) model simulations of sulfate aerosol over a section of the eastern US for 4-week periods in summer and winter 2001. The observed data come from two U.S. Environmental Protection Agency data ...

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.

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…

Nowcasting Cloud Fields for U.S. Air Force Special Operations

DTIC Science & Technology

2017-03-01

application of Bayes’ Rule offers many advantages over Kernel Density Estimation (KDE) and other commonly used statistical post-processing methods...reflectance and probability of cloud. A statistical post-processing technique is applied using Bayesian estimation to train the system from a set of past...nowcasting, low cloud forecasting, cloud reflectance, ISR, Bayesian estimation, statistical post-processing, machine learning 15. NUMBER OF PAGES

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.

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.

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

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

PubMed

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

2016-10-21

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

Bayesian 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.

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

PubMed

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

2017-10-24

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

Hierarchical Commensurate and Power Prior Models for Adaptive Incorporation of Historical Information in Clinical Trials

PubMed Central

Hobbs, Brian P.; Carlin, Bradley P.; Mandrekar, Sumithra J.; Sargent, Daniel J.

2011-01-01

Summary Bayesian clinical trial designs offer the possibility of a substantially reduced sample size, increased statistical power, and reductions in cost and ethical hazard. However when prior and current information conflict, Bayesian methods can lead to higher than expected Type I error, as well as the possibility of a costlier and lengthier trial. This motivates an investigation of the feasibility of hierarchical Bayesian methods for incorporating historical data that are adaptively robust to prior information that reveals itself to be inconsistent with the accumulating experimental data. In this paper, we present several models that allow for the commensurability of the information in the historical and current data to determine how much historical information is used. A primary tool is elaborating the traditional power prior approach based upon a measure of commensurability for Gaussian data. We compare the frequentist performance of several methods using simulations, and close with an example of a colon cancer trial that illustrates a linear models extension of our adaptive borrowing approach. Our proposed methods produce more precise estimates of the model parameters, in particular conferring statistical significance to the observed reduction in tumor size for the experimental regimen as compared to the control regimen. PMID:21361892

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

ERIC Educational Resources Information Center

König, Christoph; van de Schoot, Rens

2018-01-01

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

Nonparametric Bayesian predictive distributions for future order statistics

Treesearch

Richard A. Johnson; James W. Evans; David W. Green

1999-01-01

We derive the predictive distribution for a specified order statistic, determined from a future random sample, under a Dirichlet process prior. Two variants of the approach are treated and some limiting cases studied. A practical application to monitoring the strength of lumber is discussed including choices of prior expectation and comparisons made to a Bayesian...

Bayesian truthing and experimental validation in homeland security and defense

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Bayesian Decision Support

NASA Astrophysics Data System (ADS)

Berliner, M.

2017-12-01

Bayesian statistical decision theory offers a natural framework for decision-policy making in the presence of uncertainty. Key advantages of the approach include efficient incorporation of information and observations. However, in complicated settings it is very difficult, perhaps essentially impossible, to formalize the mathematical inputs needed in the approach. Nevertheless, using the approach as a template is useful for decision support; that is, organizing and communicating our analyses. Bayesian hierarchical modeling is valuable in quantifying and managing uncertainty such cases. I review some aspects of the idea emphasizing statistical model development and use in the context of sea-level rise.

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.

Modeling Soot Oxidation and Gasification with Bayesian Statistics

DOE PAGES

Josephson, Alexander J.; Gaffin, Neal D.; Smith, Sean T.; ...

2017-08-22

This paper presents a statistical method for model calibration using data collected from literature. The method is used to calibrate parameters for global models of soot consumption in combustion systems. This consumption is broken into two different submodels: first for oxidation where soot particles are attacked by certain oxidizing agents; second for gasification where soot particles are attacked by H 2O or CO 2 molecules. Rate data were collected from 19 studies in the literature and evaluated using Bayesian statistics to calibrate the model parameters. Bayesian statistics are valued in their ability to quantify uncertainty in modeling. The calibrated consumptionmore » model with quantified uncertainty is presented here along with a discussion of associated implications. The oxidation results are found to be consistent with previous studies. Significant variation is found in the CO 2 gasification rates.« less

Modeling Soot Oxidation and Gasification with Bayesian Statistics

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

Josephson, Alexander J.; Gaffin, Neal D.; Smith, Sean T.

This paper presents a statistical method for model calibration using data collected from literature. The method is used to calibrate parameters for global models of soot consumption in combustion systems. This consumption is broken into two different submodels: first for oxidation where soot particles are attacked by certain oxidizing agents; second for gasification where soot particles are attacked by H 2O or CO 2 molecules. Rate data were collected from 19 studies in the literature and evaluated using Bayesian statistics to calibrate the model parameters. Bayesian statistics are valued in their ability to quantify uncertainty in modeling. The calibrated consumptionmore » model with quantified uncertainty is presented here along with a discussion of associated implications. The oxidation results are found to be consistent with previous studies. Significant variation is found in the CO 2 gasification rates.« less

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.

Using Alien Coins to Test Whether Simple Inference Is Bayesian

ERIC Educational Resources Information Center

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

2016-01-01

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

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 theories of conditioning in a changing world.

PubMed

Courville, Aaron C; Daw, Nathaniel D; Touretzky, David S

2006-07-01

The recent flowering of Bayesian approaches invites the re-examination of classic issues in behavior, even in areas as venerable as Pavlovian conditioning. A statistical account can offer a new, principled interpretation of behavior, and previous experiments and theories can inform many unexplored aspects of the Bayesian enterprise. Here we consider one such issue: the finding that surprising events provoke animals to learn faster. We suggest that, in a statistical account of conditioning, surprise signals change and therefore uncertainty and the need for new learning. We discuss inference in a world that changes and show how experimental results involving surprise can be interpreted from this perspective, and also how, thus understood, these phenomena help constrain statistical theories of animal and human learning.

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.

Bayesian analyses of seasonal runoff forecasts

NASA Astrophysics Data System (ADS)

Krzysztofowicz, R.; Reese, S.

1991-12-01

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

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.

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

PubMed

Sirota, Miroslav; Kostovičová, Lenka; Juanchich, Marie

2014-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2005-02-01

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

Inference on the Genetic Basis of Eye and Skin Color in an Admixed Population via Bayesian Linear Mixed Models.

PubMed

Lloyd-Jones, Luke R; Robinson, Matthew R; Moser, Gerhard; Zeng, Jian; Beleza, Sandra; Barsh, Gregory S; Tang, Hua; Visscher, Peter M

2017-06-01

Genetic association studies in admixed populations are underrepresented in the genomics literature, with a key concern for researchers being the adequate control of spurious associations due to population structure. Linear mixed models (LMMs) are well suited for genome-wide association studies (GWAS) because they account for both population stratification and cryptic relatedness and achieve increased statistical power by jointly modeling all genotyped markers. Additionally, Bayesian LMMs allow for more flexible assumptions about the underlying distribution of genetic effects, and can concurrently estimate the proportion of phenotypic variance explained by genetic markers. Using three recently published Bayesian LMMs, Bayes R, BSLMM, and BOLT-LMM, we investigate an existing data set on eye ( n = 625) and skin ( n = 684) color from Cape Verde, an island nation off West Africa that is home to individuals with a broad range of phenotypic values for eye and skin color due to the mix of West African and European ancestry. We use simulations to demonstrate the utility of Bayesian LMMs for mapping loci and studying the genetic architecture of quantitative traits in admixed populations. The Bayesian LMMs provide evidence for two new pigmentation loci: one for eye color ( AHRR ) and one for skin color ( DDB1 ). Copyright © 2017 by the Genetics Society of America.

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

Why Bayesian Psychologists Should Change the Way They Use the Bayes Factor.

PubMed

Hoijtink, Herbert; van Kooten, Pascal; Hulsker, Koenraad

2016-01-01

The discussion following Bem's ( 2011 ) psi research highlights that applications of the Bayes factor in psychological research are not without problems. The first problem is the omission to translate subjective prior knowledge into subjective prior distributions. In the words of Savage ( 1961 ): "they make the Bayesian omelet without breaking the Bayesian egg." The second problem occurs if the Bayesian egg is not broken: the omission to choose default prior distributions such that the ensuing inferences are well calibrated. The third problem is the adherence to inadequate rules for the interpretation of the size of the Bayes factor. The current paper will elaborate these problems and show how to avoid them using the basic hypotheses and statistical model used in the first experiment described in Bem ( 2011 ). It will be argued that a thorough investigation of these problems in the context of more encompassing hypotheses and statistical models is called for if Bayesian psychologists want to add a well-founded Bayes factor to the tool kit of psychological researchers.

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.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Computational statistics using the Bayesian Inference Engine

NASA Astrophysics Data System (ADS)

Weinberg, Martin D.

2013-09-01

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

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

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

PubMed

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

2012-01-01

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

Bayesian 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.

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

PubMed

Johnson, Eric D; Tubau, Elisabet

2017-06-01

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

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

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.

Fully Bayesian tests of neutrality using genealogical summary statistics.

PubMed

Drummond, Alexei J; Suchard, Marc A

2008-10-31

Many data summary statistics have been developed to detect departures from neutral expectations of evolutionary models. However questions about the neutrality of the evolution of genetic loci within natural populations remain difficult to assess. One critical cause of this difficulty is that most methods for testing neutrality make simplifying assumptions simultaneously about the mutational model and the population size model. Consequentially, rejecting the null hypothesis of neutrality under these methods could result from violations of either or both assumptions, making interpretation troublesome. Here we harness posterior predictive simulation to exploit summary statistics of both the data and model parameters to test the goodness-of-fit of standard models of evolution. We apply the method to test the selective neutrality of molecular evolution in non-recombining gene genealogies and we demonstrate the utility of our method on four real data sets, identifying significant departures of neutrality in human influenza A virus, even after controlling for variation in population size. Importantly, by employing a full model-based Bayesian analysis, our method separates the effects of demography from the effects of selection. The method also allows multiple summary statistics to be used in concert, thus potentially increasing sensitivity. Furthermore, our method remains useful in situations where analytical expectations and variances of summary statistics are not available. This aspect has great potential for the analysis of temporally spaced data, an expanding area previously ignored for limited availability of theory and methods.

Theory-based Bayesian Models of Inductive Inference

DTIC Science & Technology

2010-07-19

Subjective randomness and natural scene statistics. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom/papers/randscenes.pdf Page 1...in press). Exemplar models as a mechanism for performing Bayesian inference. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom

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

NASA Astrophysics Data System (ADS)

Melendez, Jordan; Wesolowski, Sarah; Furnstahl, Dick

2017-09-01

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

Asteroid orbital error analysis: Theory and application

NASA Technical Reports Server (NTRS)

Muinonen, K.; Bowell, Edward

1992-01-01

We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).

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.

Variations on Bayesian Prediction and Inference

DTIC Science & Technology

2016-05-09

inference 2.2.1 Background There are a number of statistical inference problems that are not generally formulated via a full probability model...problem of inference about an unknown parameter, the Bayesian approach requires a full probability 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...the problem of inference about an unknown parameter, the Bayesian approach requires a full probability model/likelihood which can be an obstacle

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.…

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

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.

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.

To P or Not to P: Backing Bayesian Statistics.

PubMed

Buchinsky, Farrel J; Chadha, Neil K

2017-12-01

In biomedical research, it is imperative to differentiate chance variation from truth before we generalize what we see in a sample of subjects to the wider population. For decades, we have relied on null hypothesis significance testing, where we calculate P values for our data to decide whether to reject a null hypothesis. This methodology is subject to substantial misinterpretation and errant conclusions. Instead of working backward by calculating the probability of our data if the null hypothesis were true, Bayesian statistics allow us instead to work forward, calculating the probability of our hypothesis given the available data. This methodology gives us a mathematical means of incorporating our "prior probabilities" from previous study data (if any) to produce new "posterior probabilities." Bayesian statistics tell us how confidently we should believe what we believe. It is time to embrace and encourage their use in our otolaryngology research.

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

PubMed

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

2015-07-01

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. Copyright © 2015 by the Genetics Society of America.

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

NASA Technical Reports Server (NTRS)

Jefferys, William H.; Berger, James O.

1992-01-01

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

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

PubMed

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

2017-01-01

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

Neural network approaches versus statistical methods in classification of multisource remote sensing data

NASA Technical Reports Server (NTRS)

Benediktsson, Jon A.; Swain, Philip H.; Ersoy, Okan K.

1990-01-01

Neural network learning procedures and statistical classificaiton methods are applied and compared empirically in classification of multisource remote sensing and geographic data. Statistical multisource classification by means of a method based on Bayesian classification theory is also investigated and modified. The modifications permit control of the influence of the data sources involved in the classification process. Reliability measures are introduced to rank the quality of the data sources. The data sources are then weighted according to these rankings in the statistical multisource classification. Four data sources are used in experiments: Landsat MSS data and three forms of topographic data (elevation, slope, and aspect). Experimental results show that two different approaches have unique advantages and disadvantages in this classification application.

Spatial heterogeneity and risk factors for stunting among children under age five in Ethiopia: A Bayesian geo-statistical model.

PubMed

Hagos, Seifu; Hailemariam, Damen; WoldeHanna, Tasew; Lindtjørn, Bernt

2017-01-01

Understanding the spatial distribution of stunting and underlying factors operating at meso-scale is of paramount importance for intervention designing and implementations. Yet, little is known about the spatial distribution of stunting and some discrepancies are documented on the relative importance of reported risk factors. Therefore, the present study aims at exploring the spatial distribution of stunting at meso- (district) scale, and evaluates the effect of spatial dependency on the identification of risk factors and their relative contribution to the occurrence of stunting and severe stunting in a rural area of Ethiopia. A community based cross sectional study was conducted to measure the occurrence of stunting and severe stunting among children aged 0-59 months. Additionally, we collected relevant information on anthropometric measures, dietary habits, parent and child-related demographic and socio-economic status. Latitude and longitude of surveyed households were also recorded. Local Anselin Moran's I was calculated to investigate the spatial variation of stunting prevalence and identify potential local pockets (hotspots) of high prevalence. Finally, we employed a Bayesian geo-statistical model, which accounted for spatial dependency structure in the data, to identify potential risk factors for stunting in the study area. Overall, the prevalence of stunting and severe stunting in the district was 43.7% [95%CI: 40.9, 46.4] and 21.3% [95%CI: 19.5, 23.3] respectively. We identified statistically significant clusters of high prevalence of stunting (hotspots) in the eastern part of the district and clusters of low prevalence (cold spots) in the western. We found out that the inclusion of spatial structure of the data into the Bayesian model has shown to improve the fit for stunting model. The Bayesian geo-statistical model indicated that the risk of stunting increased as the child's age increased (OR 4.74; 95% Bayesian credible interval [BCI]:3.35-6.58) and among boys (OR 1.28; 95%BCI; 1.12-1.45). However, maternal education and household food security were found to be protective against stunting and severe stunting. Stunting prevalence may vary across space at different scale. For this, it's important that nutrition studies and, more importantly, control interventions take into account this spatial heterogeneity in the distribution of nutritional deficits and their underlying associated factors. The findings of this study also indicated that interventions integrating household food insecurity in nutrition programs in the district might help to avert the burden of stunting.

Bayesian stable isotope mixing models

EPA Science Inventory

In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixtur...

Bayesian Parameter Inference and Model Selection by Population Annealing in Systems Biology

PubMed Central

Murakami, Yohei

2014-01-01

Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named “posterior parameter ensemble”. We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor. PMID:25089832

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 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.

The researcher and the consultant: from testing to probability statements.

PubMed

Hamra, Ghassan B; Stang, Andreas; Poole, Charles

2015-09-01

In the first instalment of this series, Stang and Poole provided an overview of Fisher significance testing (ST), Neyman-Pearson null hypothesis testing (NHT), and their unfortunate and unintended offspring, null hypothesis significance testing. In addition to elucidating the distinction between the first two and the evolution of the third, the authors alluded to alternative models of statistical inference; namely, Bayesian statistics. Bayesian inference has experienced a revival in recent decades, with many researchers advocating for its use as both a complement and an alternative to NHT and ST. This article will continue in the direction of the first instalment, providing practicing researchers with an introduction to Bayesian inference. Our work will draw on the examples and discussion of the previous dialogue.

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

On a full Bayesian inference for force reconstruction problems

NASA Astrophysics Data System (ADS)

Aucejo, M.; De Smet, O.

2018-05-01

In a previous paper, the authors introduced a flexible methodology for reconstructing mechanical sources in the frequency domain from prior local information on both their nature and location over a linear and time invariant structure. The proposed approach was derived from Bayesian statistics, because of its ability in mathematically accounting for experimenter's prior knowledge. However, since only the Maximum a Posteriori estimate was computed, the posterior uncertainty about the regularized solution given the measured vibration field, the mechanical model and the regularization parameter was not assessed. To answer this legitimate question, this paper fully exploits the Bayesian framework to provide, from a Markov Chain Monte Carlo algorithm, credible intervals and other statistical measures (mean, median, mode) for all the parameters of the force reconstruction problem.

The Misidentified Identifiability Problem of Bayesian Knowledge Tracing

ERIC Educational Resources Information Center

Doroudi, Shayan; Brunskill, Emma

2017-01-01

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

An introduction to using Bayesian linear regression with clinical data.

PubMed

Baldwin, Scott A; Larson, Michael J

2017-11-01

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

Bayesian modeling of flexible cognitive control

PubMed Central

Jiang, Jiefeng; Heller, Katherine; Egner, Tobias

2014-01-01

“Cognitive control” describes endogenous guidance of behavior in situations where routine stimulus-response associations are suboptimal for achieving a desired goal. The computational and neural mechanisms underlying this capacity remain poorly understood. We examine recent advances stemming from the application of a Bayesian learner perspective that provides optimal prediction for control processes. In reviewing the application of Bayesian models to cognitive control, we note that an important limitation in current models is a lack of a plausible mechanism for the flexible adjustment of control over conflict levels changing at varying temporal scales. We then show that flexible cognitive control can be achieved by a Bayesian model with a volatility-driven learning mechanism that modulates dynamically the relative dependence on recent and remote experiences in its prediction of future control demand. We conclude that the emergent Bayesian perspective on computational mechanisms of cognitive control holds considerable promise, especially if future studies can identify neural substrates of the variables encoded by these models, and determine the nature (Bayesian or otherwise) of their neural implementation. PMID:24929218

Distinguishing between statistical significance and practical/clinical meaningfulness using statistical inference.

PubMed

Wilkinson, Michael

2014-03-01

Decisions about support for predictions of theories in light of data are made using statistical inference. The dominant approach in sport and exercise science is the Neyman-Pearson (N-P) significance-testing approach. When applied correctly it provides a reliable procedure for making dichotomous decisions for accepting or rejecting zero-effect null hypotheses with known and controlled long-run error rates. Type I and type II error rates must be specified in advance and the latter controlled by conducting an a priori sample size calculation. The N-P approach does not provide the probability of hypotheses or indicate the strength of support for hypotheses in light of data, yet many scientists believe it does. Outcomes of analyses allow conclusions only about the existence of non-zero effects, and provide no information about the likely size of true effects or their practical/clinical value. Bayesian inference can show how much support data provide for different hypotheses, and how personal convictions should be altered in light of data, but the approach is complicated by formulating probability distributions about prior subjective estimates of population effects. A pragmatic solution is magnitude-based inference, which allows scientists to estimate the true magnitude of population effects and how likely they are to exceed an effect magnitude of practical/clinical importance, thereby integrating elements of subjective Bayesian-style thinking. While this approach is gaining acceptance, progress might be hastened if scientists appreciate the shortcomings of traditional N-P null hypothesis significance testing.

Semiparametric time varying coefficient model for matched case-crossover studies.

PubMed

Ortega-Villa, Ana Maria; Kim, Inyoung; Kim, H

2017-03-15

In matched case-crossover studies, it is generally accepted that the covariates on which a case and associated controls are matched cannot exert a confounding effect on independent predictors included in the conditional logistic regression model. This is because any stratum effect is removed by the conditioning on the fixed number of sets of the case and controls in the stratum. Hence, the conditional logistic regression model is not able to detect any effects associated with the matching covariates by stratum. However, some matching covariates such as time often play an important role as an effect modification leading to incorrect statistical estimation and prediction. Therefore, we propose three approaches to evaluate effect modification by time. The first is a parametric approach, the second is a semiparametric penalized approach, and the third is a semiparametric Bayesian approach. Our parametric approach is a two-stage method, which uses conditional logistic regression in the first stage and then estimates polynomial regression in the second stage. Our semiparametric penalized and Bayesian approaches are one-stage approaches developed by using regression splines. Our semiparametric one stage approach allows us to not only detect the parametric relationship between the predictor and binary outcomes, but also evaluate nonparametric relationships between the predictor and time. We demonstrate the advantage of our semiparametric one-stage approaches using both a simulation study and an epidemiological example of a 1-4 bi-directional case-crossover study of childhood aseptic meningitis with drinking water turbidity. We also provide statistical inference for the semiparametric Bayesian approach using Bayes Factors. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

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.

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.

Bayesian approach to non-Gaussian field statistics for diffusive broadband terahertz pulses.

PubMed

Pearce, Jeremy; Jian, Zhongping; Mittleman, Daniel M

2005-11-01

We develop a closed-form expression for the probability distribution function for the field components of a diffusive broadband wave propagating through a random medium. We consider each spectral component to provide an individual observation of a random variable, the configurationally averaged spectral intensity. Since the intensity determines the variance of the field distribution at each frequency, this random variable serves as the Bayesian prior that determines the form of the non-Gaussian field statistics. This model agrees well with experimental results.

Probabilistic Model for Untargeted Peak Detection in LC-MS Using Bayesian Statistics.

PubMed

Woldegebriel, Michael; Vivó-Truyols, Gabriel

2015-07-21

We introduce a novel Bayesian probabilistic peak detection algorithm for liquid chromatography-mass spectroscopy (LC-MS). The final probabilistic result allows the user to make a final decision about which points in a chromatogram are affected by a chromatographic peak and which ones are only affected by noise. The use of probabilities contrasts with the traditional method in which a binary answer is given, relying on a threshold. By contrast, with the Bayesian peak detection presented here, the values of probability can be further propagated into other preprocessing steps, which will increase (or decrease) the importance of chromatographic regions into the final results. The present work is based on the use of the statistical overlap theory of component overlap from Davis and Giddings (Davis, J. M.; Giddings, J. Anal. Chem. 1983, 55, 418-424) as prior probability in the Bayesian formulation. The algorithm was tested on LC-MS Orbitrap data and was able to successfully distinguish chemical noise from actual peaks without any data preprocessing.

Rediscovery of Good-Turing estimators via Bayesian nonparametrics.

PubMed

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

2016-03-01

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

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.

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

PubMed

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

2016-01-01

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

New Insights into Handling Missing Values in Environmental Epidemiological Studies

PubMed Central

Roda, Célina; Nicolis, Ioannis; Momas, Isabelle; Guihenneuc, Chantal

2014-01-01

Missing data are unavoidable in environmental epidemiologic surveys. The aim of this study was to compare methods for handling large amounts of missing values: omission of missing values, single and multiple imputations (through linear regression or partial least squares regression), and a fully Bayesian approach. These methods were applied to the PARIS birth cohort, where indoor domestic pollutant measurements were performed in a random sample of babies' dwellings. A simulation study was conducted to assess performances of different approaches with a high proportion of missing values (from 50% to 95%). Different simulation scenarios were carried out, controlling the true value of the association (odds ratio of 1.0, 1.2, and 1.4), and varying the health outcome prevalence. When a large amount of data is missing, omitting these missing data reduced statistical power and inflated standard errors, which affected the significance of the association. Single imputation underestimated the variability, and considerably increased risk of type I error. All approaches were conservative, except the Bayesian joint model. In the case of a common health outcome, the fully Bayesian approach is the most efficient approach (low root mean square error, reasonable type I error, and high statistical power). Nevertheless for a less prevalent event, the type I error is increased and the statistical power is reduced. The estimated posterior distribution of the OR is useful to refine the conclusion. Among the methods handling missing values, no approach is absolutely the best but when usual approaches (e.g. single imputation) are not sufficient, joint modelling approach of missing process and health association is more efficient when large amounts of data are missing. PMID:25226278

Responses of calcification of massive and encrusting corals to past, present, and near-future ocean carbon dioxide concentrations.

PubMed

Iguchi, Akira; Kumagai, Naoki H; Nakamura, Takashi; Suzuki, Atsushi; Sakai, Kazuhiko; Nojiri, Yukihiro

2014-12-15

In this study, we report the acidification impact mimicking the pre-industrial, the present, and near-future oceans on calcification of two coral species (Porites australiensis, Isopora palifera) by using precise pCO2 control system which can produce acidified seawater under stable pCO2 values with low variations. In the analyses, we performed Bayesian modeling approaches incorporating the variations of pCO2 and compared the results between our modeling approach and classical statistical one. The results showed highest calcification rates in pre-industrial pCO2 level and gradual decreases of calcification in the near-future ocean acidification level, which suggests that ongoing and near-future ocean acidification would negatively impact coral calcification. In addition, it was expected that the variations of parameters of carbon chemistry may affect the inference of the best model on calcification responses to these parameters between Bayesian modeling approach and classical statistical one even under stable pCO2 values with low variations. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Abe, Sumiyoshi

2014-11-01

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

HARMONIZATION OF HUMAN AND ECOLOGICAL HEALTH ASSESSMENT: DEVELOPMENT OF BAYESIAN UPDATING TECHNIQUES TO INCORPORATE MECHANISTIC INFORMATION ACROSS SPECIES

EPA Science Inventory

Bayesian statistical techniques have proven useful in clinical and environmental epidemiological applications to evaluate and integrate available information, and in regulatory applications such as the National Ambient Air Quality Assessment for Nitrogen Oxides. A recent special...

Efficient Dependency Computation for Dynamic Hybrid Bayesian Network in On-line System Health Management Applications

DTIC Science & Technology

2014-10-02

intervals (Neil, Tailor, Marquez, Fenton , & Hear, 2007). This is cumbersome, error prone and usually inaccurate. Even though a universal framework...Science. Neil, M., Tailor, M., Marquez, D., Fenton , N., & Hear. (2007). Inference in Bayesian networks using dynamic discretisation. Statistics

A Bayesian Approach to Interactive Retrieval

ERIC Educational Resources Information Center

Tague, Jean M.

1973-01-01

A probabilistic model for interactive retrieval is presented. Bayesian statistical decision theory principles are applied: use of prior and sample information about the relationship of document descriptions to query relevance; maximization of expected value of a utility function, to the problem of optimally restructuring search strategies in an…

Personalized Multi-Student Improvement Based on Bayesian Cybernetics

ERIC Educational Resources Information Center

Kaburlasos, Vassilis G.; Marinagi, Catherine C.; Tsoukalas, Vassilis Th.

2008-01-01

This work presents innovative cybernetics (feedback) techniques based on Bayesian statistics for drawing questions from an Item Bank towards personalized multi-student improvement. A novel software tool, namely "Module for Adaptive Assessment of Students" (or, "MAAS" for short), implements the proposed (feedback) techniques. In conclusion, a pilot…

[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.

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.

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.

Compromise decision support problems for hierarchical design involving uncertainty

NASA Astrophysics Data System (ADS)

Vadde, S.; Allen, J. K.; Mistree, F.

1994-08-01

In this paper an extension to the traditional compromise Decision Support Problem (DSP) formulation is presented. Bayesian statistics is used in the formulation to model uncertainties associated with the information being used. In an earlier paper a compromise DSP that accounts for uncertainty using fuzzy set theory was introduced. The Bayesian Decision Support Problem is described in this paper. The method for hierarchical design is demonstrated by using this formulation to design a portal frame. The results are discussed and comparisons are made with those obtained using the fuzzy DSP. Finally, the efficacy of incorporating Bayesian statistics into the traditional compromise DSP formulation is discussed and some pending research issues are described. Our emphasis in this paper is on the method rather than the results per se.

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.

Machine learning approach for automated screening of malaria parasite using light microscopic images.

PubMed

Das, Dev Kumar; Ghosh, Madhumala; Pal, Mallika; Maiti, Asok K; Chakraborty, Chandan

2013-02-01

The aim of this paper is to address the development of computer assisted malaria parasite characterization and classification using machine learning approach based on light microscopic images of peripheral blood smears. In doing this, microscopic image acquisition from stained slides, illumination correction and noise reduction, erythrocyte segmentation, feature extraction, feature selection and finally classification of different stages of malaria (Plasmodium vivax and Plasmodium falciparum) have been investigated. The erythrocytes are segmented using marker controlled watershed transformation and subsequently total ninety six features describing shape-size and texture of erythrocytes are extracted in respect to the parasitemia infected versus non-infected cells. Ninety four features are found to be statistically significant in discriminating six classes. Here a feature selection-cum-classification scheme has been devised by combining F-statistic, statistical learning techniques i.e., Bayesian learning and support vector machine (SVM) in order to provide the higher classification accuracy using best set of discriminating features. Results show that Bayesian approach provides the highest accuracy i.e., 84% for malaria classification by selecting 19 most significant features while SVM provides highest accuracy i.e., 83.5% with 9 most significant features. Finally, the performance of these two classifiers under feature selection framework has been compared toward malaria parasite classification. Copyright © 2012 Elsevier Ltd. All rights reserved.

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

PubMed

Krishnamurthy, Krish

2013-12-01

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

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.

Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Xia, Ye-Mao; Pan, Jun-Hao; Lee, Sik-Yum

2011-01-01

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

The Importance of Proving the Null

ERIC Educational Resources Information Center

Gallistel, C. R.

2009-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Organism-level models: When mechanisms and statistics fail us

NASA Astrophysics Data System (ADS)

Phillips, M. H.; Meyer, J.; Smith, W. P.; Rockhill, J. K.

2014-03-01

Purpose: To describe the unique characteristics of models that represent the entire course of radiation therapy at the organism level and to highlight the uses to which such models can be put. Methods: At the level of an organism, traditional model-building runs into severe difficulties. We do not have sufficient knowledge to devise a complete biochemistry-based model. Statistical model-building fails due to the vast number of variables and the inability to control many of them in any meaningful way. Finally, building surrogate models, such as animal-based models, can result in excluding some of the most critical variables. Bayesian probabilistic models (Bayesian networks) provide a useful alternative that have the advantages of being mathematically rigorous, incorporating the knowledge that we do have, and being practical. Results: Bayesian networks representing radiation therapy pathways for prostate cancer and head & neck cancer were used to highlight the important aspects of such models and some techniques of model-building. A more specific model representing the treatment of occult lymph nodes in head & neck cancer were provided as an example of how such a model can inform clinical decisions. A model of the possible role of PET imaging in brain cancer was used to illustrate the means by which clinical trials can be modelled in order to come up with a trial design that will have meaningful outcomes. Conclusions: Probabilistic models are currently the most useful approach to representing the entire therapy outcome process.

TOWARDS A BAYESIAN PERSPECTIVE ON STATISTICAL DISCLOSURE LIMITATION

EPA Science Inventory

National statistical offices and other organizations collect data on individual subjects (person, businesses, organizations), typically while assuring the subject that data pertaining to them will be held confidential. These data provide the raw material for statistical data pro...

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

PubMed

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

2015-07-01

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

Analysis of Feature Intervisibility and Cumulative Visibility Using GIS, Bayesian and Spatial Statistics: A Study from the Mandara Mountains, Northern Cameroon

PubMed Central

Wright, David K.; MacEachern, Scott; Lee, Jaeyong

2014-01-01

The locations of diy-geδ-bay (DGB) sites in the Mandara Mountains, northern Cameroon are hypothesized to occur as a function of their ability to see and be seen from points on the surrounding landscape. A series of geostatistical, two-way and Bayesian logistic regression analyses were performed to test two hypotheses related to the intervisibility of the sites to one another and their visual prominence on the landscape. We determine that the intervisibility of the sites to one another is highly statistically significant when compared to 10 stratified-random permutations of DGB sites. Bayesian logistic regression additionally demonstrates that the visibility of the sites to points on the surrounding landscape is statistically significant. The location of sites appears to have also been selected on the basis of lower slope than random permutations of sites. Using statistical measures, many of which are not commonly employed in archaeological research, to evaluate aspects of visibility on the landscape, we conclude that the placement of DGB sites improved their conspicuousness for enhanced ritual, social cooperation and/or competition purposes. PMID:25383883

Bayesian adjustment for measurement error in continuous exposures in an individually matched case-control study.

PubMed

Espino-Hernandez, Gabriela; Gustafson, Paul; Burstyn, Igor

2011-05-14

In epidemiological studies explanatory variables are frequently subject to measurement error. The aim of this paper is to develop a Bayesian method to correct for measurement error in multiple continuous exposures in individually matched case-control studies. This is a topic that has not been widely investigated. The new method is illustrated using data from an individually matched case-control study of the association between thyroid hormone levels during pregnancy and exposure to perfluorinated acids. The objective of the motivating study was to examine the risk of maternal hypothyroxinemia due to exposure to three perfluorinated acids measured on a continuous scale. Results from the proposed method are compared with those obtained from a naive analysis. Using a Bayesian approach, the developed method considers a classical measurement error model for the exposures, as well as the conditional logistic regression likelihood as the disease model, together with a random-effect exposure model. Proper and diffuse prior distributions are assigned, and results from a quality control experiment are used to estimate the perfluorinated acids' measurement error variability. As a result, posterior distributions and 95% credible intervals of the odds ratios are computed. A sensitivity analysis of method's performance in this particular application with different measurement error variability was performed. The proposed Bayesian method to correct for measurement error is feasible and can be implemented using statistical software. For the study on perfluorinated acids, a comparison of the inferences which are corrected for measurement error to those which ignore it indicates that little adjustment is manifested for the level of measurement error actually exhibited in the exposures. Nevertheless, a sensitivity analysis shows that more substantial adjustments arise if larger measurement errors are assumed. In individually matched case-control studies, the use of conditional logistic regression likelihood as a disease model in the presence of measurement error in multiple continuous exposures can be justified by having a random-effect exposure model. The proposed method can be successfully implemented in WinBUGS to correct individually matched case-control studies for several mismeasured continuous exposures under a classical measurement error model.

Theory-based Bayesian models of inductive learning and reasoning.

PubMed

Tenenbaum, Joshua B; Griffiths, Thomas L; Kemp, Charles

2006-07-01

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.

Data free inference with processed data products

DOE PAGES

Chowdhary, K.; Najm, H. N.

2014-07-12

Here, we consider the context of probabilistic inference of model parameters given error bars or confidence intervals on model output values, when the data is unavailable. We introduce a class of algorithms in a Bayesian framework, relying on maximum entropy arguments and approximate Bayesian computation methods, to generate consistent data with the given summary statistics. Once we obtain consistent data sets, we pool the respective posteriors, to arrive at a single, averaged density on the parameters. This approach allows us to perform accurate forward uncertainty propagation consistent with the reported statistics.

Quantum-Like Representation of Non-Bayesian Inference

NASA Astrophysics Data System (ADS)

Asano, M.; Basieva, I.; Khrennikov, A.; Ohya, M.; Tanaka, Y.

2013-01-01

This research is related to the problem of "irrational decision making or inference" that have been discussed in cognitive psychology. There are some experimental studies, and these statistical data cannot be described by classical probability theory. The process of decision making generating these data cannot be reduced to the classical Bayesian inference. For this problem, a number of quantum-like coginitive models of decision making was proposed. Our previous work represented in a natural way the classical Bayesian inference in the frame work of quantum mechanics. By using this representation, in this paper, we try to discuss the non-Bayesian (irrational) inference that is biased by effects like the quantum interference. Further, we describe "psychological factor" disturbing "rationality" as an "environment" correlating with the "main system" of usual Bayesian inference.

BaTMAn: Bayesian Technique for Multi-image Analysis

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

ERIC Educational Resources Information Center

Jones, W. Paul

2003-01-01

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

A Comparison of Imputation Methods for Bayesian Factor Analysis Models

ERIC Educational Resources Information Center

Merkle, Edgar C.

2011-01-01

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

Modeling Error Distributions of Growth Curve Models through Bayesian Methods

ERIC Educational Resources Information Center

Zhang, Zhiyong

2016-01-01

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…

Application of Bayesian Methods for Detecting Fraudulent Behavior on Tests

ERIC Educational Resources Information Center

Sinharay, Sandip

2018-01-01

Producers and consumers of test scores are increasingly concerned about fraudulent behavior before and during the test. There exist several statistical or psychometric methods for detecting fraudulent behavior on tests. This paper provides a review of the Bayesian approaches among them. Four hitherto-unpublished real data examples are provided to…

Bayesian statistics: estimating plant demographic parameters

Treesearch

James S. Clark; Michael Lavine

2001-01-01

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

A baker's dozen of new particle flows for nonlinear filters, Bayesian decisions and transport

NASA Astrophysics Data System (ADS)

Daum, Fred; Huang, Jim

2015-05-01

We describe a baker's dozen of new particle flows to compute Bayes' rule for nonlinear filters, Bayesian decisions and learning as well as transport. Several of these new flows were inspired by transport theory, but others were inspired by physics or statistics or Markov chain Monte Carlo methods.

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

PubMed

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

2016-06-01

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

Uncovering robust patterns of microRNA co-expression across cancers using Bayesian Relevance Networks

PubMed Central

2017-01-01

Co-expression networks have long been used as a tool for investigating the molecular circuitry governing biological systems. However, most algorithms for constructing co-expression networks were developed in the microarray era, before high-throughput sequencing—with its unique statistical properties—became the norm for expression measurement. Here we develop Bayesian Relevance Networks, an algorithm that uses Bayesian reasoning about expression levels to account for the differing levels of uncertainty in expression measurements between highly- and lowly-expressed entities, and between samples with different sequencing depths. It combines data from groups of samples (e.g., replicates) to estimate group expression levels and confidence ranges. It then computes uncertainty-moderated estimates of cross-group correlations between entities, and uses permutation testing to assess their statistical significance. Using large scale miRNA data from The Cancer Genome Atlas, we show that our Bayesian update of the classical Relevance Networks algorithm provides improved reproducibility in co-expression estimates and lower false discovery rates in the resulting co-expression networks. Software is available at www.perkinslab.ca. PMID:28817636

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

Uncovering robust patterns of microRNA co-expression across cancers using Bayesian Relevance Networks.

PubMed

Ramachandran, Parameswaran; Sánchez-Taltavull, Daniel; Perkins, Theodore J

2017-01-01

Co-expression networks have long been used as a tool for investigating the molecular circuitry governing biological systems. However, most algorithms for constructing co-expression networks were developed in the microarray era, before high-throughput sequencing-with its unique statistical properties-became the norm for expression measurement. Here we develop Bayesian Relevance Networks, an algorithm that uses Bayesian reasoning about expression levels to account for the differing levels of uncertainty in expression measurements between highly- and lowly-expressed entities, and between samples with different sequencing depths. It combines data from groups of samples (e.g., replicates) to estimate group expression levels and confidence ranges. It then computes uncertainty-moderated estimates of cross-group correlations between entities, and uses permutation testing to assess their statistical significance. Using large scale miRNA data from The Cancer Genome Atlas, we show that our Bayesian update of the classical Relevance Networks algorithm provides improved reproducibility in co-expression estimates and lower false discovery rates in the resulting co-expression networks. Software is available at www.perkinslab.ca.

A practical Bayesian stepped wedge design for community-based cluster-randomized clinical trials: The British Columbia Telehealth Trial.

PubMed

Cunanan, Kristen M; Carlin, Bradley P; Peterson, Kevin A

2016-12-01

Many clinical trial designs are impractical for community-based clinical intervention trials. Stepped wedge trial designs provide practical advantages, but few descriptions exist of their clinical implementational features, statistical design efficiencies, and limitations. Enhance efficiency of stepped wedge trial designs by evaluating the impact of design characteristics on statistical power for the British Columbia Telehealth Trial. The British Columbia Telehealth Trial is a community-based, cluster-randomized, controlled clinical trial in rural and urban British Columbia. To determine the effect of an Internet-based telehealth intervention on healthcare utilization, 1000 subjects with an existing diagnosis of congestive heart failure or type 2 diabetes will be enrolled from 50 clinical practices. Hospital utilization is measured using a composite of disease-specific hospital admissions and emergency visits. The intervention comprises online telehealth data collection and counseling provided to support a disease-specific action plan developed by the primary care provider. The planned intervention is sequentially introduced across all participating practices. We adopt a fully Bayesian, Markov chain Monte Carlo-driven statistical approach, wherein we use simulation to determine the effect of cluster size, sample size, and crossover interval choice on type I error and power to evaluate differences in hospital utilization. For our Bayesian stepped wedge trial design, simulations suggest moderate decreases in power when crossover intervals from control to intervention are reduced from every 3 to 2 weeks, and dramatic decreases in power as the numbers of clusters decrease. Power and type I error performance were not notably affected by the addition of nonzero cluster effects or a temporal trend in hospitalization intensity. Stepped wedge trial designs that intervene in small clusters across longer periods can provide enhanced power to evaluate comparative effectiveness, while offering practical implementation advantages in geographic stratification, temporal change, use of existing data, and resource distribution. Current population estimates were used; however, models may not reflect actual event rates during the trial. In addition, temporal or spatial heterogeneity can bias treatment effect estimates. © The Author(s) 2016.

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-01-01

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

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.

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

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

Marzouk, Youssef

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

A BAYESIAN SPATIAL AND TEMPORAL MODELING APPROACH TO MAPPING GEOGRAPHIC VARIATION IN MORTALITY RATES FOR SUBNATIONAL AREAS WITH R-INLA.

PubMed

Khana, Diba; Rossen, Lauren M; Hedegaard, Holly; Warner, Margaret

2018-01-01

Hierarchical Bayes models have been used in disease mapping to examine small scale geographic variation. State level geographic variation for less common causes of mortality outcomes have been reported however county level variation is rarely examined. Due to concerns about statistical reliability and confidentiality, county-level mortality rates based on fewer than 20 deaths are suppressed based on Division of Vital Statistics, National Center for Health Statistics (NCHS) statistical reliability criteria, precluding an examination of spatio-temporal variation in less common causes of mortality outcomes such as suicide rates (SRs) at the county level using direct estimates. Existing Bayesian spatio-temporal modeling strategies can be applied via Integrated Nested Laplace Approximation (INLA) in R to a large number of rare causes of mortality outcomes to enable examination of spatio-temporal variations on smaller geographic scales such as counties. This method allows examination of spatiotemporal variation across the entire U.S., even where the data are sparse. We used mortality data from 2005-2015 to explore spatiotemporal variation in SRs, as one particular application of the Bayesian spatio-temporal modeling strategy in R-INLA to predict year and county-specific SRs. Specifically, hierarchical Bayesian spatio-temporal models were implemented with spatially structured and unstructured random effects, correlated time effects, time varying confounders and space-time interaction terms in the software R-INLA, borrowing strength across both counties and years to produce smoothed county level SRs. Model-based estimates of SRs were mapped to explore geographic variation.

The meta-Gaussian Bayesian Processor of forecasts and associated preliminary experiments

NASA Astrophysics Data System (ADS)

Chen, Fajing; Jiao, Meiyan; Chen, Jing

2013-04-01

Public weather services are trending toward providing users with probabilistic weather forecasts, in place of traditional deterministic forecasts. Probabilistic forecasting techniques are continually being improved to optimize available forecasting information. The Bayesian Processor of Forecast (BPF), a new statistical method for probabilistic forecast, can transform a deterministic forecast into a probabilistic forecast according to the historical statistical relationship between observations and forecasts generated by that forecasting system. This technique accounts for the typical forecasting performance of a deterministic forecasting system in quantifying the forecast uncertainty. The meta-Gaussian likelihood model is suitable for a variety of stochastic dependence structures with monotone likelihood ratios. The meta-Gaussian BPF adopting this kind of likelihood model can therefore be applied across many fields, including meteorology and hydrology. The Bayes theorem with two continuous random variables and the normal-linear BPF are briefly introduced. The meta-Gaussian BPF for a continuous predictand using a single predictor is then presented and discussed. The performance of the meta-Gaussian BPF is tested in a preliminary experiment. Control forecasts of daily surface temperature at 0000 UTC at Changsha and Wuhan stations are used as the deterministic forecast data. These control forecasts are taken from ensemble predictions with a 96-h lead time generated by the National Meteorological Center of the China Meteorological Administration, the European Centre for Medium-Range Weather Forecasts, and the US National Centers for Environmental Prediction during January 2008. The results of the experiment show that the meta-Gaussian BPF can transform a deterministic control forecast of surface temperature from any one of the three ensemble predictions into a useful probabilistic forecast of surface temperature. These probabilistic forecasts quantify the uncertainty of the control forecast; accordingly, the performance of the probabilistic forecasts differs based on the source of the underlying deterministic control forecasts.

Toward evidence-based medical statistics: a Bayesian analysis of double-blind placebo-controlled antidepressant trials in the treatment of anxiety disorders.

PubMed

Monden, Rei; de Vos, Stijn; Morey, Richard; Wagenmakers, Eric-Jan; de Jonge, Peter; Roest, Annelieke M

2016-12-01

The Food and Drug Administration (FDA) uses a p < 0.05 null-hypothesis significance testing framework to evaluate "substantial evidence" for drug efficacy. This framework only allows dichotomous conclusions and does not quantify the strength of evidence supporting efficacy. The efficacy of FDA-approved antidepressants for the treatment of anxiety disorders was re-evaluated in a Bayesian framework that quantifies the strength of the evidence. Data from 58 double-blind placebo-controlled trials were retrieved from the FDA for the second-generation antidepressants for the treatment of anxiety disorders. Bayes factors (BFs) were calculated for all treatment arms compared to placebo and were compared with the corresponding p-values and the FDA conclusion categories. BFs ranged from 0.07 to 131,400, indicating a range of no support of evidence to strong evidence for the efficacy. Results also indicate a varying strength of evidence between the trials with p < 0.05. In sum, there were large differences in BFs across trials. Among trials providing "substantial evidence" according to the FDA, only 27 out of 59 dose groups obtained strong support for efficacy according to the typically used cutoff of BF ≥ 20. The Bayesian framework can provide valuable information on the strength of the evidence for drug efficacy. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

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

NASA Astrophysics Data System (ADS)

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

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

Bayesian hypothesis testing for human threat conditioning research: an introduction and the condir R package

PubMed Central

Krypotos, Angelos-Miltiadis; Klugkist, Irene; Engelhard, Iris M.

2017-01-01

ABSTRACT Threat conditioning procedures have allowed the experimental investigation of the pathogenesis of Post-Traumatic Stress Disorder. The findings of these procedures have also provided stable foundations for the development of relevant intervention programs (e.g. exposure therapy). Statistical inference of threat conditioning procedures is commonly based on p-values and Null Hypothesis Significance Testing (NHST). Nowadays, however, there is a growing concern about this statistical approach, as many scientists point to the various limitations of p-values and NHST. As an alternative, the use of Bayes factors and Bayesian hypothesis testing has been suggested. In this article, we apply this statistical approach to threat conditioning data. In order to enable the easy computation of Bayes factors for threat conditioning data we present a new R package named condir, which can be used either via the R console or via a Shiny application. This article provides both a non-technical introduction to Bayesian analysis for researchers using the threat conditioning paradigm, and the necessary tools for computing Bayes factors easily. PMID:29038683

Intelligent Condition Diagnosis Method Based on Adaptive Statistic Test Filter and Diagnostic Bayesian Network

PubMed Central

Li, Ke; Zhang, Qiuju; Wang, Kun; Chen, Peng; Wang, Huaqing

2016-01-01

A new fault diagnosis method for rotating machinery based on adaptive statistic test filter (ASTF) and Diagnostic Bayesian Network (DBN) is presented in this paper. ASTF is proposed to obtain weak fault features under background noise, ASTF is based on statistic hypothesis testing in the frequency domain to evaluate similarity between reference signal (noise signal) and original signal, and remove the component of high similarity. The optimal level of significance α is obtained using particle swarm optimization (PSO). To evaluate the performance of the ASTF, evaluation factor Ipq is also defined. In addition, a simulation experiment is designed to verify the effectiveness and robustness of ASTF. A sensitive evaluation method using principal component analysis (PCA) is proposed to evaluate the sensitiveness of symptom parameters (SPs) for condition diagnosis. By this way, the good SPs that have high sensitiveness for condition diagnosis can be selected. A three-layer DBN is developed to identify condition of rotation machinery based on the Bayesian Belief Network (BBN) theory. Condition diagnosis experiment for rolling element bearings demonstrates the effectiveness of the proposed method. PMID:26761006

Intelligent Condition Diagnosis Method Based on Adaptive Statistic Test Filter and Diagnostic Bayesian Network.

PubMed

Li, Ke; Zhang, Qiuju; Wang, Kun; Chen, Peng; Wang, Huaqing

2016-01-08

A new fault diagnosis method for rotating machinery based on adaptive statistic test filter (ASTF) and Diagnostic Bayesian Network (DBN) is presented in this paper. ASTF is proposed to obtain weak fault features under background noise, ASTF is based on statistic hypothesis testing in the frequency domain to evaluate similarity between reference signal (noise signal) and original signal, and remove the component of high similarity. The optimal level of significance α is obtained using particle swarm optimization (PSO). To evaluate the performance of the ASTF, evaluation factor Ipq is also defined. In addition, a simulation experiment is designed to verify the effectiveness and robustness of ASTF. A sensitive evaluation method using principal component analysis (PCA) is proposed to evaluate the sensitiveness of symptom parameters (SPs) for condition diagnosis. By this way, the good SPs that have high sensitiveness for condition diagnosis can be selected. A three-layer DBN is developed to identify condition of rotation machinery based on the Bayesian Belief Network (BBN) theory. Condition diagnosis experiment for rolling element bearings demonstrates the effectiveness of the proposed method.

Bayesian Sensitivity Analysis of Statistical Models with Missing Data

PubMed Central

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

2013-01-01

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

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

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

PubMed

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

2014-01-01

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

A program for the Bayesian Neural Network in the ROOT framework

NASA Astrophysics Data System (ADS)

Zhong, Jiahang; Huang, Run-Sheng; Lee, Shih-Chang

2011-12-01

We present a Bayesian Neural Network algorithm implemented in the TMVA package (Hoecker et al., 2007 [1]), within the ROOT framework (Brun and Rademakers, 1997 [2]). Comparing to the conventional utilization of Neural Network as discriminator, this new implementation has more advantages as a non-parametric regression tool, particularly for fitting probabilities. It provides functionalities including cost function selection, complexity control and uncertainty estimation. An example of such application in High Energy Physics is shown. The algorithm is available with ROOT release later than 5.29. Program summaryProgram title: TMVA-BNN Catalogue identifier: AEJX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: BSD license No. of lines in distributed program, including test data, etc.: 5094 No. of bytes in distributed program, including test data, etc.: 1,320,987 Distribution format: tar.gz Programming language: C++ Computer: Any computer system or cluster with C++ compiler and UNIX-like operating system Operating system: Most UNIX/Linux systems. The application programs were thoroughly tested under Fedora and Scientific Linux CERN. Classification: 11.9 External routines: ROOT package version 5.29 or higher ( http://root.cern.ch) Nature of problem: Non-parametric fitting of multivariate distributions Solution method: An implementation of Neural Network following the Bayesian statistical interpretation. Uses Laplace approximation for the Bayesian marginalizations. Provides the functionalities of automatic complexity control and uncertainty estimation. Running time: Time consumption for the training depends substantially on the size of input sample, the NN topology, the number of training iterations, etc. For the example in this manuscript, about 7 min was used on a PC/Linux with 2.0 GHz processors.

Learning classification trees

NASA Technical Reports Server (NTRS)

Buntine, Wray

1991-01-01

Algorithms for learning classification trees have had successes in artificial intelligence and statistics over many years. How a tree learning algorithm can be derived from Bayesian decision theory is outlined. This introduces Bayesian techniques for splitting, smoothing, and tree averaging. The splitting rule turns out to be similar to Quinlan's information gain splitting rule, while smoothing and averaging replace pruning. Comparative experiments with reimplementations of a minimum encoding approach, Quinlan's C4 and Breiman et al. Cart show the full Bayesian algorithm is consistently as good, or more accurate than these other approaches though at a computational price.

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

ERIC Educational Resources Information Center

Marsman, Maarten; Wagenmakers, Eric-Jan

2017-01-01

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

Are Student Evaluations of Teaching Effectiveness Valid for Measuring Student Learning Outcomes in Business Related Classes? A Neural Network and Bayesian Analyses

ERIC Educational Resources Information Center

Galbraith, Craig S.; Merrill, Gregory B.; Kline, Doug M.

2012-01-01

In this study we investigate the underlying relational structure between student evaluations of teaching effectiveness (SETEs) and achievement of student learning outcomes in 116 business related courses. Utilizing traditional statistical techniques, a neural network analysis and a Bayesian data reduction and classification algorithm, we find…

75 FR 6209 - Guidance for Industry and Food and Drug Administration; Guidance for the Use of Bayesian...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-02-08

... DEPARTMENT OF HEALTH AND HUMAN SERVICES Food and Drug Administration [Docket No. FDA-2006-D-0410] (formerly Docket No. 2006D-0191) Guidance for Industry and Food and Drug Administration; Guidance for the Use of Bayesian Statistics in Medical Device Clinical Trials; Availability AGENCY: Food and Drug...

Stan: A Probabilistic Programming Language for Bayesian Inference and Optimization

ERIC Educational Resources Information Center

Gelman, Andrew; Lee, Daniel; Guo, Jiqiang

2015-01-01

Stan is a free and open-source C++ program that performs Bayesian inference or optimization for arbitrary user-specified models and can be called from the command line, R, Python, Matlab, or Julia and has great promise for fitting large and complex statistical models in many areas of application. We discuss Stan from users' and developers'…

A product Pearson-type VII density distribution

NASA Astrophysics Data System (ADS)

Nadarajah, Saralees; Kotz, Samuel

2008-01-01

The Pearson-type VII distributions (containing the Student's t distributions) are becoming increasing prominent and are being considered as competitors to the normal distribution. Motivated by real examples in decision sciences, Bayesian statistics, probability theory and Physics, a new Pearson-type VII distribution is introduced by taking the product of two Pearson-type VII pdfs. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Finally, an application to a Bayesian testing problem is illustrated.

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.

PubMed

Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.

A Bayesian Measurment Error Model for Misaligned Radiographic Data

DOE PAGES

Lennox, Kristin P.; Glascoe, Lee G.

2013-09-06

An understanding of the inherent variability in micro-computed tomography (micro-CT) data is essential to tasks such as statistical process control and the validation of radiographic simulation tools. The data present unique challenges to variability analysis due to the relatively low resolution of radiographs, and also due to minor variations from run to run which can result in misalignment or magnification changes between repeated measurements of a sample. Positioning changes artificially inflate the variability of the data in ways that mask true physical phenomena. We present a novel Bayesian nonparametric regression model that incorporates both additive and multiplicative measurement error inmore » addition to heteroscedasticity to address this problem. We also use this model to assess the effects of sample thickness and sample position on measurement variability for an aluminum specimen. Supplementary materials for this article are available online.« less

On Some Assumptions of the Null Hypothesis Statistical Testing

ERIC Educational Resources Information Center

Patriota, Alexandre Galvão

2017-01-01

Bayesian and classical statistical approaches are based on different types of logical principles. In order to avoid mistaken inferences and misguided interpretations, the practitioner must respect the inference rules embedded into each statistical method. Ignoring these principles leads to the paradoxical conclusions that the hypothesis…

Advances in statistics

Treesearch

Howard Stauffer; Nadav Nur

2005-01-01

The papers included in the Advances in Statistics section of the Partners in Flight (PIF) 2002 Proceedings represent a small sample of statistical topics of current importance to Partners In Flight research scientists: hierarchical modeling, estimation of detection probabilities, and Bayesian applications. Sauer et al. (this volume) examines a hierarchical model...

A review and comparison of Bayesian and likelihood-based inferences in beta regression and zero-or-one-inflated beta regression.

PubMed

Liu, Fang; Eugenio, Evercita C

2018-04-01

Beta regression is an increasingly popular statistical technique in medical research for modeling of outcomes that assume values in (0, 1), such as proportions and patient reported outcomes. When outcomes take values in the intervals [0,1), (0,1], or [0,1], zero-or-one-inflated beta (zoib) regression can be used. We provide a thorough review on beta regression and zoib regression in the modeling, inferential, and computational aspects via the likelihood-based and Bayesian approaches. We demonstrate the statistical and practical importance of correctly modeling the inflation at zero/one rather than ad hoc replacing them with values close to zero/one via simulation studies; the latter approach can lead to biased estimates and invalid inferences. We show via simulation studies that the likelihood-based approach is computationally faster in general than MCMC algorithms used in the Bayesian inferences, but runs the risk of non-convergence, large biases, and sensitivity to starting values in the optimization algorithm especially with clustered/correlated data, data with sparse inflation at zero and one, and data that warrant regularization of the likelihood. The disadvantages of the regular likelihood-based approach make the Bayesian approach an attractive alternative in these cases. Software packages and tools for fitting beta and zoib regressions in both the likelihood-based and Bayesian frameworks are also reviewed.

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.

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

PubMed Central

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

2014-01-01

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

Incorporating historical information in biosimilar trials: Challenges and a hybrid Bayesian-frequentist approach.

PubMed

Mielke, Johanna; Schmidli, Heinz; Jones, Byron

2018-05-01

For the approval of biosimilars, it is, in most cases, necessary to conduct large Phase III clinical trials in patients to convince the regulatory authorities that the product is comparable in terms of efficacy and safety to the originator product. As the originator product has already been studied in several trials beforehand, it seems natural to include this historical information into the showing of equivalent efficacy. Since all studies for the regulatory approval of biosimilars are confirmatory studies, it is required that the statistical approach has reasonable frequentist properties, most importantly, that the Type I error rate is controlled-at least in all scenarios that are realistic in practice. However, it is well known that the incorporation of historical information can lead to an inflation of the Type I error rate in the case of a conflict between the distribution of the historical data and the distribution of the trial data. We illustrate this issue and confirm, using the Bayesian robustified meta-analytic-predictive (MAP) approach as an example, that simultaneously controlling the Type I error rate over the complete parameter space and gaining power in comparison to a standard frequentist approach that only considers the data in the new study, is not possible. We propose a hybrid Bayesian-frequentist approach for binary endpoints that controls the Type I error rate in the neighborhood of the center of the prior distribution, while improving the power. We study the properties of this approach in an extensive simulation study and provide a real-world example. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

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.

Bayesian depth estimation from monocular natural images.

PubMed

Su, Che-Chun; Cormack, Lawrence K; Bovik, Alan C

2017-05-01

Estimating an accurate and naturalistic dense depth map from a single monocular photographic image is a difficult problem. Nevertheless, human observers have little difficulty understanding the depth structure implied by photographs. Two-dimensional (2D) images of the real-world environment contain significant statistical information regarding the three-dimensional (3D) structure of the world that the vision system likely exploits to compute perceived depth, monocularly as well as binocularly. Toward understanding how this might be accomplished, we propose a Bayesian model of monocular depth computation that recovers detailed 3D scene structures by extracting reliable, robust, depth-sensitive statistical features from single natural images. These features are derived using well-accepted univariate natural scene statistics (NSS) models and recent bivariate/correlation NSS models that describe the relationships between 2D photographic images and their associated depth maps. This is accomplished by building a dictionary of canonical local depth patterns from which NSS features are extracted as prior information. The dictionary is used to create a multivariate Gaussian mixture (MGM) likelihood model that associates local image features with depth patterns. A simple Bayesian predictor is then used to form spatial depth estimates. The depth results produced by the model, despite its simplicity, correlate well with ground-truth depths measured by a current-generation terrestrial light detection and ranging (LIDAR) scanner. Such a strong form of statistical depth information could be used by the visual system when creating overall estimated depth maps incorporating stereopsis, accommodation, and other conditions. Indeed, even in isolation, the Bayesian predictor delivers depth estimates that are competitive with state-of-the-art "computer vision" methods that utilize highly engineered image features and sophisticated machine learning algorithms.

Model Selection and Psychological Theory: A Discussion of the Differences between the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)

ERIC Educational Resources Information Center

Vrieze, Scott I.

2012-01-01

This article reviews the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) in model selection and the appraisal of psychological theory. The focus is on latent variable models, given their growing use in theory testing and construction. Theoretical statistical results in regression are discussed, and more important…

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...

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring

Treesearch

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

2010-01-01

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...

Selecting Summary Statistics in Approximate Bayesian Computation for Calibrating Stochastic Models

PubMed Central

Burr, Tom

2013-01-01

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

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

PubMed

Burr, Tom; Skurikhin, Alexei

2013-01-01

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

UNITY: Confronting Supernova Cosmology's Statistical and Systematic Uncertainties in a Unified Bayesian Framework

NASA Astrophysics Data System (ADS)

Rubin, D.; Aldering, G.; Barbary, K.; Boone, K.; Chappell, G.; Currie, M.; Deustua, S.; Fagrelius, P.; Fruchter, A.; Hayden, B.; Lidman, C.; Nordin, J.; Perlmutter, S.; Saunders, C.; Sofiatti, C.; Supernova Cosmology Project, The

2015-11-01

While recent supernova (SN) cosmology research has benefited from improved measurements, current analysis approaches are not statistically optimal and will prove insufficient for future surveys. This paper discusses the limitations of current SN cosmological analyses in treating outliers, selection effects, shape- and color-standardization relations, unexplained dispersion, and heterogeneous observations. We present a new Bayesian framework, called UNITY (Unified Nonlinear Inference for Type-Ia cosmologY), that incorporates significant improvements in our ability to confront these effects. We apply the framework to real SN observations and demonstrate smaller statistical and systematic uncertainties. We verify earlier results that SNe Ia require nonlinear shape and color standardizations, but we now include these nonlinear relations in a statistically well-justified way. This analysis was primarily performed blinded, in that the basic framework was first validated on simulated data before transitioning to real data. We also discuss possible extensions of the method.

Hypothesis-Testing Demands Trustworthy Data—A Simulation Approach to Inferential Statistics Advocating the Research Program Strategy

PubMed Central

Krefeld-Schwalb, Antonia; Witte, Erich H.; Zenker, Frank

2018-01-01

In psychology as elsewhere, the main statistical inference strategy to establish empirical effects is null-hypothesis significance testing (NHST). The recent failure to replicate allegedly well-established NHST-results, however, implies that such results lack sufficient statistical power, and thus feature unacceptably high error-rates. Using data-simulation to estimate the error-rates of NHST-results, we advocate the research program strategy (RPS) as a superior methodology. RPS integrates Frequentist with Bayesian inference elements, and leads from a preliminary discovery against a (random) H0-hypothesis to a statistical H1-verification. Not only do RPS-results feature significantly lower error-rates than NHST-results, RPS also addresses key-deficits of a “pure” Frequentist and a standard Bayesian approach. In particular, RPS aggregates underpowered results safely. RPS therefore provides a tool to regain the trust the discipline had lost during the ongoing replicability-crisis. PMID:29740363

Hypothesis-Testing Demands Trustworthy Data-A Simulation Approach to Inferential Statistics Advocating the Research Program Strategy.

PubMed

Krefeld-Schwalb, Antonia; Witte, Erich H; Zenker, Frank

2018-01-01

In psychology as elsewhere, the main statistical inference strategy to establish empirical effects is null-hypothesis significance testing (NHST). The recent failure to replicate allegedly well-established NHST-results, however, implies that such results lack sufficient statistical power, and thus feature unacceptably high error-rates. Using data-simulation to estimate the error-rates of NHST-results, we advocate the research program strategy (RPS) as a superior methodology. RPS integrates Frequentist with Bayesian inference elements, and leads from a preliminary discovery against a (random) H 0 -hypothesis to a statistical H 1 -verification. Not only do RPS-results feature significantly lower error-rates than NHST-results, RPS also addresses key-deficits of a "pure" Frequentist and a standard Bayesian approach. In particular, RPS aggregates underpowered results safely. RPS therefore provides a tool to regain the trust the discipline had lost during the ongoing replicability-crisis.

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

DOE PAGES

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

2015-02-05

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

Bayesian integration and non-linear feedback control in a full-body motor task.

PubMed

Stevenson, Ian H; Fernandes, Hugo L; Vilares, Iris; Wei, Kunlin; Körding, Konrad P

2009-12-01

A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots) on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter) is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller). We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.

Controlling bias and inflation in epigenome- and transcriptome-wide association studies using the empirical null distribution.

PubMed

van Iterson, Maarten; van Zwet, Erik W; Heijmans, Bastiaan T

2017-01-27

We show that epigenome- and transcriptome-wide association studies (EWAS and TWAS) are prone to significant inflation and bias of test statistics, an unrecognized phenomenon introducing spurious findings if left unaddressed. Neither GWAS-based methodology nor state-of-the-art confounder adjustment methods completely remove bias and inflation. We propose a Bayesian method to control bias and inflation in EWAS and TWAS based on estimation of the empirical null distribution. Using simulations and real data, we demonstrate that our method maximizes power while properly controlling the false positive rate. We illustrate the utility of our method in large-scale EWAS and TWAS meta-analyses of age and smoking.

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

NASA Astrophysics Data System (ADS)

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

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

Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme

NASA Astrophysics Data System (ADS)

Bakoban, Rana A.

2017-08-01

The coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.

Bayesian Tracking of Emerging Epidemics Using Ensemble Optimal Statistical Interpolation

PubMed Central

Cobb, Loren; Krishnamurthy, Ashok; Mandel, Jan; Beezley, Jonathan D.

2014-01-01

We present a preliminary test of the Ensemble Optimal Statistical Interpolation (EnOSI) method for the statistical tracking of an emerging epidemic, with a comparison to its popular relative for Bayesian data assimilation, the Ensemble Kalman Filter (EnKF). The spatial data for this test was generated by a spatial susceptible-infectious-removed (S-I-R) epidemic model of an airborne infectious disease. Both tracking methods in this test employed Poisson rather than Gaussian noise, so as to handle epidemic data more accurately. The EnOSI and EnKF tracking methods worked well on the main body of the simulated spatial epidemic, but the EnOSI was able to detect and track a distant secondary focus of infection that the EnKF missed entirely. PMID:25113590

Understanding Short-Term Nonmigrating Tidal Variability in the Ionospheric Dynamo Region from SABER Using Information Theory and Bayesian Statistics

NASA Astrophysics Data System (ADS)

Kumari, K.; Oberheide, J.

2017-12-01

Nonmigrating tidal diagnostics of SABER temperature observations in the ionospheric dynamo region reveal a large amount of variability on time-scales of a few days to weeks. In this paper, we discuss the physical reasons for the observed short-term tidal variability using a novel approach based on Information theory and Bayesian statistics. We diagnose short-term tidal variability as a function of season, QBO, ENSO, and solar cycle and other drivers using time dependent probability density functions, Shannon entropy and Kullback-Leibler divergence. The statistical significance of the approach and its predictive capability is exemplified using SABER tidal diagnostics with emphasis on the responses to the QBO and solar cycle. Implications for F-region plasma density will be discussed.

Factors contributing to academic achievement: a Bayesian structure equation modelling study

NASA Astrophysics Data System (ADS)

Payandeh Najafabadi, Amir T.; Omidi Najafabadi, Maryam; Farid-Rohani, Mohammad Reza

2013-06-01

In Iran, high school graduates enter university after taking a very difficult entrance exam called the Konkoor. Therefore, only the top-performing students are admitted by universities to continue their bachelor's education in statistics. Surprisingly, statistically, most of such students fall into the following categories: (1) do not succeed in their education despite their excellent performance on the Konkoor and in high school; (2) graduate with a grade point average (GPA) that is considerably lower than their high school GPA; (3) continue their master's education in majors other than statistics and (4) try to find jobs unrelated to statistics. This article employs the well-known and powerful statistical technique, the Bayesian structural equation modelling (SEM), to study the academic success of recent graduates who have studied statistics at Shahid Beheshti University in Iran. This research: (i) considered academic success as a latent variable, which was measured by GPA and other academic success (see below) of students in the target population; (ii) employed the Bayesian SEM, which works properly for small sample sizes and ordinal variables; (iii), which is taken from the literature, developed five main factors that affected academic success and (iv) considered several standard psychological tests and measured characteristics such as 'self-esteem' and 'anxiety'. We then study the impact of such factors on the academic success of the target population. Six factors that positively impact student academic success were identified in the following order of relative impact (from greatest to least): 'Teaching-Evaluation', 'Learner', 'Environment', 'Family', 'Curriculum' and 'Teaching Knowledge'. Particularly, influential variables within each factor have also been noted.

Spectral Analysis of B Stars: An Application of Bayesian Statistics

NASA Astrophysics Data System (ADS)

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

2012-12-01

To better understand the processes involved in stellar physics, it is necessary to obtain accurate stellar parameters (effective temperature, surface gravity, abundances…). Spectral analysis is a powerful tool for investigating stars, but it is also vital to reduce uncertainties at a decent computational cost. Here we present a spectral analysis method based on a combination of Bayesian statistics and grids of synthetic spectra obtained with TLUSTY. This method simultaneously constrains the stellar parameters by using all the lines accessible in observed spectra and thus greatly reduces uncertainties and improves the overall spectrum fitting. Preliminary results are shown using spectra from the Observatoire du Mont-Mégantic.

Suggestions for presenting the results of data analyses

USGS Publications Warehouse

Anderson, David R.; Link, William A.; Johnson, Douglas H.; Burnham, Kenneth P.

2001-01-01

We give suggestions for the presentation of research results from frequentist, information-theoretic, and Bayesian analysis paradigms, followed by several general suggestions. The information-theoretic and Bayesian methods offer alternative approaches to data analysis and inference compared to traditionally used methods. Guidance is lacking on the presentation of results under these alternative procedures and on nontesting aspects of classical frequentists methods of statistical analysis. Null hypothesis testing has come under intense criticism. We recommend less reporting of the results of statistical tests of null hypotheses in cases where the null is surely false anyway, or where the null hypothesis is of little interest to science or management.

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.

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

NASA Astrophysics Data System (ADS)

Kasibhatla, P.

2004-12-01

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

Embedding the results of focussed Bayesian fusion into a global context

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael

2014-05-01

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

Bayesian methods for the design and interpretation of clinical trials in very rare diseases

PubMed Central

Hampson, Lisa V; Whitehead, John; Eleftheriou, Despina; Brogan, Paul

2014-01-01

This paper considers the design and interpretation of clinical trials comparing treatments for conditions so rare that worldwide recruitment efforts are likely to yield total sample sizes of 50 or fewer, even when patients are recruited over several years. For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible. Rather, the expectation of any such trial has to be limited to the generation of an improved understanding of treatment options. We propose a Bayesian approach for the conduct of rare-disease trials comparing an experimental treatment with a control where patient responses are classified as a success or failure. A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters. The process of determining the prior is described, including the possibility of formally considering results from related trials. As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates. A number of allocation ratios between the two treatment groups can be considered with a view to maximising the prior probability that the trial concludes recommending the new treatment when in fact it is non-inferior to control. Consideration of the extent to which opinion can be changed, even by data from the best feasible design, can help to determine whether such a trial is worthwhile. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24957522

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

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

Population forecasts for Bangladesh, using a Bayesian methodology.

PubMed

Mahsin, Md; Hossain, Syed Shahadat

2012-12-01

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

Exoplanet Biosignatures: Future Directions.

PubMed

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

2018-06-01

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

Bayesian Networks for Modeling Dredging Decisions

DTIC Science & Technology

2011-10-01

change scenarios. Arctic Expert elicitation Netica Bacon et al . 2002 Identify factors that might lead to a change in land use from farming to...tree) algorithms developed by Lauritzen and Spiegelhalter (1988) and Jensen et al . (1990). Statistical inference is simply the process of...causality when constructing a Bayesian network (Kjaerulff and Madsen 2008, Darwiche 2009, Marcot et al . 2006). A knowledge representation approach is the

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors

PubMed Central

Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world’s deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014. PMID:28257437

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

PubMed

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

2017-01-01

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

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

PubMed Central

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

2017-01-01

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

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.

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.

Choosing the Optimal Number of B-spline Control Points (Part 1: Methodology and Approximation of Curves)

NASA Astrophysics Data System (ADS)

Harmening, Corinna; Neuner, Hans

2016-09-01

Due to the establishment of terrestrial laser scanner, the analysis strategies in engineering geodesy change from pointwise approaches to areal ones. These areal analysis strategies are commonly built on the modelling of the acquired point clouds. Freeform curves and surfaces like B-spline curves/surfaces are one possible approach to obtain space continuous information. A variety of parameters determines the B-spline's appearance; the B-spline's complexity is mostly determined by the number of control points. Usually, this number of control points is chosen quite arbitrarily by intuitive trial-and-error-procedures. In this paper, the Akaike Information Criterion and the Bayesian Information Criterion are investigated with regard to a justified and reproducible choice of the optimal number of control points of B-spline curves. Additionally, we develop a method which is based on the structural risk minimization of the statistical learning theory. Unlike the Akaike and the Bayesian Information Criteria this method doesn't use the number of parameters as complexity measure of the approximating functions but their Vapnik-Chervonenkis-dimension. Furthermore, it is also valid for non-linear models. Thus, the three methods differ in their target function to be minimized and consequently in their definition of optimality. The present paper will be continued by a second paper dealing with the choice of the optimal number of control points of B-spline surfaces.

Dealing with missing standard deviation and mean values in meta-analysis of continuous outcomes: a systematic review.

PubMed

Weir, Christopher J; Butcher, Isabella; Assi, Valentina; Lewis, Stephanie C; Murray, Gordon D; Langhorne, Peter; Brady, Marian C

2018-03-07

Rigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis. We undertook two systematic literature reviews to identify methodological approaches used to deal with missing mean or variability summary statistics. Five electronic databases were searched, in addition to the Cochrane Colloquium abstract books and the Cochrane Statistics Methods Group mailing list archive. We also conducted cited reference searching and emailed topic experts to identify recent methodological developments. Details recorded included the description of the method, the information required to implement the method, any underlying assumptions and whether the method could be readily applied in standard statistical software. We provided a summary description of the methods identified, illustrating selected methods in example meta-analysis scenarios. For missing standard deviations (SDs), following screening of 503 articles, fifteen methods were identified in addition to those reported in a previous review. These included Bayesian hierarchical modelling at the meta-analysis level; summary statistic level imputation based on observed SD values from other trials in the meta-analysis; a practical approximation based on the range; and algebraic estimation of the SD based on other summary statistics. Following screening of 1124 articles for methods estimating the mean, one approximate Bayesian computation approach and three papers based on alternative summary statistics were identified. Illustrative meta-analyses showed that when replacing a missing SD the approximation using the range minimised loss of precision and generally performed better than omitting trials. When estimating missing means, a formula using the median, lower quartile and upper quartile performed best in preserving the precision of the meta-analysis findings, although in some scenarios, omitting trials gave superior results. Methods based on summary statistics (minimum, maximum, lower quartile, upper quartile, median) reported in the literature facilitate more comprehensive inclusion of randomised controlled trials with missing mean or variability summary statistics within meta-analyses.

pyblocxs: Bayesian Low-Counts X-ray Spectral Analysis in Sherpa

NASA Astrophysics Data System (ADS)

Siemiginowska, A.; Kashyap, V.; Refsdal, B.; van Dyk, D.; Connors, A.; Park, T.

2011-07-01

Typical X-ray spectra have low counts and should be modeled using the Poisson distribution. However, χ2 statistic is often applied as an alternative and the data are assumed to follow the Gaussian distribution. A variety of weights to the statistic or a binning of the data is performed to overcome the low counts issues. However, such modifications introduce biases or/and a loss of information. Standard modeling packages such as XSPEC and Sherpa provide the Poisson likelihood and allow computation of rudimentary MCMC chains, but so far do not allow for setting a full Bayesian model. We have implemented a sophisticated Bayesian MCMC-based algorithm to carry out spectral fitting of low counts sources in the Sherpa environment. The code is a Python extension to Sherpa and allows to fit a predefined Sherpa model to high-energy X-ray spectral data and other generic data. We present the algorithm and discuss several issues related to the implementation, including flexible definition of priors and allowing for variations in the calibration information.

Estimation of Lithological Classification in Taipei Basin: A Bayesian Maximum Entropy Method

NASA Astrophysics Data System (ADS)

Wu, Meng-Ting; Lin, Yuan-Chien; Yu, Hwa-Lung

2015-04-01

In environmental or other scientific applications, we must have a certain understanding of geological lithological composition. Because of restrictions of real conditions, only limited amount of data can be acquired. To find out the lithological distribution in the study area, many spatial statistical methods used to estimate the lithological composition on unsampled points or grids. This study applied the Bayesian Maximum Entropy (BME method), which is an emerging method of the geological spatiotemporal statistics field. The BME method can identify the spatiotemporal correlation of the data, and combine not only the hard data but the soft data to improve estimation. The data of lithological classification is discrete categorical data. Therefore, this research applied Categorical BME to establish a complete three-dimensional Lithological estimation model. Apply the limited hard data from the cores and the soft data generated from the geological dating data and the virtual wells to estimate the three-dimensional lithological classification in Taipei Basin. Keywords: Categorical Bayesian Maximum Entropy method, Lithological Classification, Hydrogeological Setting

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

PubMed Central

Pérez Sánchez, Carlos Javier

2014-01-01

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

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

PubMed

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

2016-05-01

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

Bayesian analysis of the kinetics of quantal transmitter secretion at the neuromuscular junction.

PubMed

Saveliev, Anatoly; Khuzakhmetova, Venera; Samigullin, Dmitry; Skorinkin, Andrey; Kovyazina, Irina; Nikolsky, Eugeny; Bukharaeva, Ellya

2015-10-01

The timing of transmitter release from nerve endings is considered nowadays as one of the factors determining the plasticity and efficacy of synaptic transmission. In the neuromuscular junction, the moments of release of individual acetylcholine quanta are related to the synaptic delays of uniquantal endplate currents recorded under conditions of lowered extracellular calcium. Using Bayesian modelling, we performed a statistical analysis of synaptic delays in mouse neuromuscular junction with different patterns of rhythmic nerve stimulation and when the entry of calcium ions into the nerve terminal was modified. We have obtained a statistical model of the release timing which is represented as the summation of two independent statistical distributions. The first of these is the exponentially modified Gaussian distribution. The mixture of normal and exponential components in this distribution can be interpreted as a two-stage mechanism of early and late periods of phasic synchronous secretion. The parameters of this distribution depend on both the stimulation frequency of the motor nerve and the calcium ions' entry conditions. The second distribution was modelled as quasi-uniform, with parameters independent of nerve stimulation frequency and calcium entry. Two different probability density functions for the distribution of synaptic delays suggest at least two independent processes controlling the time course of secretion, one of them potentially involving two stages. The relative contribution of these processes to the total number of mediator quanta released depends differently on the motor nerve stimulation pattern and on calcium ion entry into nerve endings.

Bayesian selection of Markov models for symbol sequences: application to microsaccadic eye movements.

PubMed

Bettenbühl, Mario; Rusconi, Marco; Engbert, Ralf; Holschneider, Matthias

2012-01-01

Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.

The frequentist implications of optional stopping on Bayesian hypothesis tests.

PubMed

Sanborn, Adam N; Hills, Thomas T

2014-04-01

Null hypothesis significance testing (NHST) is the most commonly used statistical methodology in psychology. The probability of achieving a value as extreme or more extreme than the statistic obtained from the data is evaluated, and if it is low enough, the null hypothesis is rejected. However, because common experimental practice often clashes with the assumptions underlying NHST, these calculated probabilities are often incorrect. Most commonly, experimenters use tests that assume that sample sizes are fixed in advance of data collection but then use the data to determine when to stop; in the limit, experimenters can use data monitoring to guarantee that the null hypothesis will be rejected. Bayesian hypothesis testing (BHT) provides a solution to these ills because the stopping rule used is irrelevant to the calculation of a Bayes factor. In addition, there are strong mathematical guarantees on the frequentist properties of BHT that are comforting for researchers concerned that stopping rules could influence the Bayes factors produced. Here, we show that these guaranteed bounds have limited scope and often do not apply in psychological research. Specifically, we quantitatively demonstrate the impact of optional stopping on the resulting Bayes factors in two common situations: (1) when the truth is a combination of the hypotheses, such as in a heterogeneous population, and (2) when a hypothesis is composite-taking multiple parameter values-such as the alternative hypothesis in a t-test. We found that, for these situations, while the Bayesian interpretation remains correct regardless of the stopping rule used, the choice of stopping rule can, in some situations, greatly increase the chance of experimenters finding evidence in the direction they desire. We suggest ways to control these frequentist implications of stopping rules on BHT.

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

ABrox-A user-friendly Python module for approximate Bayesian computation with a focus on model comparison.

PubMed

Mertens, Ulf Kai; Voss, Andreas; Radev, Stefan

2018-01-01

We give an overview of the basic principles of approximate Bayesian computation (ABC), a class of stochastic methods that enable flexible and likelihood-free model comparison and parameter estimation. Our new open-source software called ABrox is used to illustrate ABC for model comparison on two prominent statistical tests, the two-sample t-test and the Levene-Test. We further highlight the flexibility of ABC compared to classical Bayesian hypothesis testing by computing an approximate Bayes factor for two multinomial processing tree models. Last but not least, throughout the paper, we introduce ABrox using the accompanied graphical user interface.

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

PubMed Central

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

2014-01-01

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

Comparison Between Linear and Non-parametric Regression Models for Genome-Enabled Prediction in Wheat

PubMed Central

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-01-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models. PMID:23275882

Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat.

PubMed

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-12-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.

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

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

Development of a Bayesian response-adaptive trial design for the Dexamethasone for Excessive Menstruation study.

PubMed

Holm Hansen, Christian; Warner, Pamela; Parker, Richard A; Walker, Brian R; Critchley, Hilary Od; Weir, Christopher J

2017-12-01

It is often unclear what specific adaptive trial design features lead to an efficient design which is also feasible to implement. This article describes the preparatory simulation study for a Bayesian response-adaptive dose-finding trial design. Dexamethasone for Excessive Menstruation aims to assess the efficacy of Dexamethasone in reducing excessive menstrual bleeding and to determine the best dose for further study. To maximise learning about the dose response, patients receive placebo or an active dose with randomisation probabilities adapting based on evidence from patients already recruited. The dose-response relationship is estimated using a flexible Bayesian Normal Dynamic Linear Model. Several competing design options were considered including: number of doses, proportion assigned to placebo, adaptation criterion, and number and timing of adaptations. We performed a fractional factorial study using SAS software to simulate virtual trial data for candidate adaptive designs under a variety of scenarios and to invoke WinBUGS for Bayesian model estimation. We analysed the simulated trial results using Normal linear models to estimate the effects of each design feature on empirical type I error and statistical power. Our readily-implemented approach using widely available statistical software identified a final design which performed robustly across a range of potential trial scenarios.

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.

Astrocytic tracer dynamics estimated from [1-¹¹C]-acetate PET measurements.

PubMed

Arnold, Andrea; Calvetti, Daniela; Gjedde, Albert; Iversen, Peter; Somersalo, Erkki

2015-12-01

We address the problem of estimating the unknown parameters of a model of tracer kinetics from sequences of positron emission tomography (PET) scan data using a statistical sequential algorithm for the inference of magnitudes of dynamic parameters. The method, based on Bayesian statistical inference, is a modification of a recently proposed particle filtering and sequential Monte Carlo algorithm, where instead of preassigning the accuracy in the propagation of each particle, we fix the time step and account for the numerical errors in the innovation term. We apply the algorithm to PET images of [1-¹¹C]-acetate-derived tracer accumulation, estimating the transport rates in a three-compartment model of astrocytic uptake and metabolism of the tracer for a cohort of 18 volunteers from 3 groups, corresponding to healthy control individuals, cirrhotic liver and hepatic encephalopathy patients. The distribution of the parameters for the individuals and for the groups presented within the Bayesian framework support the hypothesis that the parameters for the hepatic encephalopathy group follow a significantly different distribution than the other two groups. The biological implications of the findings are also discussed. © The Authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Bayesian evaluation of budgets for endemic disease control: An example using management changes to reduce milk somatic cell count early in the first lactation of Irish dairy cows.

PubMed

Archer, S C; Mc Coy, F; Wapenaar, W; Green, M J

2014-01-01

The aim of this research was to determine budgets for specific management interventions to control heifer mastitis in Irish dairy herds as an example of evidence synthesis and 1-step Bayesian micro-simulation in a veterinary context. Budgets were determined for different decision makers based on their willingness to pay. Reducing the prevalence of heifers with a high milk somatic cell count (SCC) early in the first lactation could be achieved through herd level management interventions for pre- and peri-partum heifers, however the cost effectiveness of these interventions is unknown. A synthesis of multiple sources of evidence, accounting for variability and uncertainty in the available data is invaluable to inform decision makers around likely economic outcomes of investing in disease control measures. One analytical approach to this is Bayesian micro-simulation, where the trajectory of different individuals undergoing specific interventions is simulated. The classic micro-simulation framework was extended to encompass synthesis of evidence from 2 separate statistical models and previous research, with the outcome for an individual cow or herd assessed in terms of changes in lifetime milk yield, disposal risk, and likely financial returns conditional on the interventions being simultaneously applied. The 3 interventions tested were storage of bedding inside, decreasing transition yard stocking density, and spreading of bedding evenly in the calving area. Budgets for the interventions were determined based on the minimum expected return on investment, and the probability of the desired outcome. Budgets for interventions to control heifer mastitis were highly dependent on the decision maker's willingness to pay, and hence minimum expected return on investment. Understanding the requirements of decision makers and their rational spending limits would be useful for the development of specific interventions for particular farms to control heifer mastitis, and other endemic diseases. Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.

Bayesian statistics and Monte Carlo methods

NASA Astrophysics Data System (ADS)

Koch, K. R.

2018-03-01

The Bayesian approach allows an intuitive way to derive the methods of statistics. Probability is defined as a measure of the plausibility of statements or propositions. Three rules are sufficient to obtain the laws of probability. If the statements refer to the numerical values of variables, the so-called random variables, univariate and multivariate distributions follow. They lead to the point estimation by which unknown quantities, i.e. unknown parameters, are computed from measurements. The unknown parameters are random variables, they are fixed quantities in traditional statistics which is not founded on Bayes' theorem. Bayesian statistics therefore recommends itself for Monte Carlo methods, which generate random variates from given distributions. Monte Carlo methods, of course, can also be applied in traditional statistics. The unknown parameters, are introduced as functions of the measurements, and the Monte Carlo methods give the covariance matrix and the expectation of these functions. A confidence region is derived where the unknown parameters are situated with a given probability. Following a method of traditional statistics, hypotheses are tested by determining whether a value for an unknown parameter lies inside or outside the confidence region. The error propagation of a random vector by the Monte Carlo methods is presented as an application. If the random vector results from a nonlinearly transformed vector, its covariance matrix and its expectation follow from the Monte Carlo estimate. This saves a considerable amount of derivatives to be computed, and errors of the linearization are avoided. The Monte Carlo method is therefore efficient. If the functions of the measurements are given by a sum of two or more random vectors with different multivariate distributions, the resulting distribution is generally not known. TheMonte Carlo methods are then needed to obtain the covariance matrix and the expectation of the sum.

High correlations between MRI brain volume measurements based on NeuroQuant® and FreeSurfer.

PubMed

Ross, David E; Ochs, Alfred L; Tate, David F; Tokac, Umit; Seabaugh, John; Abildskov, Tracy J; Bigler, Erin D

2018-05-30

NeuroQuant ® (NQ) and FreeSurfer (FS) are commonly used computer-automated programs for measuring MRI brain volume. Previously they were reported to have high intermethod reliabilities but often large intermethod effect size differences. We hypothesized that linear transformations could be used to reduce the large effect sizes. This study was an extension of our previously reported study. We performed NQ and FS brain volume measurements on 60 subjects (including normal controls, patients with traumatic brain injury, and patients with Alzheimer's disease). We used two statistical approaches in parallel to develop methods for transforming FS volumes into NQ volumes: traditional linear regression, and Bayesian linear regression. For both methods, we used regression analyses to develop linear transformations of the FS volumes to make them more similar to the NQ volumes. The FS-to-NQ transformations based on traditional linear regression resulted in effect sizes which were small to moderate. The transformations based on Bayesian linear regression resulted in all effect sizes being trivially small. To our knowledge, this is the first report describing a method for transforming FS to NQ data so as to achieve high reliability and low effect size differences. Machine learning methods like Bayesian regression may be more useful than traditional methods. Copyright © 2018 Elsevier B.V. All rights reserved.

Why Are People Bad at Detecting Randomness? A Statistical Argument

ERIC Educational Resources Information Center

Williams, Joseph J.; Griffiths, Thomas L.

2013-01-01

Errors in detecting randomness are often explained in terms of biases and misconceptions. We propose and provide evidence for an account that characterizes the contribution of the inherent statistical difficulty of the task. Our account is based on a Bayesian statistical analysis, focusing on the fact that a random process is a special case of…

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.

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.

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.

Learning what to expect (in visual perception)

PubMed Central

Seriès, Peggy; Seitz, Aaron R.

2013-01-01

Expectations are known to greatly affect our experience of the world. A growing theory in computational neuroscience is that perception can be successfully described using Bayesian inference models and that the brain is “Bayes-optimal” under some constraints. In this context, expectations are particularly interesting, because they can be viewed as prior beliefs in the statistical inference process. A number of questions remain unsolved, however, for example: How fast do priors change over time? Are there limits in the complexity of the priors that can be learned? How do an individual’s priors compare to the true scene statistics? Can we unlearn priors that are thought to correspond to natural scene statistics? Where and what are the neural substrate of priors? Focusing on the perception of visual motion, we here review recent studies from our laboratories and others addressing these issues. We discuss how these data on motion perception fit within the broader literature on perceptual Bayesian priors, perceptual expectations, and statistical and perceptual learning and review the possible neural basis of priors. PMID:24187536

Towards Validation of an Adaptive Flight Control Simulation Using Statistical Emulation

NASA Technical Reports Server (NTRS)

He, Yuning; Lee, Herbert K. H.; Davies, Misty D.

2012-01-01

Traditional validation of flight control systems is based primarily upon empirical testing. Empirical testing is sufficient for simple systems in which a.) the behavior is approximately linear and b.) humans are in-the-loop and responsible for off-nominal flight regimes. A different possible concept of operation is to use adaptive flight control systems with online learning neural networks (OLNNs) in combination with a human pilot for off-nominal flight behavior (such as when a plane has been damaged). Validating these systems is difficult because the controller is changing during the flight in a nonlinear way, and because the pilot and the control system have the potential to co-adapt in adverse ways traditional empirical methods are unlikely to provide any guarantees in this case. Additionally, the time it takes to find unsafe regions within the flight envelope using empirical testing means that the time between adaptive controller design iterations is large. This paper describes a new concept for validating adaptive control systems using methods based on Bayesian statistics. This validation framework allows the analyst to build nonlinear models with modal behavior, and to have an uncertainty estimate for the difference between the behaviors of the model and system under test.

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 pleiotropy-informed Bayesian false discovery rate adapted to a shared control design finds new disease associations from GWAS summary statistics.

PubMed

Liley, James; Wallace, Chris

2015-02-01

Genome-wide association studies (GWAS) have been successful in identifying single nucleotide polymorphisms (SNPs) associated with many traits and diseases. However, at existing sample sizes, these variants explain only part of the estimated heritability. Leverage of GWAS results from related phenotypes may improve detection without the need for larger datasets. The Bayesian conditional false discovery rate (cFDR) constitutes an upper bound on the expected false discovery rate (FDR) across a set of SNPs whose p values for two diseases are both less than two disease-specific thresholds. Calculation of the cFDR requires only summary statistics and have several advantages over traditional GWAS analysis. However, existing methods require distinct control samples between studies. Here, we extend the technique to allow for some or all controls to be shared, increasing applicability. Several different SNP sets can be defined with the same cFDR value, and we show that the expected FDR across the union of these sets may exceed expected FDR in any single set. We describe a procedure to establish an upper bound for the expected FDR among the union of such sets of SNPs. We apply our technique to pairwise analysis of p values from ten autoimmune diseases with variable sharing of controls, enabling discovery of 59 SNP-disease associations which do not reach GWAS significance after genomic control in individual datasets. Most of the SNPs we highlight have previously been confirmed using replication studies or larger GWAS, a useful validation of our technique; we report eight SNP-disease associations across five diseases not previously declared. Our technique extends and strengthens the previous algorithm, and establishes robust limits on the expected FDR. This approach can improve SNP detection in GWAS, and give insight into shared aetiology between phenotypically related conditions.

A Bayesian perspective on Markovian dynamics and the fluctuation theorem

NASA Astrophysics Data System (ADS)

Virgo, Nathaniel

2013-08-01

One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.

On compensation of mismatched recording conditions in the Bayesian approach for forensic automatic speaker recognition.

PubMed

Botti, F; Alexander, A; Drygajlo, A

2004-12-02

This paper deals with a procedure to compensate for mismatched recording conditions in forensic speaker recognition, using a statistical score normalization. Bayesian interpretation of the evidence in forensic automatic speaker recognition depends on three sets of recordings in order to perform forensic casework: reference (R) and control (C) recordings of the suspect, and a potential population database (P), as well as a questioned recording (QR) . The requirement of similar recording conditions between suspect control database (C) and the questioned recording (QR) is often not satisfied in real forensic cases. The aim of this paper is to investigate a procedure of normalization of scores, which is based on an adaptation of the Test-normalization (T-norm) [2] technique used in the speaker verification domain, to compensate for the mismatch. Polyphone IPSC-02 database and ASPIC (an automatic speaker recognition system developed by EPFL and IPS-UNIL in Lausanne, Switzerland) were used in order to test the normalization procedure. Experimental results for three different recording condition scenarios are presented using Tippett plots and the effect of the compensation on the evaluation of the strength of the evidence is discussed.

Bayesian Nonparametric Prediction and Statistical Inference

DTIC Science & Technology

1989-09-07

Kadane, J. (1980), "Bayesian decision theory and the sim- plification of models," in Evaluation of Econometric Models, J. Kmenta and J. Ramsey , eds...the random model and weighted least squares regression," in Evaluation of Econometric Models, ed. by J. Kmenta and J. Ramsey , Academic Press, 197-217...likelihood function. On the other hand, H. Jeffreys’s theory of hypothesis testing covers the most important situations in which the prior is not diffuse. See

Bayesian inference and decision theory - A framework for decision making in natural resource management

USGS Publications Warehouse

Dorazio, R.M.; Johnson, F.A.

2003-01-01

Bayesian inference and decision theory may be used in the solution of relatively complex problems of natural resource management, owing to recent advances in statistical theory and computing. In particular, Markov chain Monte Carlo algorithms provide a computational framework for fitting models of adequate complexity and for evaluating the expected consequences of alternative management actions. We illustrate these features using an example based on management of waterfowl habitat.

Predicting coastal cliff erosion using a Bayesian probabilistic model

USGS Publications Warehouse

Hapke, Cheryl J.; Plant, Nathaniel G.

2010-01-01

Regional coastal cliff retreat is difficult to model due to the episodic nature of failures and the along-shore variability of retreat events. There is a growing demand, however, for predictive models that can be used to forecast areas vulnerable to coastal erosion hazards. Increasingly, probabilistic models are being employed that require data sets of high temporal density to define the joint probability density function that relates forcing variables (e.g. wave conditions) and initial conditions (e.g. cliff geometry) to erosion events. In this study we use a multi-parameter Bayesian network to investigate correlations between key variables that control and influence variations in cliff retreat processes. The network uses Bayesian statistical methods to estimate event probabilities using existing observations. Within this framework, we forecast the spatial distribution of cliff retreat along two stretches of cliffed coast in Southern California. The input parameters are the height and slope of the cliff, a descriptor of material strength based on the dominant cliff-forming lithology, and the long-term cliff erosion rate that represents prior behavior. The model is forced using predicted wave impact hours. Results demonstrate that the Bayesian approach is well-suited to the forward modeling of coastal cliff retreat, with the correct outcomes forecast in 70–90% of the modeled transects. The model also performs well in identifying specific locations of high cliff erosion, thus providing a foundation for hazard mapping. This approach can be employed to predict cliff erosion at time-scales ranging from storm events to the impacts of sea-level rise at the century-scale.

Combining statistical inference and decisions in ecology

USGS Publications Warehouse

Williams, Perry J.; Hooten, Mevin B.

2016-01-01

Statistical decision theory (SDT) is a sub-field of decision theory that formally incorporates statistical investigation into a decision-theoretic framework to account for uncertainties in a decision problem. SDT provides a unifying analysis of three types of information: statistical results from a data set, knowledge of the consequences of potential choices (i.e., loss), and prior beliefs about a system. SDT links the theoretical development of a large body of statistical methods including point estimation, hypothesis testing, and confidence interval estimation. The theory and application of SDT have mainly been developed and published in the fields of mathematics, statistics, operations research, and other decision sciences, but have had limited exposure in ecology. Thus, we provide an introduction to SDT for ecologists and describe its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework. We describe the basic framework of both Bayesian and frequentist SDT, its traditional use in statistics, and discuss its application to decision problems that occur in ecology. We demonstrate SDT with two types of decisions: Bayesian point estimation, and an applied management problem of selecting a prescribed fire rotation for managing a grassland bird species. Central to SDT, and decision theory in general, are loss functions. Thus, we also provide basic guidance and references for constructing loss functions for an SDT problem.

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.

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.

Noninformative prior in the quantum statistical model of pure states

NASA Astrophysics Data System (ADS)

Tanaka, Fuyuhiko

2012-06-01

In the present paper, we consider a suitable definition of a noninformative prior on the quantum statistical model of pure states. While the full pure-states model is invariant under unitary rotation and admits the Haar measure, restricted models, which we often see in quantum channel estimation and quantum process tomography, have less symmetry and no compelling rationale for any choice. We adopt a game-theoretic approach that is applicable to classical Bayesian statistics and yields a noninformative prior for a general class of probability distributions. We define the quantum detection game and show that there exist noninformative priors for a general class of a pure-states model. Theoretically, it gives one of the ways that we represent ignorance on the given quantum system with partial information. Practically, our method proposes a default distribution on the model in order to use the Bayesian technique in the quantum-state tomography with a small sample.

BATMAN: Bayesian Technique for Multi-image Analysis

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

PubMed Central

2012-01-01

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

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

PubMed

Adrion, Christine; Mansmann, Ulrich

2012-09-10

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

Comparing Trend and Gap Statistics across Tests: Distributional Change Using Ordinal Methods and Bayesian Inference

ERIC Educational Resources Information Center

Denbleyker, John Nickolas

2012-01-01

The shortcomings of the proportion above cut (PAC) statistic used so prominently in the educational landscape renders it a very problematic measure for making correct inferences with student test data. The limitations of PAC-based statistics are more pronounced with cross-test comparisons due to their dependency on cut-score locations. A better…

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.

Prediction of Individual Serum Infliximab Concentrations in Inflammatory Bowel Disease by a Bayesian Dashboard System.

PubMed

Eser, Alexander; Primas, Christian; Reinisch, Sieglinde; Vogelsang, Harald; Novacek, Gottfried; Mould, Diane R; Reinisch, Walter

2018-01-30

Despite a robust exposure-response relationship of infliximab in inflammatory bowel disease (IBD), attempts to adjust dosing to individually predicted serum concentrations of infliximab (SICs) are lacking. Compared with labor-intensive conventional software for pharmacokinetic (PK) modeling (eg, NONMEM) dashboards are easy-to-use programs incorporating complex Bayesian statistics to determine individual pharmacokinetics. We evaluated various infliximab detection assays and the number of samples needed to precisely forecast individual SICs using a Bayesian dashboard. We assessed long-term infliximab retention in patients being dosed concordantly versus discordantly with Bayesian dashboard recommendations. Three hundred eighty-two serum samples from 117 adult IBD patients on infliximab maintenance therapy were analyzed by 3 commercially available assays. Data from each assay was modeled using NONMEM and a Bayesian dashboard. PK parameter precision and residual variability were assessed. Forecast concentrations from both systems were compared with observed concentrations. Infliximab retention was assessed by prediction for dose intensification via Bayesian dashboard versus real-life practice. Forecast precision of SICs varied between detection assays. At least 3 SICs from a reliable assay are needed for an accurate forecast. The Bayesian dashboard performed similarly to NONMEM to predict SICs. Patients dosed concordantly with Bayesian dashboard recommendations had a significantly longer median drug survival than those dosed discordantly (51.5 versus 4.6 months, P < .0001). The Bayesian dashboard helps to assess the diagnostic performance of infliximab detection assays. Three, not single, SICs provide sufficient information for individualized dose adjustment when incorporated into the Bayesian dashboard. Treatment adjusted to forecasted SICs is associated with longer drug retention of infliximab. © 2018, The American College of Clinical Pharmacology.

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.

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.

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

PubMed

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

2006-07-01

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

Bayesian analysis of CCDM models

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Bayesian learning of visual chunks by human observers

PubMed Central

Orbán, Gergő; Fiser, József; Aslin, Richard N.; Lengyel, Máté

2008-01-01

Efficient and versatile processing of any hierarchically structured information requires a learning mechanism that combines lower-level features into higher-level chunks. We investigated this chunking mechanism in humans with a visual pattern-learning paradigm. We developed an ideal learner based on Bayesian model comparison that extracts and stores only those chunks of information that are minimally sufficient to encode a set of visual scenes. Our ideal Bayesian chunk learner not only reproduced the results of a large set of previous empirical findings in the domain of human pattern learning but also made a key prediction that we confirmed experimentally. In accordance with Bayesian learning but contrary to associative learning, human performance was well above chance when pair-wise statistics in the exemplars contained no relevant information. Thus, humans extract chunks from complex visual patterns by generating accurate yet economical representations and not by encoding the full correlational structure of the input. PMID:18268353

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Predicting Rotator Cuff Tears Using Data Mining and Bayesian Likelihood Ratios

PubMed Central

Lu, Hsueh-Yi; Huang, Chen-Yuan; Su, Chwen-Tzeng; Lin, Chen-Chiang

2014-01-01

Objectives Rotator cuff tear is a common cause of shoulder diseases. Correct diagnosis of rotator cuff tears can save patients from further invasive, costly and painful tests. This study used predictive data mining and Bayesian theory to improve the accuracy of diagnosing rotator cuff tears by clinical examination alone. Methods In this retrospective study, 169 patients who had a preliminary diagnosis of rotator cuff tear on the basis of clinical evaluation followed by confirmatory MRI between 2007 and 2011 were identified. MRI was used as a reference standard to classify rotator cuff tears. The predictor variable was the clinical assessment results, which consisted of 16 attributes. This study employed 2 data mining methods (ANN and the decision tree) and a statistical method (logistic regression) to classify the rotator cuff diagnosis into “tear” and “no tear” groups. Likelihood ratio and Bayesian theory were applied to estimate the probability of rotator cuff tears based on the results of the prediction models. Results Our proposed data mining procedures outperformed the classic statistical method. The correction rate, sensitivity, specificity and area under the ROC curve of predicting a rotator cuff tear were statistical better in the ANN and decision tree models compared to logistic regression. Based on likelihood ratios derived from our prediction models, Fagan's nomogram could be constructed to assess the probability of a patient who has a rotator cuff tear using a pretest probability and a prediction result (tear or no tear). Conclusions Our predictive data mining models, combined with likelihood ratios and Bayesian theory, appear to be good tools to classify rotator cuff tears as well as determine the probability of the presence of the disease to enhance diagnostic decision making for rotator cuff tears. PMID:24733553

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 BAYESIAN STATISTICAL APPROACHES FOR THE EVALUATION OF CMAQ

EPA Science Inventory

This research focuses on the application of spatial statistical techniques for the evaluation of the Community Multiscale Air Quality (CMAQ) model. The upcoming release version of the CMAQ model was run for the calendar year 2001 and is in the process of being evaluated by EPA an...

Modeling Statistical Insensitivity: Sources of Suboptimal Behavior

ERIC Educational Resources Information Center

Gagliardi, Annie; Feldman, Naomi H.; Lidz, Jeffrey

2017-01-01

Children acquiring languages with noun classes (grammatical gender) have ample statistical information available that characterizes the distribution of nouns into these classes, but their use of this information to classify novel nouns differs from the predictions made by an optimal Bayesian classifier. We use rational analysis to investigate the…

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

PubMed

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

2004-01-01

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

Investigating the collision energy dependence of η /s in the beam energy scan at the BNL Relativistic Heavy Ion Collider using Bayesian statistics

NASA Astrophysics Data System (ADS)

Auvinen, Jussi; Bernhard, Jonah E.; Bass, Steffen A.; Karpenko, Iurii

2018-04-01

We determine the probability distributions of the shear viscosity over the entropy density ratio η /s in the quark-gluon plasma formed in Au + Au collisions at √{sN N}=19.6 ,39 , and 62.4 GeV , using Bayesian inference and Gaussian process emulators for a model-to-data statistical analysis that probes the full input parameter space of a transport + viscous hydrodynamics hybrid model. We find the most likely value of η /s to be larger at smaller √{sN N}, although the uncertainties still allow for a constant value between 0.10 and 0.15 for the investigated collision energy range.

A robust bayesian estimate of the concordance correlation coefficient.

PubMed

Feng, Dai; Baumgartner, Richard; Svetnik, Vladimir

2015-01-01

A need for assessment of agreement arises in many situations including statistical biomarker qualification or assay or method validation. Concordance correlation coefficient (CCC) is one of the most popular scaled indices reported in evaluation of agreement. Robust methods for CCC estimation currently present an important statistical challenge. Here, we propose a novel Bayesian method of robust estimation of CCC based on multivariate Student's t-distribution and compare it with its alternatives. Furthermore, we extend the method to practically relevant settings, enabling incorporation of confounding covariates and replications. The superiority of the new approach is demonstrated using simulation as well as real datasets from biomarker application in electroencephalography (EEG). This biomarker is relevant in neuroscience for development of treatments for insomnia.

Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective

USGS Publications Warehouse

Barker, Richard J.; Link, William A.

2015-01-01

Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.

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.

Genome-wide regression and prediction with the BGLR statistical package.

PubMed

Pérez, Paulino; de los Campos, Gustavo

2014-10-01

Many modern genomic data analyses require implementing regressions where the number of parameters (p, e.g., the number of marker effects) exceeds sample size (n). Implementing these large-p-with-small-n regressions poses several statistical and computational challenges, some of which can be confronted using Bayesian methods. This approach allows integrating various parametric and nonparametric shrinkage and variable selection procedures in a unified and consistent manner. The BGLR R-package implements a large collection of Bayesian regression models, including parametric variable selection and shrinkage methods and semiparametric procedures (Bayesian reproducing kernel Hilbert spaces regressions, RKHS). The software was originally developed for genomic applications; however, the methods implemented are useful for many nongenomic applications as well. The response can be continuous (censored or not) or categorical (either binary or ordinal). The algorithm is based on a Gibbs sampler with scalar updates and the implementation takes advantage of efficient compiled C and Fortran routines. In this article we describe the methods implemented in BGLR, present examples of the use of the package, and discuss practical issues emerging in real-data analysis. Copyright © 2014 by the Genetics Society of America.

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%.

Application of Bayesian inference to the study of hierarchical organization in self-organized complex adaptive systems

NASA Astrophysics Data System (ADS)

Knuth, K. H.

2001-05-01

We consider the application of Bayesian inference to the study of self-organized structures in complex adaptive systems. In particular, we examine the distribution of elements, agents, or processes in systems dominated by hierarchical structure. We demonstrate that results obtained by Caianiello [1] on Hierarchical Modular Systems (HMS) can be found by applying Jaynes' Principle of Group Invariance [2] to a few key assumptions about our knowledge of hierarchical organization. Subsequent application of the Principle of Maximum Entropy allows inferences to be made about specific systems. The utility of the Bayesian method is considered by examining both successes and failures of the hierarchical model. We discuss how Caianiello's original statements suffer from the Mind Projection Fallacy [3] and we restate his assumptions thus widening the applicability of the HMS model. The relationship between inference and statistical physics, described by Jaynes [4], is reiterated with the expectation that this realization will aid the field of complex systems research by moving away from often inappropriate direct application of statistical mechanics to a more encompassing inferential methodology.

Mapping malaria risk among children in Côte d'Ivoire using Bayesian geo-statistical models.

PubMed

Raso, Giovanna; Schur, Nadine; Utzinger, Jürg; Koudou, Benjamin G; Tchicaya, Emile S; Rohner, Fabian; N'goran, Eliézer K; Silué, Kigbafori D; Matthys, Barbara; Assi, Serge; Tanner, Marcel; Vounatsou, Penelope

2012-05-09

In Côte d'Ivoire, an estimated 767,000 disability-adjusted life years are due to malaria, placing the country at position number 14 with regard to the global burden of malaria. Risk maps are important to guide control interventions, and hence, the aim of this study was to predict the geographical distribution of malaria infection risk in children aged <16 years in Côte d'Ivoire at high spatial resolution. Using different data sources, a systematic review was carried out to compile and geo-reference survey data on Plasmodium spp. infection prevalence in Côte d'Ivoire, focusing on children aged <16 years. The period from 1988 to 2007 was covered. A suite of Bayesian geo-statistical logistic regression models was fitted to analyse malaria risk. Non-spatial models with and without exchangeable random effect parameters were compared to stationary and non-stationary spatial models. Non-stationarity was modelled assuming that the underlying spatial process is a mixture of separate stationary processes in each ecological zone. The best fitting model based on the deviance information criterion was used to predict Plasmodium spp. infection risk for entire Côte d'Ivoire, including uncertainty. Overall, 235 data points at 170 unique survey locations with malaria prevalence data for individuals aged <16 years were extracted. Most data points (n = 182, 77.4%) were collected between 2000 and 2007. A Bayesian non-stationary regression model showed the best fit with annualized rainfall and maximum land surface temperature identified as significant environmental covariates. This model was used to predict malaria infection risk at non-sampled locations. High-risk areas were mainly found in the north-central and western area, while relatively low-risk areas were located in the north at the country border, in the north-east, in the south-east around Abidjan, and in the central-west between two high prevalence areas. The malaria risk map at high spatial resolution gives an important overview of the geographical distribution of the disease in Côte d'Ivoire. It is a useful tool for the national malaria control programme and can be utilized for spatial targeting of control interventions and rational resource allocation.

Mapping malaria risk among children in Côte d’Ivoire using Bayesian geo-statistical models

PubMed Central

2012-01-01

Background In Côte d’Ivoire, an estimated 767,000 disability-adjusted life years are due to malaria, placing the country at position number 14 with regard to the global burden of malaria. Risk maps are important to guide control interventions, and hence, the aim of this study was to predict the geographical distribution of malaria infection risk in children aged <16 years in Côte d’Ivoire at high spatial resolution. Methods Using different data sources, a systematic review was carried out to compile and geo-reference survey data on Plasmodium spp. infection prevalence in Côte d’Ivoire, focusing on children aged <16 years. The period from 1988 to 2007 was covered. A suite of Bayesian geo-statistical logistic regression models was fitted to analyse malaria risk. Non-spatial models with and without exchangeable random effect parameters were compared to stationary and non-stationary spatial models. Non-stationarity was modelled assuming that the underlying spatial process is a mixture of separate stationary processes in each ecological zone. The best fitting model based on the deviance information criterion was used to predict Plasmodium spp. infection risk for entire Côte d’Ivoire, including uncertainty. Results Overall, 235 data points at 170 unique survey locations with malaria prevalence data for individuals aged <16 years were extracted. Most data points (n = 182, 77.4%) were collected between 2000 and 2007. A Bayesian non-stationary regression model showed the best fit with annualized rainfall and maximum land surface temperature identified as significant environmental covariates. This model was used to predict malaria infection risk at non-sampled locations. High-risk areas were mainly found in the north-central and western area, while relatively low-risk areas were located in the north at the country border, in the north-east, in the south-east around Abidjan, and in the central-west between two high prevalence areas. Conclusion The malaria risk map at high spatial resolution gives an important overview of the geographical distribution of the disease in Côte d’Ivoire. It is a useful tool for the national malaria control programme and can be utilized for spatial targeting of control interventions and rational resource allocation. PMID:22571469

Efficient Algorithms for Bayesian Network Parameter Learning from Incomplete Data

DTIC Science & Technology

2015-07-01

Efficient Algorithms for Bayesian Network Parameter Learning from Incomplete Data Guy Van den Broeck∗ and Karthika Mohan∗ and Arthur Choi and Adnan ...notwithstanding any other provision of law , no person shall be subject to a penalty for failing to comply with a collection of information if it does...Wasserman, L. (2011). All of Statistics. Springer Science & Business Media. Yaramakala, S., & Margaritis, D. (2005). Speculative markov blanket discovery for optimal feature selection. In Proceedings of ICDM.

Inverse and forward modeling under uncertainty using MRE-based Bayesian approach

NASA Astrophysics Data System (ADS)

Hou, Z.; Rubin, Y.

2004-12-01

A stochastic inverse approach for subsurface characterization is proposed and applied to shallow vadose zone at a winery field site in north California and to a gas reservoir at the Ormen Lange field site in the North Sea. The approach is formulated in a Bayesian-stochastic framework, whereby the unknown parameters are identified in terms of their statistical moments or their probabilities. Instead of the traditional single-valued estimation /prediction provided by deterministic methods, the approach gives a probability distribution for an unknown parameter. This allows calculating the mean, the mode, and the confidence interval, which is useful for a rational treatment of uncertainty and its consequences. The approach also allows incorporating data of various types and different error levels, including measurements of state variables as well as information such as bounds on or statistical moments of the unknown parameters, which may represent prior information. To obtain minimally subjective prior probabilities required for the Bayesian approach, the principle of Minimum Relative Entropy (MRE) is employed. The approach is tested in field sites for flow parameters identification and soil moisture estimation in the vadose zone and for gas saturation estimation at great depth below the ocean floor. Results indicate the potential of coupling various types of field data within a MRE-based Bayesian formalism for improving the estimation of the parameters of interest.

Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems

NASA Technical Reports Server (NTRS)

He, Yuning; Davies, Misty Dawn

2014-01-01

The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries.

Statistical Symbolic Execution with Informed Sampling

NASA Technical Reports Server (NTRS)

Filieri, Antonio; Pasareanu, Corina S.; Visser, Willem; Geldenhuys, Jaco

2014-01-01

Symbolic execution techniques have been proposed recently for the probabilistic analysis of programs. These techniques seek to quantify the likelihood of reaching program events of interest, e.g., assert violations. They have many promising applications but have scalability issues due to high computational demand. To address this challenge, we propose a statistical symbolic execution technique that performs Monte Carlo sampling of the symbolic program paths and uses the obtained information for Bayesian estimation and hypothesis testing with respect to the probability of reaching the target events. To speed up the convergence of the statistical analysis, we propose Informed Sampling, an iterative symbolic execution that first explores the paths that have high statistical significance, prunes them from the state space and guides the execution towards less likely paths. The technique combines Bayesian estimation with a partial exact analysis for the pruned paths leading to provably improved convergence of the statistical analysis. We have implemented statistical symbolic execution with in- formed sampling in the Symbolic PathFinder tool. We show experimentally that the informed sampling obtains more precise results and converges faster than a purely statistical analysis and may also be more efficient than an exact symbolic analysis. When the latter does not terminate symbolic execution with informed sampling can give meaningful results under the same time and memory limits.

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.

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.

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

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

NASA Astrophysics Data System (ADS)

Cox, M.; Shirono, K.

2017-10-01

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

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

PubMed

Karabatsos, George

2017-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

Perspectives on the Use of Null Hypothesis Statistical Testing. Part III: the Various Nuts and Bolts of Statistical and Hypothesis Testing

ERIC Educational Resources Information Center

Marmolejo-Ramos, Fernando; Cousineau, Denis

2017-01-01

The number of articles showing dissatisfaction with the null hypothesis statistical testing (NHST) framework has been progressively increasing over the years. Alternatives to NHST have been proposed and the Bayesian approach seems to have achieved the highest amount of visibility. In this last part of the special issue, a few alternative…

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.

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.

Improving satellite-based PM2.5 estimates in China using Gaussian processes modeling in a Bayesian hierarchical setting.

PubMed

Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun

2017-08-01

Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM 2.5 is a promising way to fill the areas that are not covered by ground PM 2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM 2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM 2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R 2  = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM 2.5 estimates.

Bayesian inference for the spatio-temporal invasion of alien species.

PubMed

Cook, Alex; Marion, Glenn; Butler, Adam; Gibson, Gavin

2007-08-01

In this paper we develop a Bayesian approach to parameter estimation in a stochastic spatio-temporal model of the spread of invasive species across a landscape. To date, statistical techniques, such as logistic and autologistic regression, have outstripped stochastic spatio-temporal models in their ability to handle large numbers of covariates. Here we seek to address this problem by making use of a range of covariates describing the bio-geographical features of the landscape. Relative to regression techniques, stochastic spatio-temporal models are more transparent in their representation of biological processes. They also explicitly model temporal change, and therefore do not require the assumption that the species' distribution (or other spatial pattern) has already reached equilibrium as is often the case with standard statistical approaches. In order to illustrate the use of such techniques we apply them to the analysis of data detailing the spread of an invasive plant, Heracleum mantegazzianum, across Britain in the 20th Century using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitates statistical assessments of differences in the suitability of different habitat classes for H. mantegazzianum, and enables predictions of future spread to account for parametric uncertainty and system variability. Our results show that ignoring such covariate information may lead to biased estimates of key processes and implausible predictions of future distributions.

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

PubMed

Harrigan, George G; Harrison, Jay M

2012-01-01

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

Statistical analysis of textural features for improved classification of oral histopathological images.

PubMed

Muthu Rama Krishnan, M; Shah, Pratik; Chakraborty, Chandan; Ray, Ajoy K

2012-04-01

The objective of this paper is to provide an improved technique, which can assist oncopathologists in correct screening of oral precancerous conditions specially oral submucous fibrosis (OSF) with significant accuracy on the basis of collagen fibres in the sub-epithelial connective tissue. The proposed scheme is composed of collagen fibres segmentation, its textural feature extraction and selection, screening perfomance enhancement under Gaussian transformation and finally classification. In this study, collagen fibres are segmented on R,G,B color channels using back-probagation neural network from 60 normal and 59 OSF histological images followed by histogram specification for reducing the stain intensity variation. Henceforth, textural features of collgen area are extracted using fractal approaches viz., differential box counting and brownian motion curve . Feature selection is done using Kullback-Leibler (KL) divergence criterion and the screening performance is evaluated based on various statistical tests to conform Gaussian nature. Here, the screening performance is enhanced under Gaussian transformation of the non-Gaussian features using hybrid distribution. Moreover, the routine screening is designed based on two statistical classifiers viz., Bayesian classification and support vector machines (SVM) to classify normal and OSF. It is observed that SVM with linear kernel function provides better classification accuracy (91.64%) as compared to Bayesian classifier. The addition of fractal features of collagen under Gaussian transformation improves Bayesian classifier's performance from 80.69% to 90.75%. Results are here studied and discussed.

Uncertainty quantification for nuclear density functional theory and information content of new measurements.

PubMed

McDonnell, J D; Schunck, N; Higdon, D; Sarich, J; Wild, S M; Nazarewicz, W

2015-03-27

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. The example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

Automating approximate Bayesian computation by local linear regression.

PubMed

Thornton, Kevin R

2009-07-07

In several biological contexts, parameter inference often relies on computationally-intensive techniques. "Approximate Bayesian Computation", or ABC, methods based on summary statistics have become increasingly popular. A particular flavor of ABC based on using a linear regression to approximate the posterior distribution of the parameters, conditional on the summary statistics, is computationally appealing, yet no standalone tool exists to automate the procedure. Here, I describe a program to implement the method. The software package ABCreg implements the local linear-regression approach to ABC. The advantages are: 1. The code is standalone, and fully-documented. 2. The program will automatically process multiple data sets, and create unique output files for each (which may be processed immediately in R), facilitating the testing of inference procedures on simulated data, or the analysis of multiple data sets. 3. The program implements two different transformation methods for the regression step. 4. Analysis options are controlled on the command line by the user, and the program is designed to output warnings for cases where the regression fails. 5. The program does not depend on any particular simulation machinery (coalescent, forward-time, etc.), and therefore is a general tool for processing the results from any simulation. 6. The code is open-source, and modular.Examples of applying the software to empirical data from Drosophila melanogaster, and testing the procedure on simulated data, are shown. In practice, the ABCreg simplifies implementing ABC based on local-linear regression.

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

PubMed

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

2013-01-01

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

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 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.

Combining statistical inference and decisions in ecology.

PubMed

Williams, Perry J; Hooten, Mevin B

2016-09-01

Statistical decision theory (SDT) is a sub-field of decision theory that formally incorporates statistical investigation into a decision-theoretic framework to account for uncertainties in a decision problem. SDT provides a unifying analysis of three types of information: statistical results from a data set, knowledge of the consequences of potential choices (i.e., loss), and prior beliefs about a system. SDT links the theoretical development of a large body of statistical methods, including point estimation, hypothesis testing, and confidence interval estimation. The theory and application of SDT have mainly been developed and published in the fields of mathematics, statistics, operations research, and other decision sciences, but have had limited exposure in ecology. Thus, we provide an introduction to SDT for ecologists and describe its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework. We describe the basic framework of both Bayesian and frequentist SDT, its traditional use in statistics, and discuss its application to decision problems that occur in ecology. We demonstrate SDT with two types of decisions: Bayesian point estimation and an applied management problem of selecting a prescribed fire rotation for managing a grassland bird species. Central to SDT, and decision theory in general, are loss functions. Thus, we also provide basic guidance and references for constructing loss functions for an SDT problem. © 2016 by the Ecological Society of America.

Factors Contributing to Academic Achievement: A Bayesian Structure Equation Modelling Study

ERIC Educational Resources Information Center

Payandeh Najafabadi, Amir T.; Najafabadi, Maryam Omidi; Farid-Rohani, Mohammad Reza

2013-01-01

In Iran, high school graduates enter university after taking a very difficult entrance exam called the Konkoor. Therefore, only the top-performing students are admitted by universities to continue their bachelor's education in statistics. Surprisingly, statistically, most of such students fall into the following categories: (1) do not succeed in…

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.

The effect of wall thickness distribution on mechanical reliability and strength in unidirectional porous ceramics.

PubMed

Seuba, Jordi; Deville, Sylvain; Guizard, Christian; Stevenson, Adam J

2016-01-01

Macroporous ceramics exhibit an intrinsic strength variability caused by the random distribution of defects in their structure. However, the precise role of microstructural features, other than pore volume, on reliability is still unknown. Here, we analyze the applicability of the Weibull analysis to unidirectional macroporous yttria-stabilized-zirconia (YSZ) prepared by ice-templating. First, we performed crush tests on samples with controlled microstructural features with the loading direction parallel to the porosity. The compressive strength data were fitted using two different fitting techniques, ordinary least squares and Bayesian Markov Chain Monte Carlo, to evaluate whether Weibull statistics are an adequate descriptor of the strength distribution. The statistical descriptors indicated that the strength data are well described by the Weibull statistical approach, for both fitting methods used. Furthermore, we assess the effect of different microstructural features (volume, size, densification of the walls, and morphology) on Weibull modulus and strength. We found that the key microstructural parameter controlling reliability is wall thickness. In contrast, pore volume is the main parameter controlling the strength. The highest Weibull modulus ([Formula: see text]) and mean strength (198.2 MPa) were obtained for the samples with the smallest and narrowest wall thickness distribution (3.1 [Formula: see text]m) and lower pore volume (54.5%).

The effect of wall thickness distribution on mechanical reliability and strength in unidirectional porous ceramics

NASA Astrophysics Data System (ADS)

Seuba, Jordi; Deville, Sylvain; Guizard, Christian; Stevenson, Adam J.

2016-01-01

Macroporous ceramics exhibit an intrinsic strength variability caused by the random distribution of defects in their structure. However, the precise role of microstructural features, other than pore volume, on reliability is still unknown. Here, we analyze the applicability of the Weibull analysis to unidirectional macroporous yttria-stabilized-zirconia (YSZ) prepared by ice-templating. First, we performed crush tests on samples with controlled microstructural features with the loading direction parallel to the porosity. The compressive strength data were fitted using two different fitting techniques, ordinary least squares and Bayesian Markov Chain Monte Carlo, to evaluate whether Weibull statistics are an adequate descriptor of the strength distribution. The statistical descriptors indicated that the strength data are well described by the Weibull statistical approach, for both fitting methods used. Furthermore, we assess the effect of different microstructural features (volume, size, densification of the walls, and morphology) on Weibull modulus and strength. We found that the key microstructural parameter controlling reliability is wall thickness. In contrast, pore volume is the main parameter controlling the strength. The highest Weibull modulus (?) and mean strength (198.2 MPa) were obtained for the samples with the smallest and narrowest wall thickness distribution (3.1 ?m) and lower pore volume (54.5%).

Control charts for monitoring accumulating adverse event count frequencies from single and multiple blinded trials.

PubMed

Gould, A Lawrence

2016-12-30

Conventional practice monitors accumulating information about drug safety in terms of the numbers of adverse events reported from trials in a drug development program. Estimates of between-treatment adverse event risk differences can be obtained readily from unblinded trials with adjustment for differences among trials using conventional statistical methods. Recent regulatory guidelines require monitoring the cumulative frequency of adverse event reports to identify possible between-treatment adverse event risk differences without unblinding ongoing trials. Conventional statistical methods for assessing between-treatment adverse event risks cannot be applied when the trials are blinded. However, CUSUM charts can be used to monitor the accumulation of adverse event occurrences. CUSUM charts for monitoring adverse event occurrence in a Bayesian paradigm are based on assumptions about the process generating the adverse event counts in a trial as expressed by informative prior distributions. This article describes the construction of control charts for monitoring adverse event occurrence based on statistical models for the processes, characterizes their statistical properties, and describes how to construct useful prior distributions. Application of the approach to two adverse events of interest in a real trial gave nearly identical results for binomial and Poisson observed event count likelihoods. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Optimal speech motor control and token-to-token variability: a Bayesian modeling approach.

PubMed

Patri, Jean-François; Diard, Julien; Perrier, Pascal

2015-12-01

The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way.

From Wald to Savage: homo economicus becomes a Bayesian statistician.

PubMed

Giocoli, Nicola

2013-01-01

Bayesian rationality is the paradigm of rational behavior in neoclassical economics. An economic agent is deemed rational when she maximizes her subjective expected utility and consistently revises her beliefs according to Bayes's rule. The paper raises the question of how, when and why this characterization of rationality came to be endorsed by mainstream economists. Though no definitive answer is provided, it is argued that the question is of great historiographic importance. The story begins with Abraham Wald's behaviorist approach to statistics and culminates with Leonard J. Savage's elaboration of subjective expected utility theory in his 1954 classic The Foundations of Statistics. The latter's acknowledged fiasco to achieve a reinterpretation of traditional inference techniques along subjectivist and behaviorist lines raises the puzzle of how a failed project in statistics could turn into such a big success in economics. Possible answers call into play the emphasis on consistency requirements in neoclassical theory and the impact of the postwar transformation of U.S. business schools. © 2012 Wiley Periodicals, Inc.

Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part III: Application to statistical modal analysis

NASA Astrophysics Data System (ADS)

Yan, Wang-Ji; Ren, Wei-Xin

2018-01-01

This study applies the theoretical findings of circularly-symmetric complex normal ratio distribution Yan and Ren (2016) [1,2] to transmissibility-based modal analysis from a statistical viewpoint. A probabilistic model of transmissibility function in the vicinity of the resonant frequency is formulated in modal domain, while some insightful comments are offered. It theoretically reveals that the statistics of transmissibility function around the resonant frequency is solely dependent on 'noise-to-signal' ratio and mode shapes. As a sequel to the development of the probabilistic model of transmissibility function in modal domain, this study poses the process of modal identification in the context of Bayesian framework by borrowing a novel paradigm. Implementation issues unique to the proposed approach are resolved by Lagrange multiplier approach. Also, this study explores the possibility of applying Bayesian analysis in distinguishing harmonic components and structural ones. The approaches are verified through simulated data and experimentally testing data. The uncertainty behavior due to variation of different factors is also discussed in detail.

Non-arbitrage in financial markets: A Bayesian approach for verification

NASA Astrophysics Data System (ADS)

Cerezetti, F. V.; Stern, Julio Michael

2012-10-01

The concept of non-arbitrage plays an essential role in finance theory. Under certain regularity conditions, the Fundamental Theorem of Asset Pricing states that, in non-arbitrage markets, prices of financial instruments are martingale processes. In this theoretical framework, the analysis of the statistical distributions of financial assets can assist in understanding how participants behave in the markets, and may or may not engender arbitrage conditions. Assuming an underlying Variance Gamma statistical model, this study aims to test, using the FBST - Full Bayesian Significance Test, if there is a relevant price difference between essentially the same financial asset traded at two distinct locations. Specifically, we investigate and compare the behavior of call options on the BOVESPA Index traded at (a) the Equities Segment and (b) the Derivatives Segment of BM&FBovespa. Our results seem to point out significant statistical differences. To what extent this evidence is actually the expression of perennial arbitrage opportunities is still an open question.

Revised standards for statistical evidence.

PubMed

Johnson, Valen E

2013-11-26

Recent advances in Bayesian hypothesis testing have led to the development of uniformly most powerful Bayesian tests, which represent an objective, default class of Bayesian hypothesis tests that have the same rejection regions as classical significance tests. Based on the correspondence between these two classes of tests, it is possible to equate the size of classical hypothesis tests with evidence thresholds in Bayesian tests, and to equate P values with Bayes factors. An examination of these connections suggest that recent concerns over the lack of reproducibility of scientific studies can be attributed largely to the conduct of significance tests at unjustifiably high levels of significance. To correct this problem, evidence thresholds required for the declaration of a significant finding should be increased to 25-50:1, and to 100-200:1 for the declaration of a highly significant finding. In terms of classical hypothesis tests, these evidence standards mandate the conduct of tests at the 0.005 or 0.001 level of significance.

Confidence of compliance: a Bayesian approach for percentile standards.

PubMed

McBride, G B; Ellis, J C

2001-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2005-10-01

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

Bayesian networks for evaluation of evidence from forensic entomology.

PubMed

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

2013-09-01

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

Randomized clinical trials in implant therapy: relationships among methodological, statistical, clinical, paratextual features and number of citations.

PubMed

Nieri, Michele; Clauser, Carlo; Franceschi, Debora; Pagliaro, Umberto; Saletta, Daniele; Pini-Prato, Giovanpaolo

2007-08-01

The aim of the present study was to investigate the relationships among reported methodological, statistical, clinical and paratextual variables of randomized clinical trials (RCTs) in implant therapy, and their influence on subsequent research. The material consisted of the RCTs in implant therapy published through the end of the year 2000. Methodological, statistical, clinical and paratextual features of the articles were assessed and recorded. The perceived clinical relevance was subjectively evaluated by an experienced clinician on anonymous abstracts. The impact on research was measured by the number of citations found in the Science Citation Index. A new statistical technique (Structural learning of Bayesian Networks) was used to assess the relationships among the considered variables. Descriptive statistics revealed that the reported methodology and statistics of RCTs in implant therapy were defective. Follow-up of the studies was generally short. The perceived clinical relevance appeared to be associated with the objectives of the studies and with the number of published images in the original articles. The impact on research was related to the nationality of the involved institutions and to the number of published images. RCTs in implant therapy (until 2000) show important methodological and statistical flaws and may not be appropriate for guiding clinicians in their practice. The methodological and statistical quality of the studies did not appear to affect their impact on practice and research. Bayesian Networks suggest new and unexpected relationships among the methodological, statistical, clinical and paratextual features of RCTs.

ANUBIS: artificial neuromodulation using a Bayesian inference system.

PubMed

Smith, Benjamin J H; Saaj, Chakravarthini M; Allouis, Elie

2013-01-01

Gain tuning is a crucial part of controller design and depends not only on an accurate understanding of the system in question, but also on the designer's ability to predict what disturbances and other perturbations the system will encounter throughout its operation. This letter presents ANUBIS (artificial neuromodulation using a Bayesian inference system), a novel biologically inspired technique for automatically tuning controller parameters in real time. ANUBIS is based on the Bayesian brain concept and modifies it by incorporating a model of the neuromodulatory system comprising four artificial neuromodulators. It has been applied to the controller of EchinoBot, a prototype walking rover for Martian exploration. ANUBIS has been implemented at three levels of the controller; gait generation, foot trajectory planning using Bézier curves, and foot trajectory tracking using a terminal sliding mode controller. We compare the results to a similar system that has been tuned using a multilayer perceptron. The use of Bayesian inference means that the system retains mathematical interpretability, unlike other intelligent tuning techniques, which use neural networks, fuzzy logic, or evolutionary algorithms. The simulation results show that ANUBIS provides significant improvements in efficiency and adaptability of the three controller components; it allows the robot to react to obstacles and uncertainties faster than the system tuned with the MLP, while maintaining stability and accuracy. As well as advancing rover autonomy, ANUBIS could also be applied to other situations where operating conditions are likely to change or cannot be accurately modeled in advance, such as process control. In addition, it demonstrates one way in which neuromodulation could fit into the Bayesian brain framework.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Nonlinear Bayesian filtering and learning: a neuronal dynamics for perception.

PubMed

Kutschireiter, Anna; Surace, Simone Carlo; Sprekeler, Henning; Pfister, Jean-Pascal

2017-08-18

The robust estimation of dynamical hidden features, such as the position of prey, based on sensory inputs is one of the hallmarks of perception. This dynamical estimation can be rigorously formulated by nonlinear Bayesian filtering theory. Recent experimental and behavioral studies have shown that animals' performance in many tasks is consistent with such a Bayesian statistical interpretation. However, it is presently unclear how a nonlinear Bayesian filter can be efficiently implemented in a network of neurons that satisfies some minimum constraints of biological plausibility. Here, we propose the Neural Particle Filter (NPF), a sampling-based nonlinear Bayesian filter, which does not rely on importance weights. We show that this filter can be interpreted as the neuronal dynamics of a recurrently connected rate-based neural network receiving feed-forward input from sensory neurons. Further, it captures properties of temporal and multi-sensory integration that are crucial for perception, and it allows for online parameter learning with a maximum likelihood approach. The NPF holds the promise to avoid the 'curse of dimensionality', and we demonstrate numerically its capability to outperform weighted particle filters in higher dimensions and when the number of particles is limited.

Bayesian networks in neuroscience: a survey.

PubMed

Bielza, Concha; Larrañaga, Pedro

2014-01-01

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

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

PubMed Central

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

2016-01-01

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

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 networks in neuroscience: a survey

PubMed Central

Bielza, Concha; Larrañaga, Pedro

2014-01-01

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

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.

On the blind use of statistical tools in the analysis of globular cluster stars

NASA Astrophysics Data System (ADS)

D'Antona, Francesca; Caloi, Vittoria; Tailo, Marco

2018-04-01

As with most data analysis methods, the Bayesian method must be handled with care. We show that its application to determine stellar evolution parameters within globular clusters can lead to paradoxical results if used without the necessary precautions. This is a cautionary tale on the use of statistical tools for big data analysis.

Quantifying falsifiability of scientific theories

NASA Astrophysics Data System (ADS)

Nemenman, Ilya

I argue that the notion of falsifiability, a key concept in defining a valid scientific theory, can be quantified using Bayesian Model Selection, which is a standard tool in modern statistics. This relates falsifiability to the quantitative version of the statistical Occam's razor, and allows transforming some long-running arguments about validity of scientific theories from philosophical discussions to rigorous mathematical calculations.

Bayesian models for cost-effectiveness analysis in the presence of structural zero costs

PubMed Central

Baio, Gianluca

2014-01-01

Bayesian modelling for cost-effectiveness data has received much attention in both the health economics and the statistical literature, in recent years. Cost-effectiveness data are characterised by a relatively complex structure of relationships linking a suitable measure of clinical benefit (e.g. quality-adjusted life years) and the associated costs. Simplifying assumptions, such as (bivariate) normality of the underlying distributions, are usually not granted, particularly for the cost variable, which is characterised by markedly skewed distributions. In addition, individual-level data sets are often characterised by the presence of structural zeros in the cost variable. Hurdle models can be used to account for the presence of excess zeros in a distribution and have been applied in the context of cost data. We extend their application to cost-effectiveness data, defining a full Bayesian specification, which consists of a model for the individual probability of null costs, a marginal model for the costs and a conditional model for the measure of effectiveness (given the observed costs). We presented the model using a working example to describe its main features. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24343868

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.

Bayesian models for cost-effectiveness analysis in the presence of structural zero costs.

PubMed

Baio, Gianluca

2014-05-20

Bayesian modelling for cost-effectiveness data has received much attention in both the health economics and the statistical literature, in recent years. Cost-effectiveness data are characterised by a relatively complex structure of relationships linking a suitable measure of clinical benefit (e.g. quality-adjusted life years) and the associated costs. Simplifying assumptions, such as (bivariate) normality of the underlying distributions, are usually not granted, particularly for the cost variable, which is characterised by markedly skewed distributions. In addition, individual-level data sets are often characterised by the presence of structural zeros in the cost variable. Hurdle models can be used to account for the presence of excess zeros in a distribution and have been applied in the context of cost data. We extend their application to cost-effectiveness data, defining a full Bayesian specification, which consists of a model for the individual probability of null costs, a marginal model for the costs and a conditional model for the measure of effectiveness (given the observed costs). We presented the model using a working example to describe its main features. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

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.

SIG-VISA: Signal-based Vertically Integrated Seismic Monitoring

NASA Astrophysics Data System (ADS)

Moore, D.; Mayeda, K. M.; Myers, S. C.; Russell, S.

2013-12-01

Traditional seismic monitoring systems rely on discrete detections produced by station processing software; however, while such detections may constitute a useful summary of station activity, they discard large amounts of information present in the original recorded signal. We present SIG-VISA (Signal-based Vertically Integrated Seismic Analysis), a system for seismic monitoring through Bayesian inference on seismic signals. By directly modeling the recorded signal, our approach incorporates additional information unavailable to detection-based methods, enabling higher sensitivity and more accurate localization using techniques such as waveform matching. SIG-VISA's Bayesian forward model of seismic signal envelopes includes physically-derived models of travel times and source characteristics as well as Gaussian process (kriging) statistical models of signal properties that combine interpolation of historical data with extrapolation of learned physical trends. Applying Bayesian inference, we evaluate the model on earthquakes as well as the 2009 DPRK test event, demonstrating a waveform matching effect as part of the probabilistic inference, along with results on event localization and sensitivity. In particular, we demonstrate increased sensitivity from signal-based modeling, in which the SIGVISA signal model finds statistical evidence for arrivals even at stations for which the IMS station processing failed to register any detection.

Bayesian Atmospheric Radiative Transfer (BART) Code and Application to WASP-43b

NASA Astrophysics Data System (ADS)

Blecic, Jasmina; Harrington, Joseph; Cubillos, Patricio; Bowman, Oliver; Rojo, Patricio; Stemm, Madison; Lust, Nathaniel B.; Challener, Ryan; Foster, Austin James; Foster, Andrew S.; Blumenthal, Sarah D.; Bruce, Dylan

2016-01-01

We present a new open-source Bayesian radiative-transfer framework, Bayesian Atmospheric Radiative Transfer (BART, https://github.com/exosports/BART), and its application to WASP-43b. BART initializes a model for the atmospheric retrieval calculation, generates thousands of theoretical model spectra using parametrized pressure and temperature profiles and line-by-line radiative-transfer calculation, and employs a statistical package to compare the models with the observations. It consists of three self-sufficient modules available to the community under the reproducible-research license, the Thermochemical Equilibrium Abundances module (TEA, https://github.com/dzesmin/TEA, Blecic et al. 2015}, the radiative-transfer module (Transit, https://github.com/exosports/transit), and the Multi-core Markov-chain Monte Carlo statistical module (MCcubed, https://github.com/pcubillos/MCcubed, Cubillos et al. 2015). We applied BART on all available WASP-43b secondary eclipse data from the space- and ground-based observations constraining the temperature-pressure profile and molecular abundances of the dayside atmosphere of WASP-43b. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G. JB holds a NASA Earth and Space Science Fellowship.

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.

A Bayesian-frequentist two-stage single-arm phase II clinical trial design.

PubMed

Dong, Gaohong; Shih, Weichung Joe; Moore, Dirk; Quan, Hui; Marcella, Stephen

2012-08-30

It is well-known that both frequentist and Bayesian clinical trial designs have their own advantages and disadvantages. To have better properties inherited from these two types of designs, we developed a Bayesian-frequentist two-stage single-arm phase II clinical trial design. This design allows both early acceptance and rejection of the null hypothesis ( H(0) ). The measures (for example probability of trial early termination, expected sample size, etc.) of the design properties under both frequentist and Bayesian settings are derived. Moreover, under the Bayesian setting, the upper and lower boundaries are determined with predictive probability of trial success outcome. Given a beta prior and a sample size for stage I, based on the marginal distribution of the responses at stage I, we derived Bayesian Type I and Type II error rates. By controlling both frequentist and Bayesian error rates, the Bayesian-frequentist two-stage design has special features compared with other two-stage designs. Copyright © 2012 John Wiley & Sons, Ltd.

Statistical methods for change-point detection in surface temperature records

NASA Astrophysics Data System (ADS)

Pintar, A. L.; Possolo, A.; Zhang, N. F.

2013-09-01

We describe several statistical methods to detect possible change-points in a time series of values of surface temperature measured at a meteorological station, and to assess the statistical significance of such changes, taking into account the natural variability of the measured values, and the autocorrelations between them. These methods serve to determine whether the record may suffer from biases unrelated to the climate signal, hence whether there may be a need for adjustments as considered by M. J. Menne and C. N. Williams (2009) "Homogenization of Temperature Series via Pairwise Comparisons", Journal of Climate 22 (7), 1700-1717. We also review methods to characterize patterns of seasonality (seasonal decomposition using monthly medians or robust local regression), and explain the role they play in the imputation of missing values, and in enabling robust decompositions of the measured values into a seasonal component, a possible climate signal, and a station-specific remainder. The methods for change-point detection that we describe include statistical process control, wavelet multi-resolution analysis, adaptive weights smoothing, and a Bayesian procedure, all of which are applicable to single station records.

Fisher's method of combining dependent statistics using generalizations of the gamma distribution with applications to genetic pleiotropic associations.

PubMed

Li, Qizhai; Hu, Jiyuan; Ding, Juan; Zheng, Gang

2014-04-01

A classical approach to combine independent test statistics is Fisher's combination of $p$-values, which follows the $\\chi ^2$ distribution. When the test statistics are dependent, the gamma distribution (GD) is commonly used for the Fisher's combination test (FCT). We propose to use two generalizations of the GD: the generalized and the exponentiated GDs. We study some properties of mis-using the GD for the FCT to combine dependent statistics when one of the two proposed distributions are true. Our results show that both generalizations have better control of type I error rates than the GD, which tends to have inflated type I error rates at more extreme tails. In practice, common model selection criteria (e.g. Akaike information criterion/Bayesian information criterion) can be used to help select a better distribution to use for the FCT. A simple strategy of the two generalizations of the GD in genome-wide association studies is discussed. Applications of the results to genetic pleiotrophic associations are described, where multiple traits are tested for association with a single marker.

Analyzing thresholds and efficiency with hierarchical Bayesian logistic regression.

PubMed

Houpt, Joseph W; Bittner, Jennifer L

2018-07-01

Ideal observer analysis is a fundamental tool used widely in vision science for analyzing the efficiency with which a cognitive or perceptual system uses available information. The performance of an ideal observer provides a formal measure of the amount of information in a given experiment. The ratio of human to ideal performance is then used to compute efficiency, a construct that can be directly compared across experimental conditions while controlling for the differences due to the stimuli and/or task specific demands. In previous research using ideal observer analysis, the effects of varying experimental conditions on efficiency have been tested using ANOVAs and pairwise comparisons. In this work, we present a model that combines Bayesian estimates of psychometric functions with hierarchical logistic regression for inference about both unadjusted human performance metrics and efficiencies. Our approach improves upon the existing methods by constraining the statistical analysis using a standard model connecting stimulus intensity to human observer accuracy and by accounting for variability in the estimates of human and ideal observer performance scores. This allows for both individual and group level inferences. Copyright © 2018 Elsevier Ltd. All rights reserved.

How can investment in the landscape or the interface reduce the risk of house loss from wildfires? A comparative study between Sydney, Australia and California, USA

NASA Astrophysics Data System (ADS)

Penman, Trent; Bradstock, Ross; Collins, Luke; Fotheringham, Cj; Keeley, Jon; Labiosa, Bill; Price, Owen; Syphard, Alex

2013-04-01

Wildfire can result in significant losses to people and property. Management agencies undertake a range of actions in the landscape and at the interface to reduce this risk. Data relating to the success of individual treatments varies, with some approaches well understood and others less so. Research has rarely attempted to consider the interactive effects of treatments in order to determine optimal management strategies that reduce the risk of loss. Bayesian Networks provide a statistical framework for undertaking such an analysis. Here we apply Bayesian Networks to examine the trade-offs in investment in preventative actions (e.g., fuel treatment, community education, development controls) and suppressive actions (e.g., initial attack, landscape suppression, property protection) in two fire prone regions -Sydney, Australia and California, USA. Investment in management actions at the interface resulted in the greatest reduction in the risk of house loss for both of the study regions. Landscape treatments had a limited ability to change the risk of house loss.

Bayesian Image Segmentations by Potts Prior and Loopy Belief Propagation

NASA Astrophysics Data System (ADS)

Tanaka, Kazuyuki; Kataoka, Shun; Yasuda, Muneki; Waizumi, Yuji; Hsu, Chiou-Ting

2014-12-01

This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in loopy belief propagations for Potts models influence our hyperparameter estimation procedures.

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

PubMed

Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W

2007-07-01

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

Cortical Hierarchies Perform Bayesian Causal Inference in Multisensory Perception

PubMed Central

Rohe, Tim; Noppeney, Uta

2015-01-01

To form a veridical percept of the environment, the brain needs to integrate sensory signals from a common source but segregate those from independent sources. Thus, perception inherently relies on solving the “causal inference problem.” Behaviorally, humans solve this problem optimally as predicted by Bayesian Causal Inference; yet, the underlying neural mechanisms are unexplored. Combining psychophysics, Bayesian modeling, functional magnetic resonance imaging (fMRI), and multivariate decoding in an audiovisual spatial localization task, we demonstrate that Bayesian Causal Inference is performed by a hierarchy of multisensory processes in the human brain. At the bottom of the hierarchy, in auditory and visual areas, location is represented on the basis that the two signals are generated by independent sources (= segregation). At the next stage, in posterior intraparietal sulcus, location is estimated under the assumption that the two signals are from a common source (= forced fusion). Only at the top of the hierarchy, in anterior intraparietal sulcus, the uncertainty about the causal structure of the world is taken into account and sensory signals are combined as predicted by Bayesian Causal Inference. Characterizing the computational operations of signal interactions reveals the hierarchical nature of multisensory perception in human neocortex. It unravels how the brain accomplishes Bayesian Causal Inference, a statistical computation fundamental for perception and cognition. Our results demonstrate how the brain combines information in the face of uncertainty about the underlying causal structure of the world. PMID:25710328

Bayesian evaluation of effect size after replicating an original study

PubMed Central

van Aert, Robbie C. M.; van Assen, Marcel A. L. M.

2017-01-01

The vast majority of published results in the literature is statistically significant, which raises concerns about their reliability. The Reproducibility Project Psychology (RPP) and Experimental Economics Replication Project (EE-RP) both replicated a large number of published studies in psychology and economics. The original study and replication were statistically significant in 36.1% in RPP and 68.8% in EE-RP suggesting many null effects among the replicated studies. However, evidence in favor of the null hypothesis cannot be examined with null hypothesis significance testing. We developed a Bayesian meta-analysis method called snapshot hybrid that is easy to use and understand and quantifies the amount of evidence in favor of a zero, small, medium and large effect. The method computes posterior model probabilities for a zero, small, medium, and large effect and adjusts for publication bias by taking into account that the original study is statistically significant. We first analytically approximate the methods performance, and demonstrate the necessity to control for the original study’s significance to enable the accumulation of evidence for a true zero effect. Then we applied the method to the data of RPP and EE-RP, showing that the underlying effect sizes of the included studies in EE-RP are generally larger than in RPP, but that the sample sizes of especially the included studies in RPP are often too small to draw definite conclusions about the true effect size. We also illustrate how snapshot hybrid can be used to determine the required sample size of the replication akin to power analysis in null hypothesis significance testing and present an easy to use web application (https://rvanaert.shinyapps.io/snapshot/) and R code for applying the method. PMID:28388646

Analysis of nasopharyngeal carcinoma risk factors with Bayesian networks.

PubMed

Aussem, Alex; de Morais, Sérgio Rodrigues; Corbex, Marilys

2012-01-01

We propose a new graphical framework for extracting the relevant dietary, social and environmental risk factors that are associated with an increased risk of nasopharyngeal carcinoma (NPC) on a case-control epidemiologic study that consists of 1289 subjects and 150 risk factors. This framework builds on the use of Bayesian networks (BNs) for representing statistical dependencies between the random variables. We discuss a novel constraint-based procedure, called Hybrid Parents and Children (HPC), that builds recursively a local graph that includes all the relevant features statistically associated to the NPC, without having to find the whole BN first. The local graph is afterwards directed by the domain expert according to his knowledge. It provides a statistical profile of the recruited population, and meanwhile helps identify the risk factors associated to NPC. Extensive experiments on synthetic data sampled from known BNs show that the HPC outperforms state-of-the-art algorithms that appeared in the recent literature. From a biological perspective, the present study confirms that chemical products, pesticides and domestic fume intake from incomplete combustion of coal and wood are significantly associated with NPC risk. These results suggest that industrial workers are often exposed to noxious chemicals and poisonous substances that are used in the course of manufacturing. This study also supports previous findings that the consumption of a number of preserved food items, like house made proteins and sheep fat, are a major risk factor for NPC. BNs are valuable data mining tools for the analysis of epidemiologic data. They can explicitly combine both expert knowledge from the field and information inferred from the data. These techniques therefore merit consideration as valuable alternatives to traditional multivariate regression techniques in epidemiologic studies. Copyright © 2011 Elsevier B.V. All rights reserved.

Bayesian estimation of the transmissivity spatial structure from pumping test data

NASA Astrophysics Data System (ADS)

Demir, Mehmet Taner; Copty, Nadim K.; Trinchero, Paolo; Sanchez-Vila, Xavier

2017-06-01

Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.

Emerging Concepts of Data Integration in Pathogen Phylodynamics.

PubMed

Baele, Guy; Suchard, Marc A; Rambaut, Andrew; Lemey, Philippe

2017-01-01

Phylodynamics has become an increasingly popular statistical framework to extract evolutionary and epidemiological information from pathogen genomes. By harnessing such information, epidemiologists aim to shed light on the spatio-temporal patterns of spread and to test hypotheses about the underlying interaction of evolutionary and ecological dynamics in pathogen populations. Although the field has witnessed a rich development of statistical inference tools with increasing levels of sophistication, these tools initially focused on sequences as their sole primary data source. Integrating various sources of information, however, promises to deliver more precise insights in infectious diseases and to increase opportunities for statistical hypothesis testing. Here, we review how the emerging concept of data integration is stimulating new advances in Bayesian evolutionary inference methodology which formalize a marriage of statistical thinking and evolutionary biology. These approaches include connecting sequence to trait evolution, such as for host, phenotypic and geographic sampling information, but also the incorporation of covariates of evolutionary and epidemic processes in the reconstruction procedures. We highlight how a full Bayesian approach to covariate modeling and testing can generate further insights into sequence evolution, trait evolution, and population dynamics in pathogen populations. Specific examples demonstrate how such approaches can be used to test the impact of host on rabies and HIV evolutionary rates, to identify the drivers of influenza dispersal as well as the determinants of rabies cross-species transmissions, and to quantify the evolutionary dynamics of influenza antigenicity. Finally, we briefly discuss how data integration is now also permeating through the inference of transmission dynamics, leading to novel insights into tree-generative processes and detailed reconstructions of transmission trees. [Bayesian inference; birth–death models; coalescent models; continuous trait evolution; covariates; data integration; discrete trait evolution; pathogen phylodynamics.

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.

Emerging Concepts of Data Integration in Pathogen Phylodynamics

PubMed Central

Baele, Guy; Suchard, Marc A.; Rambaut, Andrew; Lemey, Philippe

2017-01-01

Phylodynamics has become an increasingly popular statistical framework to extract evolutionary and epidemiological information from pathogen genomes. By harnessing such information, epidemiologists aim to shed light on the spatio-temporal patterns of spread and to test hypotheses about the underlying interaction of evolutionary and ecological dynamics in pathogen populations. Although the field has witnessed a rich development of statistical inference tools with increasing levels of sophistication, these tools initially focused on sequences as their sole primary data source. Integrating various sources of information, however, promises to deliver more precise insights in infectious diseases and to increase opportunities for statistical hypothesis testing. Here, we review how the emerging concept of data integration is stimulating new advances in Bayesian evolutionary inference methodology which formalize a marriage of statistical thinking and evolutionary biology. These approaches include connecting sequence to trait evolution, such as for host, phenotypic and geographic sampling information, but also the incorporation of covariates of evolutionary and epidemic processes in the reconstruction procedures. We highlight how a full Bayesian approach to covariate modeling and testing can generate further insights into sequence evolution, trait evolution, and population dynamics in pathogen populations. Specific examples demonstrate how such approaches can be used to test the impact of host on rabies and HIV evolutionary rates, to identify the drivers of influenza dispersal as well as the determinants of rabies cross-species transmissions, and to quantify the evolutionary dynamics of influenza antigenicity. Finally, we briefly discuss how data integration is now also permeating through the inference of transmission dynamics, leading to novel insights into tree-generative processes and detailed reconstructions of transmission trees. [Bayesian inference; birth–death models; coalescent models; continuous trait evolution; covariates; data integration; discrete trait evolution; pathogen phylodynamics. PMID:28173504

Analysis and meta-analysis of single-case designs: an introduction.

PubMed

Shadish, William R

2014-04-01

The last 10 years have seen great progress in the analysis and meta-analysis of single-case designs (SCDs). This special issue includes five articles that provide an overview of current work on that topic, including standardized mean difference statistics, multilevel models, Bayesian statistics, and generalized additive models. Each article analyzes a common example across articles and presents syntax or macros for how to do them. These articles are followed by commentaries from single-case design researchers and journal editors. This introduction briefly describes each article and then discusses several issues that must be addressed before we can know what analyses will eventually be best to use in SCD research. These issues include modeling trend, modeling error covariances, computing standardized effect size estimates, assessing statistical power, incorporating more accurate models of outcome distributions, exploring whether Bayesian statistics can improve estimation given the small samples common in SCDs, and the need for annotated syntax and graphical user interfaces that make complex statistics accessible to SCD researchers. The article then discusses reasons why SCD researchers are likely to incorporate statistical analyses into their research more often in the future, including changing expectations and contingencies regarding SCD research from outside SCD communities, changes and diversity within SCD communities, corrections of erroneous beliefs about the relationship between SCD research and statistics, and demonstrations of how statistics can help SCD researchers better meet their goals. Copyright © 2013 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

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

NASA Technical Reports Server (NTRS)

Vangelder, B. H. W.

1978-01-01

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

Uncertainty quantification for nuclear density functional theory and information content of new measurements

DOE PAGES

McDonnell, J. D.; Schunck, N.; Higdon, D.; ...

2015-03-24

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squaresmore » optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. In addition, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.« less

Uncertainty quantification for nuclear density functional theory and information content of new measurements

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

McDonnell, J. D.; Schunck, N.; Higdon, D.

2015-03-24

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squaresmore » optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. As a result, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.« less

A statistical model investigating the prevalence of tuberculosis in New York City using counting processes with two change-points

PubMed Central

ACHCAR, J. A.; MARTINEZ, E. Z.; RUFFINO-NETTO, A.; PAULINO, C. D.; SOARES, P.

2008-01-01

SUMMARY We considered a Bayesian analysis for the prevalence of tuberculosis cases in New York City from 1970 to 2000. This counting dataset presented two change-points during this period. We modelled this counting dataset considering non-homogeneous Poisson processes in the presence of the two-change points. A Bayesian analysis for the data is considered using Markov chain Monte Carlo methods. Simulated Gibbs samples for the parameters of interest were obtained using WinBugs software. PMID:18346287

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

A Bayesian approach to modeling diffraction profiles and application to ferroelectric materials

DOE PAGES

Iamsasri, Thanakorn; Guerrier, Jonathon; Esteves, Giovanni; ...

2017-02-01

A new statistical approach for modeling diffraction profiles is introduced, using Bayesian inference and a Markov chain Monte Carlo (MCMC) algorithm. This method is demonstrated by modeling the degenerate reflections during application of an electric field to two different ferroelectric materials: thin-film lead zirconate titanate (PZT) of composition PbZr 0.3Ti 0.7O 3and a bulk commercial PZT polycrystalline ferroelectric. Here, the new method offers a unique uncertainty quantification of the model parameters that can be readily propagated into new calculated parameters.

Ecological statistics of Gestalt laws for the perceptual organization of contours.

PubMed

Elder, James H; Goldberg, Richard M

2002-01-01

Although numerous studies have measured the strength of visual grouping cues for controlled psychophysical stimuli, little is known about the statistical utility of these various cues for natural images. In this study, we conducted experiments in which human participants trace perceived contours in natural images. These contours are automatically mapped to sequences of discrete tangent elements detected in the image. By examining relational properties between pairs of successive tangents on these traced curves, and between randomly selected pairs of tangents, we are able to estimate the likelihood distributions required to construct an optimal Bayesian model for contour grouping. We employed this novel methodology to investigate the inferential power of three classical Gestalt cues for contour grouping: proximity, good continuation, and luminance similarity. The study yielded a number of important results: (1) these cues, when appropriately defined, are approximately uncorrelated, suggesting a simple factorial model for statistical inference; (2) moderate image-to-image variation of the statistics indicates the utility of general probabilistic models for perceptual organization; (3) these cues differ greatly in their inferential power, proximity being by far the most powerful; and (4) statistical modeling of the proximity cue indicates a scale-invariant power law in close agreement with prior psychophysics.

New Stopping Criteria for Segmenting DNA Sequences

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

Li, Wentian

2001-06-18

We propose a solution on the stopping criterion in segmenting inhomogeneous DNA sequences with complex statistical patterns. This new stopping criterion is based on Bayesian information criterion in the model selection framework. When this criterion is applied to telomere of S.cerevisiae and the complete sequence of E.coli, borders of biologically meaningful units were identified, and a more reasonable number of domains was obtained. We also introduce a measure called segmentation strength which can be used to control the delineation of large domains. The relationship between the average domain size and the threshold of segmentation strength is determined for several genomemore » sequences.« less

Confidence Intervals for the Between-Study Variance in Random Effects Meta-Analysis Using Generalised Cochran Heterogeneity Statistics

ERIC Educational Resources Information Center

Jackson, Dan

2013-01-01

Statistical inference is problematic in the common situation in meta-analysis where the random effects model is fitted to just a handful of studies. In particular, the asymptotic theory of maximum likelihood provides a poor approximation, and Bayesian methods are sensitive to the prior specification. Hence, less efficient, but easily computed and…

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.

A Bayesian Framework for Word Segmentation: Exploring the Effects of Context

ERIC Educational Resources Information Center

Goldwater, Sharon; Griffiths, Thomas L.; Johnson, Mark

2009-01-01

Since the experiments of Saffran et al. [Saffran, J., Aslin, R., & Newport, E. (1996). Statistical learning in 8-month-old infants. "Science," 274, 1926-1928], there has been a great deal of interest in the question of how statistical regularities in the speech stream might be used by infants to begin to identify individual words. In this work, we…

Particle identification in ALICE: a Bayesian approach

NASA Astrophysics Data System (ADS)

Adam, J.; Adamová, D.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Alam, S. N.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alexandre, D.; Alfaro Molina, R.; Alici, A.; Alkin, A.; Almaraz, J. R. M.; Alme, J.; Alt, T.; Altinpinar, S.; Altsybeev, I.; Alves Garcia Prado, C.; Andrei, C.; Andronic, A.; Anguelov, V.; Antičić, T.; Antinori, F.; Antonioli, P.; Aphecetche, L.; Appelshäuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badalà, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Balasubramanian, S.; Baldisseri, A.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barnaföldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartke, J.; Bartsch, E.; Basile, M.; Bastid, N.; Basu, S.; Bathen, B.; Batigne, G.; Batista Camejo, A.; Batyunya, B.; Batzing, P. C.; Bearden, I. G.; Beck, H.; Bedda, C.; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Belmont, R.; Belmont-Moreno, E.; Belyaev, V.; Benacek, P.; Bencedi, G.; Beole, S.; Berceanu, I.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.; Berzano, D.; Betev, L.; Bhasin, A.; Bhat, I. R.; Bhati, A. K.; Bhattacharjee, B.; Bhom, J.; Bianchi, L.; Bianchi, N.; Bianchin, C.; Bielčík, J.; Bielčíková, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Bjelogrlic, S.; Blair, J. T.; Blau, D.; Blume, C.; Bock, F.; Bogdanov, A.; Bøggild, H.; Boldizsár, L.; Bombara, M.; Book, J.; Borel, H.; Borissov, A.; Borri, M.; Bossú, F.; Botta, E.; Bourjau, C.; Braun-Munzinger, P.; Bregant, M.; Breitner, T.; Broker, T. A.; Browning, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Cai, X.; Caines, H.; Calero Diaz, L.; Caliva, A.; Calvo Villar, E.; Camerini, P.; Carena, F.; Carena, W.; Carnesecchi, F.; Castillo Castellanos, J.; Castro, A. J.; Casula, E. A. R.; Ceballos Sanchez, C.; Cepila, J.; Cerello, P.; Cerkala, J.; Chang, B.; Chapeland, S.; Chartier, M.; Charvet, J. L.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Chelnokov, V.; Cherney, M.; Cheshkov, C.; Cheynis, B.; Chibante Barroso, V.; Chinellato, D. D.; Cho, S.; Chochula, P.; Choi, K.; Chojnacki, M.; Choudhury, S.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Chung, S. U.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Conesa Balbastre, G.; Conesa del Valle, Z.; Connors, M. E.; Contreras, J. G.; Cormier, T. M.; Corrales Morales, Y.; Cortés Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Crochet, P.; Cruz Albino, R.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, D.; Das, I.; Das, S.; Dash, A.; Dash, S.; De, S.; De Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; De Falco, A.; De Gruttola, D.; De Marco, N.; De Pasquale, S.; Deisting, A.; Deloff, A.; Dénes, E.; Deplano, C.; Dhankher, P.; Di Bari, D.; Di Mauro, A.; Di Nezza, P.; Diaz Corchero, M. A.; Dietel, T.; Dillenseger, P.; Divià, R.; Djuvsland, Ø.; Dobrin, A.; Domenicis Gimenez, D.; Dönigus, B.; Dordic, O.; Drozhzhova, T.; Dubey, A. K.; Dubla, A.; Ducroux, L.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erdemir, I.; Erhardt, F.; Espagnon, B.; Estienne, M.; Esumi, S.; Eum, J.; Evans, D.; Evdokimov, S.; Eyyubova, G.; Fabbietti, L.; Fabris, D.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Ferencei, J.; Fernández Téllez, A.; Ferreiro, E. G.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Fiore, E. M.; Fleck, M. G.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Fusco Girard, M.; Gaardhøje, J. J.; Gagliardi, M.; Gago, A. M.; Gallio, M.; Gangadharan, D. R.; Ganoti, P.; Gao, C.; Garabatos, C.; Garcia-Solis, E.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Germain, M.; Gheata, A.; Gheata, M.; Ghosh, P.; Ghosh, S. K.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glässel, P.; Goméz Coral, D. M.; Gomez Ramirez, A.; Gonzalez, A. S.; Gonzalez, V.; González-Zamora, P.; Gorbunov, S.; Görlich, L.; Gotovac, S.; Grabski, V.; Grachov, O. A.; Graczykowski, L. K.; Graham, K. L.; Grelli, A.; Grigoras, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Grinyov, B.; Grion, N.; Gronefeld, J. M.; Grosse-Oetringhaus, J. F.; Grosso, R.; Guber, F.; Guernane, R.; Guerzoni, B.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Gupta, R.; Haake, R.; Haaland, Ø.; Hadjidakis, C.; Haiduc, M.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Harris, J. W.; Harton, A.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbär, E.; Helstrup, H.; Herghelegiu, A.; Herrera Corral, G.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hippolyte, B.; Horak, D.; Hosokawa, R.; Hristov, P.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Ilkaev, R.; Inaba, M.; Incani, E.; Ippolitov, M.; Irfan, M.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacazio, N.; Jacobs, P. M.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jahnke, C.; Jakubowska, M. J.; Jang, H. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jena, S.; Jimenez Bustamante, R. T.; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kamin, J.; Kang, J. H.; Kaplin, V.; Kar, S.; Karasu Uysal, A.; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.; Keil, M.; Mohisin Khan, M.; Khan, P.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Kileng, B.; Kim, D. W.; Kim, D. J.; Kim, D.; Kim, H.; Kim, J. S.; Kim, M.; Kim, S.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein, J.; Klein-Bösing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Kollegger, T.; Kolojvari, A.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Kopcik, M.; Kostarakis, P.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Koyithatta Meethaleveedu, G.; Králik, I.; Kravčáková, A.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.; Kubera, A. M.; Kučera, V.; Kuhn, C.; Kuijer, P. G.; Kumar, A.; Kumar, J.; Kumar, L.; Kumar, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Ladron de Guevara, P.; Lagana Fernandes, C.; Lakomov, I.; Langoy, R.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lea, R.; Leardini, L.; Lee, G. R.; Lee, S.; Lehas, F.; Lemmon, R. C.; Lenti, V.; Leogrande, E.; León Monzón, I.; León Vargas, H.; Leoncino, M.; Lévai, P.; Li, S.; Li, X.; Lien, J.; Lietava, R.; Lindal, S.; Lindenstruth, V.; Lippmann, C.; Lisa, M. A.; Ljunggren, H. M.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Lopez, X.; López Torres, E.; Lowe, A.; Luettig, P.; Lunardon, M.; Luparello, G.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahajan, S.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Maldonado Cervantes, I.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Marchisone, M.; Mareš, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.; Marín, A.; Markert, C.; Marquard, M.; Martin, N. A.; Martin Blanco, J.; Martinengo, P.; Martínez, M. I.; Martínez García, G.; Martinez Pedreira, M.; Mas, A.; Masciocchi, S.; Masera, M.; Masoni, A.; Mastroserio, A.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzoni, M. A.; Mcdonald, D.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Mercado Pérez, J.; Meres, M.; Miake, Y.; Mieskolainen, M. M.; Mikhaylov, K.; Milano, L.; Milosevic, J.; Mischke, A.; Mishra, A. N.; Miśkowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.; Mohanty, B.; Molnar, L.; Montaño Zetina, L.; Montes, E.; Moreira De Godoy, D. A.; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Mühlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Nedosekin, A.; Nellen, L.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Noferini, F.; Nomokonov, P.; Nooren, G.; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, S.; Oh, S. K.; Ohlson, A.; Okatan, A.; Okubo, T.; Olah, L.; Oleniacz, J.; Oliveira Da Silva, A. C.; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Ozdemir, M.; Pachmayer, Y.; Pagano, D.; Pagano, P.; Paić, G.; Pal, S. K.; Pan, J.; Pandey, A. K.; Papikyan, V.; Pappalardo, G. S.; Pareek, P.; Park, W. J.; Parmar, S.; Passfeld, A.; Paticchio, V.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.; Pereira Da Costa, H.; Peresunko, D.; Pérez Lara, C. E.; Perez Lezama, E.; Peskov, V.; Pestov, Y.; Petráček, V.; Petrov, V.; Petrovici, M.; Petta, C.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Płoskoń, M.; Planinic, M.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Porteboeuf-Houssais, S.; Porter, J.; Pospisil, J.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Puddu, G.; Pujahari, P.; Punin, V.; Putschke, J.; Qvigstad, H.; Rachevski, A.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Raniwala, R.; Raniwala, S.; Räsänen, S. S.; Rascanu, B. T.; Rathee, D.; Read, K. F.; Redlich, K.; Reed, R. J.; Rehman, A.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reolon, A. R.; Reshetin, A.; Reygers, K.; Riabov, V.; Ricci, R. A.; Richert, T.; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Rocco, E.; Rodríguez Cahuantzi, M.; Rodriguez Manso, A.; Røed, K.; Rogochaya, E.; Rohr, D.; Röhrich, D.; Ronchetti, F.; Ronflette, L.; Rosnet, P.; Rossi, A.; Roukoutakis, F.; Roy, A.; Roy, C.; Roy, P.; Rubio Montero, A. J.; Rui, R.; Russo, R.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Šafařík, K.; Sahlmuller, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Šándor, L.; Sandoval, A.; Sano, M.; Sarkar, D.; Sarkar, N.; Sarma, P.; Scapparone, E.; Scarlassara, F.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schuchmann, S.; Schukraft, J.; Schulc, M.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Scott, R.; Šefčík, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shadura, O.; Shahoyan, R.; Shahzad, M. I.; Shangaraev, A.; Sharma, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silvermyr, D.; Silvestre, C.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singha, S.; Singhal, V.; Sinha, B. C.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.; Snellman, T. W.; Song, J.; Song, M.; Song, Z.; Soramel, F.; Sorensen, S.; Souza, R. D. de; Sozzi, F.; Spacek, M.; Spiriti, E.; Sputowska, I.; Spyropoulou-Stassinaki, M.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Steyn, G.; Stiller, J. H.; Stocco, D.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Šumbera, M.; Sumowidagdo, S.; Szabo, A.; Szanto de Toledo, A.; Szarka, I.; Szczepankiewicz, A.; Szymanski, M.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Tejeda Muñoz, G.; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thäder, J.; Thakur, D.; Thomas, D.; Tieulent, R.; Timmins, A. R.; Toia, A.; Trogolo, S.; Trombetta, G.; Trubnikov, V.; Trzaska, W. H.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; Valencia Palomo, L.; Vallero, S.; Van Der Maarel, J.; Van Hoorne, J. W.; van Leeuwen, M.; Vanat, T.; Vande Vyvre, P.; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Vechernin, V.; Veen, A. M.; Veldhoen, M.; Velure, A.; Vercellin, E.; Vergara Limón, S.; Vernet, R.; Verweij, M.; Vickovic, L.; Viesti, G.; Viinikainen, J.; Vilakazi, Z.; Villalobos Baillie, O.; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Vinogradov, Y.; Virgili, T.; Vislavicius, V.; Viyogi, Y. P.; Vodopyanov, A.; Völkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Vranic, D.; Vrláková, J.; Vulpescu, B.; Wagner, B.; Wagner, J.; Wang, H.; Wang, M.; Watanabe, D.; Watanabe, Y.; Weber, M.; Weber, S. G.; Weiser, D. F.; Wessels, J. P.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Williams, M. C. S.; Windelband, B.; Winn, M.; Yang, H.; Yang, P.; Yano, S.; Yasin, Z.; Yin, Z.; Yokoyama, H.; Yoo, I.-K.; Yoon, J. H.; Yurchenko, V.; Yushmanov, I.; Zaborowska, A.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zaporozhets, S.; Zardoshti, N.; Zarochentsev, A.; Závada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zgura, I. S.; Zhalov, M.; Zhang, H.; Zhang, X.; Zhang, Y.; Zhang, C.; Zhang, Z.; Zhao, C.; Zhigareva, N.; Zhou, D.; Zhou, Y.; Zhou, Z.; Zhu, H.; Zhu, J.; Zichichi, A.; Zimmermann, A.; Zimmermann, M. B.; Zinovjev, G.; Zyzak, M.

2016-05-01

We present a Bayesian approach to particle identification (PID) within the ALICE experiment. The aim is to more effectively combine the particle identification capabilities of its various detectors. After a brief explanation of the adopted methodology and formalism, the performance of the Bayesian PID approach for charged pions, kaons and protons in the central barrel of ALICE is studied. PID is performed via measurements of specific energy loss ( d E/d x) and time of flight. PID efficiencies and misidentification probabilities are extracted and compared with Monte Carlo simulations using high-purity samples of identified particles in the decay channels K0S → π-π+, φ→ K-K+, and Λ→ p π- in p-Pb collisions at √{s_{NN}}=5.02 TeV. In order to thoroughly assess the validity of the Bayesian approach, this methodology was used to obtain corrected pT spectra of pions, kaons, protons, and D0 mesons in pp collisions at √{s}=7 TeV. In all cases, the results using Bayesian PID were found to be consistent with previous measurements performed by ALICE using a standard PID approach. For the measurement of D0 → K-π+, it was found that a Bayesian PID approach gave a higher signal-to-background ratio and a similar or larger statistical significance when compared with standard PID selections, despite a reduced identification efficiency. Finally, we present an exploratory study of the measurement of Λc+ → p K-π+ in pp collisions at √{s}=7 TeV, using the Bayesian approach for the identification of its decay products.

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.

Nondestructive Evaluation (NDE) Technology Initiatives (NTIP). Delivery Order 0039: Statistical Comparison of Competing Material Models

DTIC Science & Technology

2003-01-01

adapted from Kass and Rafferty (1995) and Congdon (2001). Page 10 of 57 density adjusted for resin content, z, since resin contributes to the density...c.f.: Congdon , 2001). How to Download the WinBUGS Software Package BUGS was originally a statistical research project at the Medical Research...Likelihood Estimation,” July 2002, working paper to be published. 18) Congdon , Peter, Bayesian Statistical Modeling, Wiley, 2001 19) Cox, D. R. and

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

NASA Technical Reports Server (NTRS)

Pohorille, Andrew

2006-01-01

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Bug Distribution and Statistical Pattern Classification.

ERIC Educational Resources Information Center

Tatsuoka, Kikumi K.; Tatsuoka, Maurice M.

1987-01-01

The rule space model permits measurement of cognitive skill acquisition and error diagnosis. Further discussion introduces Bayesian hypothesis testing and bug distribution. An illustration involves an artificial intelligence approach to testing fractions and arithmetic. (Author/GDC)

Case studies in Bayesian microbial risk assessments.

PubMed

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

2009-12-21

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

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.

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

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function.

PubMed

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A; Lu, Zhong-Lin; Myung, Jay I

2016-01-01

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias.

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function

PubMed Central

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A.; Lu, Zhong-Lin; Myung, Jay I.

2016-01-01

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias. PMID:27105061

MAFsnp: A Multi-Sample Accurate and Flexible SNP Caller Using Next-Generation Sequencing Data

PubMed Central

Hu, Jiyuan; Li, Tengfei; Xiu, Zidi; Zhang, Hong

2015-01-01

Most existing statistical methods developed for calling single nucleotide polymorphisms (SNPs) using next-generation sequencing (NGS) data are based on Bayesian frameworks, and there does not exist any SNP caller that produces p-values for calling SNPs in a frequentist framework. To fill in this gap, we develop a new method MAFsnp, a Multiple-sample based Accurate and Flexible algorithm for calling SNPs with NGS data. MAFsnp is based on an estimated likelihood ratio test (eLRT) statistic. In practical situation, the involved parameter is very close to the boundary of the parametric space, so the standard large sample property is not suitable to evaluate the finite-sample distribution of the eLRT statistic. Observing that the distribution of the test statistic is a mixture of zero and a continuous part, we propose to model the test statistic with a novel two-parameter mixture distribution. Once the parameters in the mixture distribution are estimated, p-values can be easily calculated for detecting SNPs, and the multiple-testing corrected p-values can be used to control false discovery rate (FDR) at any pre-specified level. With simulated data, MAFsnp is shown to have much better control of FDR than the existing SNP callers. Through the application to two real datasets, MAFsnp is also shown to outperform the existing SNP callers in terms of calling accuracy. An R package “MAFsnp” implementing the new SNP caller is freely available at http://homepage.fudan.edu.cn/zhangh/softwares/. PMID:26309201

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.

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.

Bayesian mixture modeling for blood sugar levels of diabetes mellitus patients (case study in RSUD Saiful Anwar Malang Indonesia)

NASA Astrophysics Data System (ADS)

Budi Astuti, Ani; Iriawan, Nur; Irhamah; Kuswanto, Heri; Sasiarini, Laksmi

2017-10-01

Bayesian statistics proposes an approach that is very flexible in the number of samples and distribution of data. Bayesian Mixture Model (BMM) is a Bayesian approach for multimodal models. Diabetes Mellitus (DM) is more commonly known in the Indonesian community as sweet pee. This disease is one type of chronic non-communicable diseases but it is very dangerous to humans because of the effects of other diseases complications caused. WHO reports in 2013 showed DM disease was ranked 6th in the world as the leading causes of human death. In Indonesia, DM disease continues to increase over time. These research would be studied patterns and would be built the BMM models of the DM data through simulation studies where the simulation data built on cases of blood sugar levels of DM patients in RSUD Saiful Anwar Malang. The results have been successfully demonstrated pattern of distribution of the DM data which has a normal mixture distribution. The BMM models have succeed to accommodate the real condition of the DM data based on the data driven concept.

Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system.

PubMed

Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C

2016-02-01

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

Instruction in information structuring improves Bayesian judgment in intelligence analysts.

PubMed

Mandel, David R

2015-01-01

An experiment was conducted to test the effectiveness of brief instruction in information structuring (i.e., representing and integrating information) for improving the coherence of probability judgments and binary choices among intelligence analysts. Forty-three analysts were presented with comparable sets of Bayesian judgment problems before and immediately after instruction. After instruction, analysts' probability judgments were more coherent (i.e., more additive and compliant with Bayes theorem). Instruction also improved the coherence of binary choices regarding category membership: after instruction, subjects were more likely to invariably choose the category to which they assigned the higher probability of a target's membership. The research provides a rare example of evidence-based validation of effectiveness in instruction to improve the statistical assessment skills of intelligence analysts. Such instruction could also be used to improve the assessment quality of other types of experts who are required to integrate statistical information or make probabilistic assessments.

Inference of missing data and chemical model parameters using experimental statistics

NASA Astrophysics Data System (ADS)

Casey, Tiernan; Najm, Habib

2017-11-01

A method for determining the joint parameter density of Arrhenius rate expressions through the inference of missing experimental data is presented. This approach proposes noisy hypothetical data sets from target experiments and accepts those which agree with the reported statistics, in the form of nominal parameter values and their associated uncertainties. The data exploration procedure is formalized using Bayesian inference, employing maximum entropy and approximate Bayesian computation methods to arrive at a joint density on data and parameters. The method is demonstrated in the context of reactions in the H2-O2 system for predictive modeling of combustion systems of interest. Work supported by the US DOE BES CSGB. Sandia National Labs is a multimission lab managed and operated by Nat. Technology and Eng'g Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell Intl, for the US DOE NCSA under contract DE-NA-0003525.

The mean time-limited crash rate of stock price

NASA Astrophysics Data System (ADS)

Li, Yun-Xian; Li, Jiang-Cheng; Yang, Ai-Jun; Tang, Nian-Sheng

2017-05-01

In this article we investigate the occurrence of stock market crash in an economy cycle. Bayesian approach, Heston model and statistical-physical method are considered. Specifically, Heston model and an effective potential are employed to address the dynamic changes of stock price. Bayesian approach has been utilized to estimate the Heston model's unknown parameters. Statistical physical method is used to investigate the occurrence of stock market crash by calculating the mean time-limited crash rate. The real financial data from the Shanghai Composite Index is analyzed with the proposed methods. The mean time-limited crash rate of stock price is used to describe the occurrence of stock market crash in an economy cycle. The monotonous and nonmonotonous behaviors are observed in the behavior of the mean time-limited crash rate versus volatility of stock for various cross correlation coefficient between volatility and price. Also a minimum occurrence of stock market crash matching an optimal volatility is discovered.

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

PubMed

Verde, Pablo E

2010-12-30

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

Predicting the effect of maternal docosahexaenoic acid (DHA) supplementation to reduce early preterm birth in Australia and the United States using results of within country randomized controlled trials

PubMed Central

Yelland, LN; Gajewski, BJ; Colombo, J; Gibson, RA; Makrides, M; Carlson, SE

2016-01-01

SUMMARY The DHA to Optimize Mother Infant Outcome (DOMInO) and Kansas DHA Outcomes Study (KUDOS) were randomized controlled trials that supplemented mothers with 800 and 600 mg DHA/day, respectively, or a placebo during pregnancy. DOMInO was conducted in Australia and KUDOS in the United States. Both trials found an unanticipated and statistically significant reduction in early preterm birth (ePTB; i.e., birth before 34 weeks gestation). However, in each trial, the number of ePTBs were small. We used a novel Bayesian approach and an arbitrary sample of 120,000 pregnancies to estimate statistically derived low, moderate or high risk for ePTB, and to test for differences between the DHA and placebo groups. In both trials, the model predicted DHA would significantly reduce the expected proportion of deliveries in the high risk group under the trial conditions of the parent studies. From these proportions we estimated the number of ePTB that could be prevented. PMID:27637340

Iterative Assessment of Statistically-Oriented and Standard Algorithms for Determining Muscle Onset with Intramuscular Electromyography.

PubMed

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

2017-12-01

The onset of muscle activity, as measured by electromyography (EMG), is a commonly applied metric in biomechanics. Intramuscular EMG is often used to examine deep musculature and there are currently no studies examining the effectiveness of algorithms for intramuscular EMG onset. The present study examines standard surface EMG onset algorithms (linear envelope, Teager-Kaiser Energy Operator, and sample entropy) and novel algorithms (time series mean-variance analysis, sequential/batch processing with parametric and nonparametric methods, and Bayesian changepoint analysis). Thirteen male and 5 female subjects had intramuscular EMG collected during isolated biceps brachii and vastus lateralis contractions, resulting in 103 trials. EMG onset was visually determined twice by 3 blinded reviewers. Since the reliability of visual onset was high (ICC (1,1) : 0.92), the mean of the 6 visual assessments was contrasted with the algorithmic approaches. Poorly performing algorithms were stepwise eliminated via (1) root mean square error analysis, (2) algorithm failure to identify onset/premature onset, (3) linear regression analysis, and (4) Bland-Altman plots. The top performing algorithms were all based on Bayesian changepoint analysis of rectified EMG and were statistically indistinguishable from visual analysis. Bayesian changepoint analysis has the potential to produce more reliable, accurate, and objective intramuscular EMG onset results than standard methodologies.

Bayesian Monte Carlo and Maximum Likelihood Approach for ...

EPA Pesticide Factsheets

Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficien

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

Bayesian change point analysis of abundance trends for pelagic fishes in the upper San Francisco Estuary.

PubMed

Thomson, James R; Kimmerer, Wim J; Brown, Larry R; Newman, Ken B; Mac Nally, Ralph; Bennett, William A; Feyrer, Frederick; Fleishman, Erica

2010-07-01

We examined trends in abundance of four pelagic fish species (delta smelt, longfin smelt, striped bass, and threadfin shad) in the upper San Francisco Estuary, California, USA, over 40 years using Bayesian change point models. Change point models identify times of abrupt or unusual changes in absolute abundance (step changes) or in rates of change in abundance (trend changes). We coupled Bayesian model selection with linear regression splines to identify biotic or abiotic covariates with the strongest associations with abundances of each species. We then refitted change point models conditional on the selected covariates to explore whether those covariates could explain statistical trends or change points in species abundances. We also fitted a multispecies change point model that identified change points common to all species. All models included hierarchical structures to model data uncertainties, including observation errors and missing covariate values. There were step declines in abundances of all four species in the early 2000s, with a likely common decline in 2002. Abiotic variables, including water clarity, position of the 2 per thousand isohaline (X2), and the volume of freshwater exported from the estuary, explained some variation in species' abundances over the time series, but no selected covariates could explain statistically the post-2000 change points for any species.

PyClone: statistical inference of clonal population structure in cancer.

PubMed

Roth, Andrew; Khattra, Jaswinder; Yap, Damian; Wan, Adrian; Laks, Emma; Biele, Justina; Ha, Gavin; Aparicio, Samuel; Bouchard-Côté, Alexandre; Shah, Sohrab P

2014-04-01

We introduce PyClone, a statistical model for inference of clonal population structures in cancers. PyClone is a Bayesian clustering method for grouping sets of deeply sequenced somatic mutations into putative clonal clusters while estimating their cellular prevalences and accounting for allelic imbalances introduced by segmental copy-number changes and normal-cell contamination. Single-cell sequencing validation demonstrates PyClone's accuracy.

Improved head direction command classification using an optimised Bayesian neural network.

PubMed

Nguyen, Son T; Nguyen, Hung T; Taylor, Philip B; Middleton, James

2006-01-01

Assistive technologies have recently emerged to improve the quality of life of severely disabled people by enhancing their independence in daily activities. Since many of those individuals have limited or non-existing control from the neck downward, alternative hands-free input modalities have become very important for these people to access assistive devices. In hands-free control, head movement has been proved to be a very effective user interface as it can provide a comfortable, reliable and natural way to access the device. Recently, neural networks have been shown to be useful not only for real-time pattern recognition but also for creating user-adaptive models. Since multi-layer perceptron neural networks trained using standard back-propagation may cause poor generalisation, the Bayesian technique has been proposed to improve the generalisation and robustness of these networks. This paper describes the use of Bayesian neural networks in developing a hands-free wheelchair control system. The experimental results show that with the optimised architecture, classification Bayesian neural networks can detect head commands of wheelchair users accurately irrespective to their levels of injuries.

Bayesian transformation cure frailty models with multivariate failure time data.

PubMed

Yin, Guosheng

2008-12-10

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

Exploiting Data Missingness in Bayesian Network Modeling

NASA Astrophysics Data System (ADS)

Rodrigues de Morais, Sérgio; Aussem, Alex

This paper proposes a framework built on the use of Bayesian networks (BN) for representing statistical dependencies between the existing random variables and additional dummy boolean variables, which represent the presence/absence of the respective random variable value. We show how augmenting the BN with these additional variables helps pinpoint the mechanism through which missing data contributes to the classification task. The missing data mechanism is thus explicitly taken into account to predict the class variable using the data at hand. Extensive experiments on synthetic and real-world incomplete data sets reveals that the missingness information improves classification accuracy.

Bayesian hierarchical modeling for detecting safety signals in clinical trials.

PubMed

Xia, H Amy; Ma, Haijun; Carlin, Bradley P

2011-09-01

Detection of safety signals from clinical trial adverse event data is critical in drug development, but carries a challenging statistical multiplicity problem. Bayesian hierarchical mixture modeling is appealing for its ability to borrow strength across subgroups in the data, as well as moderate extreme findings most likely due merely to chance. We implement such a model for subject incidence (Berry and Berry, 2004 ) using a binomial likelihood, and extend it to subject-year adjusted incidence rate estimation under a Poisson likelihood. We use simulation to choose a signal detection threshold, and illustrate some effective graphics for displaying the flagged signals.

A Bayesian Model for the Prediction and Early Diagnosis of Alzheimer's Disease.

PubMed

Alexiou, Athanasios; Mantzavinos, Vasileios D; Greig, Nigel H; Kamal, Mohammad A

2017-01-01

Alzheimer's disease treatment is still an open problem. The diversity of symptoms, the alterations in common pathophysiology, the existence of asymptomatic cases, the different types of sporadic and familial Alzheimer's and their relevance with other types of dementia and comorbidities, have already created a myth-fear against the leading disease of the twenty first century. Many failed latest clinical trials and novel medications have revealed the early diagnosis as the most critical treatment solution, even though scientists tested the amyloid hypothesis and few related drugs. Unfortunately, latest studies have indicated that the disease begins at the very young ages thus making it difficult to determine the right time of proper treatment. By taking into consideration all these multivariate aspects and unreliable factors against an appropriate treatment, we focused our research on a non-classic statistical evaluation of the most known and accepted Alzheimer's biomarkers. Therefore, in this paper, the code and few experimental results of a computational Bayesian tool have being reported, dedicated to the correlation and assessment of several Alzheimer's biomarkers to export a probabilistic medical prognostic process. This new statistical software is executable in the Bayesian software Winbugs, based on the latest Alzheimer's classification and the formulation of the known relative probabilities of the various biomarkers, correlated with Alzheimer's progression, through a set of discrete distributions. A user-friendly web page has been implemented for the supporting of medical doctors and researchers, to upload Alzheimer's tests and receive statistics on the occurrence of Alzheimer's disease development or presence, due to abnormal testing in one or more biomarkers.

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

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin; Feeney, Stephen

2018-07-01

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

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

PubMed

Kwon, Deukwoo; Reis, Isildinha M

2015-08-12

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

Perceptual integration of kinematic components in the recognition of emotional facial expressions.

PubMed

Chiovetto, Enrico; Curio, Cristóbal; Endres, Dominik; Giese, Martin

2018-04-01

According to a long-standing hypothesis in motor control, complex body motion is organized in terms of movement primitives, reducing massively the dimensionality of the underlying control problems. For body movements, this low-dimensional organization has been convincingly demonstrated by the learning of low-dimensional representations from kinematic and EMG data. In contrast, the effective dimensionality of dynamic facial expressions is unknown, and dominant analysis approaches have been based on heuristically defined facial "action units," which reflect contributions of individual face muscles. We determined the effective dimensionality of dynamic facial expressions by learning of a low-dimensional model from 11 facial expressions. We found an amazingly low dimensionality with only two movement primitives being sufficient to simulate these dynamic expressions with high accuracy. This low dimensionality is confirmed statistically, by Bayesian model comparison of models with different numbers of primitives, and by a psychophysical experiment that demonstrates that expressions, simulated with only two primitives, are indistinguishable from natural ones. In addition, we find statistically optimal integration of the emotion information specified by these primitives in visual perception. Taken together, our results indicate that facial expressions might be controlled by a very small number of independent control units, permitting very low-dimensional parametrization of the associated facial expression.

NDE reliability and probability of detection (POD) evolution and paradigm shift

NASA Astrophysics Data System (ADS)

Singh, Surendra

2014-02-01

The subject of NDE Reliability and POD has gone through multiple phases since its humble beginning in the late 1960s. This was followed by several programs including the important one nicknamed "Have Cracks - Will Travel" or in short "Have Cracks" by Lockheed Georgia Company for US Air Force during 1974-1978. This and other studies ultimately led to a series of developments in the field of reliability and POD starting from the introduction of fracture mechanics and Damaged Tolerant Design (DTD) to statistical framework by Bernes and Hovey in 1981 for POD estimation to MIL-STD HDBK 1823 (1999) and 1823A (2009). During the last decade, various groups and researchers have further studied the reliability and POD using Model Assisted POD (MAPOD), Simulation Assisted POD (SAPOD), and applying Bayesian Statistics. All and each of these developments had one objective, i.e., improving accuracy of life prediction in components that to a large extent depends on the reliability and capability of NDE methods. Therefore, it is essential to have a reliable detection and sizing of large flaws in components. Currently, POD is used for studying reliability and capability of NDE methods, though POD data offers no absolute truth regarding NDE reliability, i.e., system capability, effects of flaw morphology, and quantifying the human factors. Furthermore, reliability and POD have been reported alike in meaning but POD is not NDE reliability. POD is a subset of the reliability that consists of six phases: 1) samples selection using DOE, 2) NDE equipment setup and calibration, 3) System Measurement Evaluation (SME) including Gage Repeatability &Reproducibility (Gage R&R) and Analysis Of Variance (ANOVA), 4) NDE system capability and electronic and physical saturation, 5) acquiring and fitting data to a model, and data analysis, and 6) POD estimation. This paper provides an overview of all major POD milestones for the last several decades and discuss rationale for using Integrated Computational Materials Engineering (ICME), MAPOD, SAPOD, and Bayesian statistics for studying controllable and non-controllable variables including human factors for estimating POD. Another objective is to list gaps between "hoped for" versus validated or fielded failed hardware.

Alterations in the inferior longitudinal fasciculus in autism and associations with visual processing: a diffusion-weighted MRI study.

PubMed

Boets, Bart; Van Eylen, Lien; Sitek, Kevin; Moors, Pieter; Noens, Ilse; Steyaert, Jean; Sunaert, Stefan; Wagemans, Johan

2018-01-01

One of the most reported neural features of autism spectrum disorder (ASD) is the alteration of multiple long-range white matter fiber tracts, as assessed by diffusion-weighted imaging and indexed by reduced fractional anisotropy (FA). Recent methodological advances, however, have shown that this same pattern of reduced FA may be an artifact resulting from excessive head motion and poorer data quality and that aberrant structural connectivity in children with ASD is confined to the right inferior longitudinal fasciculus (ILF). This study aimed at replicating the observation of reduced FA along the right ILF in ASD, while controlling for group differences in head motion and data quality. In addition, we explored associations between reduced FA in the right ILF and quantitative ASD characteristics, and the involvement of the right ILF in visual processing, which is known to be altered in ASD. Global probabilistic tractography was performed on diffusion-weighted imaging data of 17 adolescent boys with ASD and 17 typically developing boys, matched for age, performance IQ, handedness, and data quality. Four tasks were administered to measure various aspects of visual information processing, together with questionnaires assessing ASD characteristics. Group differences were examined and the neural data were integrated with previously published findings using Bayesian statistics to quantify evidence for replication and to pool data and thus increase statistical power. (Partial) correlations were calculated to investigate associations between measures. The ASD group showed consistently reduced FA only in the right ILF and slower performance on the visual search task. Bayesian statistics pooling data across studies confirmed that group differences in FA were confined to the right ILF only, with the evidence for altered FA in the left ILF being indecisive. Lower FA in the right ILF tended to covary with slower visual search and a more fragmented part-oriented processing style. Individual differences in FA of the right ILF were not reliably associated with the severity of ASD traits after controlling for clinical status. Our findings support the growing evidence for reduced FA along a specific fiber tract in ASD, the right ILF.

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.

Bayesian Inference on Proportional Elections

PubMed Central

Brunello, Gabriel Hideki Vatanabe; Nakano, Eduardo Yoshio

2015-01-01

Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software. PMID:25786259

A Bayesian sequential processor approach to spectroscopic portal system decisions

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

Sale, K; Candy, J; Breitfeller, E

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

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

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

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

Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γmore » = 3α H {sub 0} model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.« less

Bayesian component separation: The Planck experience

NASA Astrophysics Data System (ADS)

Wehus, Ingunn Kathrine; Eriksen, Hans Kristian

2018-05-01

Bayesian component separation techniques have played a central role in the data reduction process of Planck. The most important strength of this approach is its global nature, in which a parametric and physical model is fitted to the data. Such physical modeling allows the user to constrain very general data models, and jointly probe cosmological, astrophysical and instrumental parameters. This approach also supports statistically robust goodness-of-fit tests in terms of data-minus-model residual maps, which are essential for identifying residual systematic effects in the data. The main challenges are high code complexity and computational cost. Whether or not these costs are justified for a given experiment depends on its final uncertainty budget. We therefore predict that the importance of Bayesian component separation techniques is likely to increase with time for intensity mapping experiments, similar to what has happened in the CMB field, as observational techniques mature, and their overall sensitivity improves.

Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Ben Abdessalem, Anis; Dervilis, Nikolaos; Wagg, David; Worden, Keith

2018-01-01

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours.

Bayesian inference on proportional elections.

PubMed

Brunello, Gabriel Hideki Vatanabe; Nakano, Eduardo Yoshio

2015-01-01

Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software.

Assessing noninferiority in a three-arm trial using the Bayesian approach.

PubMed

Ghosh, Pulak; Nathoo, Farouk; Gönen, Mithat; Tiwari, Ram C

2011-07-10

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm trial consists of a placebo, a reference and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with comparing this reference to an experimental treatment. In this paper, we consider the analysis of non-inferiority trials using Bayesian methods which incorporate both parametric as well as semi-parametric models. The resulting testing approach is both flexible and robust. The benefit of the proposed Bayesian methods is assessed via simulation, based on a study examining home-based blood pressure interventions. Copyright © 2011 John Wiley & Sons, Ltd.

A Dynamic Bayesian Network Model for the Production and Inventory Control

NASA Astrophysics Data System (ADS)

Shin, Ji-Sun; Takazaki, Noriyuki; Lee, Tae-Hong; Kim, Jin-Il; Lee, Hee-Hyol

In general, the production quantities and delivered goods are changed randomly and then the total stock is also changed randomly. This paper deals with the production and inventory control using the Dynamic Bayesian Network. Bayesian Network is a probabilistic model which represents the qualitative dependence between two or more random variables by the graph structure, and indicates the quantitative relations between individual variables by the conditional probability. The probabilistic distribution of the total stock is calculated through the propagation of the probability on the network. Moreover, an adjusting rule of the production quantities to maintain the probability of a lower limit and a ceiling of the total stock to certain values is shown.

Why Current Statistics of Complementary Alternative Medicine Clinical Trials is Invalid.

PubMed

Pandolfi, Maurizio; Carreras, Giulia

2018-06-07

It is not sufficiently known that frequentist statistics cannot provide direct information on the probability that the research hypothesis tested is correct. The error resulting from this misunderstanding is compounded when the hypotheses under scrutiny have precarious scientific bases, which, generally, those of complementary alternative medicine (CAM) are. In such cases, it is mandatory to use inferential statistics, considering the prior probability that the hypothesis tested is true, such as the Bayesian statistics. The authors show that, under such circumstances, no real statistical significance can be achieved in CAM clinical trials. In this respect, CAM trials involving human material are also hardly defensible from an ethical viewpoint.

Error-in-variables models in calibration

NASA Astrophysics Data System (ADS)

Lira, I.; Grientschnig, D.

2017-12-01

In many calibration operations, the stimuli applied to the measuring system or instrument under test are derived from measurement standards whose values may be considered to be perfectly known. In that case, it is assumed that calibration uncertainty arises solely from inexact measurement of the responses, from imperfect control of the calibration process and from the possible inaccuracy of the calibration model. However, the premise that the stimuli are completely known is never strictly fulfilled and in some instances it may be grossly inadequate. Then, error-in-variables (EIV) regression models have to be employed. In metrology, these models have been approached mostly from the frequentist perspective. In contrast, not much guidance is available on their Bayesian analysis. In this paper, we first present a brief summary of the conventional statistical techniques that have been developed to deal with EIV models in calibration. We then proceed to discuss the alternative Bayesian framework under some simplifying assumptions. Through a detailed example about the calibration of an instrument for measuring flow rates, we provide advice on how the user of the calibration function should employ the latter framework for inferring the stimulus acting on the calibrated device when, in use, a certain response is measured.

Nonparametric Bayesian clustering to detect bipolar methylated genomic loci.

PubMed

Wu, Xiaowei; Sun, Ming-An; Zhu, Hongxiao; Xie, Hehuang

2015-01-16

With recent development in sequencing technology, a large number of genome-wide DNA methylation studies have generated massive amounts of bisulfite sequencing data. The analysis of DNA methylation patterns helps researchers understand epigenetic regulatory mechanisms. Highly variable methylation patterns reflect stochastic fluctuations in DNA methylation, whereas well-structured methylation patterns imply deterministic methylation events. Among these methylation patterns, bipolar patterns are important as they may originate from allele-specific methylation (ASM) or cell-specific methylation (CSM). Utilizing nonparametric Bayesian clustering followed by hypothesis testing, we have developed a novel statistical approach to identify bipolar methylated genomic regions in bisulfite sequencing data. Simulation studies demonstrate that the proposed method achieves good performance in terms of specificity and sensitivity. We used the method to analyze data from mouse brain and human blood methylomes. The bipolar methylated segments detected are found highly consistent with the differentially methylated regions identified by using purified cell subsets. Bipolar DNA methylation often indicates epigenetic heterogeneity caused by ASM or CSM. With allele-specific events filtered out or appropriately taken into account, our proposed approach sheds light on the identification of cell-specific genes/pathways under strong epigenetic control in a heterogeneous cell population.

Bayesian Modeling of a Human MMORPG Player

NASA Astrophysics Data System (ADS)

Synnaeve, Gabriel; Bessière, Pierre

2011-03-01

This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.

Modified Bayesian Kriging for Noisy Response Problems for Reliability Analysis

DTIC Science & Technology

2015-01-01

52242, USA nicholas-gaul@uiowa.edu Mary Kathryn Cowles Department of Statistics & Actuarial Science College of Liberal Arts and Sciences , The...Forrester, A. I. J., & Keane, A. J. (2009). Recent advances in surrogate-based optimization. Progress in Aerospace Sciences , 45(1–3), 50-79. doi...Wiley. [27] Sacks, J., Welch, W. J., Toby J. Mitchell, & Wynn, H. P. (1989). Design and analysis of computer experiments. Statistical Science , 4

Density-based empirical likelihood procedures for testing symmetry of data distributions and K-sample comparisons.

PubMed

Vexler, Albert; Tanajian, Hovig; Hutson, Alan D

In practice, parametric likelihood-ratio techniques are powerful statistical tools. In this article, we propose and examine novel and simple distribution-free test statistics that efficiently approximate parametric likelihood ratios to analyze and compare distributions of K groups of observations. Using the density-based empirical likelihood methodology, we develop a Stata package that applies to a test for symmetry of data distributions and compares K -sample distributions. Recognizing that recent statistical software packages do not sufficiently address K -sample nonparametric comparisons of data distributions, we propose a new Stata command, vxdbel, to execute exact density-based empirical likelihood-ratio tests using K samples. To calculate p -values of the proposed tests, we use the following methods: 1) a classical technique based on Monte Carlo p -value evaluations; 2) an interpolation technique based on tabulated critical values; and 3) a new hybrid technique that combines methods 1 and 2. The third, cutting-edge method is shown to be very efficient in the context of exact-test p -value computations. This Bayesian-type method considers tabulated critical values as prior information and Monte Carlo generations of test statistic values as data used to depict the likelihood function. In this case, a nonparametric Bayesian method is proposed to compute critical values of exact tests.

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

Unraveling multiple changes in complex climate time series using Bayesian inference

NASA Astrophysics Data System (ADS)

Berner, Nadine; Trauth, Martin H.; Holschneider, Matthias

2016-04-01

Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of observations. Unraveling such transitions yields essential information for the understanding of the observed system. The precise detection and basic characterization of underlying changes is therefore of particular importance in environmental sciences. We present a kernel-based Bayesian inference approach to investigate direct as well as indirect climate observations for multiple generic transition events. In order to develop a diagnostic approach designed to capture a variety of natural processes, the basic statistical features of central tendency and dispersion are used to locally approximate a complex time series by a generic transition model. A Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of such a transition. To systematically investigate time series for multiple changes occurring at different temporal scales, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. Thus, based on a generic transition model a probability expression is derived that is capable to indicate multiple changes within a complex time series. We discuss the method's performance by investigating direct and indirect climate observations. The approach is applied to environmental time series (about 100 a), from the weather station in Tuscaloosa, Alabama, and confirms documented instrumentation changes. Moreover, the approach is used to investigate a set of complex terrigenous dust records from the ODP sites 659, 721/722 and 967 interpreted as climate indicators of the African region of the Plio-Pleistocene period (about 5 Ma). The detailed inference unravels multiple transitions underlying the indirect climate observations coinciding with established global climate events.

Bayesian inferences suggest that Amazon Yunga Natives diverged from Andeans less than 5000 ybp: implications for South American prehistory.

PubMed

Scliar, Marilia O; Gouveia, Mateus H; Benazzo, Andrea; Ghirotto, Silvia; Fagundes, Nelson J R; Leal, Thiago P; Magalhães, Wagner C S; Pereira, Latife; Rodrigues, Maira R; Soares-Souza, Giordano B; Cabrera, Lilia; Berg, Douglas E; Gilman, Robert H; Bertorelle, Giorgio; Tarazona-Santos, Eduardo

2014-09-30

Archaeology reports millenary cultural contacts between Peruvian Coast-Andes and the Amazon Yunga, a rainforest transitional region between Andes and Lower Amazonia. To clarify the relationships between cultural and biological evolution of these populations, in particular between Amazon Yungas and Andeans, we used DNA-sequence data, a model-based Bayesian approach and several statistical validations to infer a set of demographic parameters. We found that the genetic diversity of the Shimaa (an Amazon Yunga population) is a subset of that of Quechuas from Central-Andes. Using the Isolation-with-Migration population genetics model, we inferred that the Shimaa ancestors were a small subgroup that split less than 5300 years ago (after the development of complex societies) from an ancestral Andean population. After the split, the most plausible scenario compatible with our results is that the ancestors of Shimaas moved toward the Peruvian Amazon Yunga and incorporated the culture and language of some of their neighbors, but not a substantial amount of their genes. We validated our results using Approximate Bayesian Computations, posterior predictive tests and the analysis of pseudo-observed datasets. We presented a case study in which model-based Bayesian approaches, combined with necessary statistical validations, shed light into the prehistoric demographic relationship between Andeans and a population from the Amazon Yunga. Our results offer a testable model for the peopling of this large transitional environmental region between the Andes and the Lower Amazonia. However, studies on larger samples and involving more populations of these regions are necessary to confirm if the predominant Andean biological origin of the Shimaas is the rule, and not the exception.

From empirical Bayes to full Bayes : methods for analyzing traffic safety data.

DOT National Transportation Integrated Search

2004-10-24

Traffic safety engineers are among the early adopters of Bayesian statistical tools for : analyzing crash data. As in many other areas of application, empirical Bayes methods were : their first choice, perhaps because they represent an intuitively ap...

A novel approach for examining future US domestic water demand

EPA Science Inventory

Costs of repairing and expanding aging infrastructure and competing demands for water from other sectors such as industry and agriculture are stretching policy makers’ abilities to meet essential domestic drinking water needs for future generations. Using Bayesian statistic...

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

Weaver, Brian Phillip

The purpose of this document is to describe the statistical modeling effort for gas concentrations in WIPP storage containers. The concentration (in ppm) of CO 2 in the headspace volume of standard waste box (SWB) 68685 is shown. A Bayesian approach and an adaptive Metropolis-Hastings algorithm were used.

A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data

PubMed Central

Huynh, Tran; Quick, Harrison; Ramachandran, Gurumurthy; Banerjee, Sudipto; Stenzel, Mark; Sandler, Dale P.; Engel, Lawrence S.; Kwok, Richard K.; Blair, Aaron; Stewart, Patricia A.

2016-01-01

Classical statistical methods for analyzing exposure data with values below the detection limits are well described in the occupational hygiene literature, but an evaluation of a Bayesian approach for handling such data is currently lacking. Here, we first describe a Bayesian framework for analyzing censored data. We then present the results of a simulation study conducted to compare the β-substitution method with a Bayesian method for exposure datasets drawn from lognormal distributions and mixed lognormal distributions with varying sample sizes, geometric standard deviations (GSDs), and censoring for single and multiple limits of detection. For each set of factors, estimates for the arithmetic mean (AM), geometric mean, GSD, and the 95th percentile (X0.95) of the exposure distribution were obtained. We evaluated the performance of each method using relative bias, the root mean squared error (rMSE), and coverage (the proportion of the computed 95% uncertainty intervals containing the true value). The Bayesian method using non-informative priors and the β-substitution method were generally comparable in bias and rMSE when estimating the AM and GM. For the GSD and the 95th percentile, the Bayesian method with non-informative priors was more biased and had a higher rMSE than the β-substitution method, but use of more informative priors generally improved the Bayesian method’s performance, making both the bias and the rMSE more comparable to the β-substitution method. An advantage of the Bayesian method is that it provided estimates of uncertainty for these parameters of interest and good coverage, whereas the β-substitution method only provided estimates of uncertainty for the AM, and coverage was not as consistent. Selection of one or the other method depends on the needs of the practitioner, the availability of prior information, and the distribution characteristics of the measurement data. We suggest the use of Bayesian methods if the practitioner has the computational resources and prior information, as the method would generally provide accurate estimates and also provides the distributions of all of the parameters, which could be useful for making decisions in some applications. PMID:26209598

Predicting Time Series Outputs and Time-to-Failure for an Aircraft Controller Using Bayesian Modeling

NASA Technical Reports Server (NTRS)

He, Yuning

2015-01-01

Safety of unmanned aerial systems (UAS) is paramount, but the large number of dynamically changing controller parameters makes it hard to determine if the system is currently stable, and the time before loss of control if not. We propose a hierarchical statistical model using Treed Gaussian Processes to predict (i) whether a flight will be stable (success) or become unstable (failure), (ii) the time-to-failure if unstable, and (iii) time series outputs for flight variables. We first classify the current flight input into success or failure types, and then use separate models for each class to predict the time-to-failure and time series outputs. As different inputs may cause failures at different times, we have to model variable length output curves. We use a basis representation for curves and learn the mappings from input to basis coefficients. We demonstrate the effectiveness of our prediction methods on a NASA neuro-adaptive flight control system.

Bayesian estimation inherent in a Mexican-hat-type neural network

NASA Astrophysics Data System (ADS)

Takiyama, Ken

2016-05-01

Brain functions, such as perception, motor control and learning, and decision making, have been explained based on a Bayesian framework, i.e., to decrease the effects of noise inherent in the human nervous system or external environment, our brain integrates sensory and a priori information in a Bayesian optimal manner. However, it remains unclear how Bayesian computations are implemented in the brain. Herein, I address this issue by analyzing a Mexican-hat-type neural network, which was used as a model of the visual cortex, motor cortex, and prefrontal cortex. I analytically demonstrate that the dynamics of an order parameter in the model corresponds exactly to a variational inference of a linear Gaussian state-space model, a Bayesian estimation, when the strength of recurrent synaptic connectivity is appropriately stronger than that of an external stimulus, a plausible condition in the brain. This exact correspondence can reveal the relationship between the parameters in the Bayesian estimation and those in the neural network, providing insight for understanding brain functions.

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 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.

Using Campylobacter spp. and Escherichia coli data and Bayesian microbial risk assessment to examine public health risks in agricultural watersheds under tile drainage management.

PubMed

Schmidt, P J; Pintar, K D M; Fazil, A M; Flemming, C A; Lanthier, M; Laprade, N; Sunohara, M D; Simhon, A; Thomas, J L; Topp, E; Wilkes, G; Lapen, D R

2013-06-15

Human campylobacteriosis is the leading bacterial gastrointestinal illness in Canada; environmental transmission has been implicated in addition to transmission via consumption of contaminated food. Information about Campylobacter spp. occurrence at the watershed scale will enhance our understanding of the associated public health risks and the efficacy of source water protection strategies. The overriding purpose of this study is to provide a quantitative framework to assess and compare the relative public health significance of watershed microbial water quality associated with agricultural BMPs. A microbial monitoring program was expanded from fecal indicator analyses and Campylobacter spp. presence/absence tests to the development of a novel, 11-tube most probable number (MPN) method that targeted Campylobacter jejuni, Campylobacter coli, and Campylobacter lari. These three types of data were used to make inferences about theoretical risks in a watershed in which controlled tile drainage is widely practiced, an adjacent watershed with conventional (uncontrolled) tile drainage, and reference sites elsewhere in the same river basin. E. coli concentrations (MPN and plate count) in the controlled tile drainage watershed were statistically higher (2008-11), relative to the uncontrolled tile drainage watershed, but yearly variation was high as well. Escherichia coli loading for years 2008-11 combined were statistically higher in the controlled watershed, relative to the uncontrolled tile drainage watershed, but Campylobacter spp. loads for 2010-11 were generally higher for the uncontrolled tile drainage watershed (but not statistically significant). Using MPN data and a Bayesian modelling approach, higher mean Campylobacter spp. concentrations were found in the controlled tile drainage watershed relative to the uncontrolled tile drainage watershed (2010, 2011). A second-order quantitative microbial risk assessment (QMRA) was used, in a relative way, to identify differences in mean Campylobacter spp. infection risks among monitoring sites for a hypothetical exposure scenario. Greater relative mean risks were obtained for sites in the controlled tile drainage watershed than in the uncontrolled tile drainage watershed in each year of monitoring with pair-wise posterior probabilities exceeding 0.699, and the lowest relative mean risks were found at a downstream drinking water intake reference site. The second-order modelling approach was used to partition sources of uncertainty, which revealed that an adequate representation of the temporal variation in Campylobacter spp. concentrations for risk assessment was achieved with as few as 10 MPN data per site. This study demonstrates for the first time how QMRA can be implemented to evaluate, in a relative sense, the public health implications of controlled tile drainage on watershed-scale water quality. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

Bayesian Correlation Analysis for Sequence Count Data

PubMed Central

Lau, Nelson; Perkins, Theodore J.

2016-01-01

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

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.

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.

Inference of reaction rate parameters based on summary statistics from experiments

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

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

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

Inference of reaction rate parameters based on summary statistics from experiments

DOE PAGES

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

2016-10-15

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

A Test by Any Other Name: P Values, Bayes Factors, and Statistical Inference.

PubMed

Stern, Hal S

2016-01-01

Procedures used for statistical inference are receiving increased scrutiny as the scientific community studies the factors associated with insuring reproducible research. This note addresses recent negative attention directed at p values, the relationship of confidence intervals and tests, and the role of Bayesian inference and Bayes factors, with an eye toward better understanding these different strategies for statistical inference. We argue that researchers and data analysts too often resort to binary decisions (e.g., whether to reject or accept the null hypothesis) in settings where this may not be required.

An Analysis of Operational Suitability for Test and Evaluation of Highly Reliable Systems

DTIC Science & Technology

1994-03-04

Exposition," Journal of the American Statistical A iation-59: 353-375 (June 1964). 17. SYS 229, Test and Evaluation Management Coursebook , School of Systems...in hours, 0 is 2-5 the desired MTBCF in hours, R is the number of critical failures, and a is the P[type-I error] of the X2 statistic with 2*R+2...design of experiments (DOE) tables and the use of Bayesian statistics to increase the confidence level of the test results that will be obtained from

Statistical Modeling for Radiation Hardness Assurance

NASA Technical Reports Server (NTRS)

Ladbury, Raymond L.

2014-01-01

We cover the models and statistics associated with single event effects (and total ionizing dose), why we need them, and how to use them: What models are used, what errors exist in real test data, and what the model allows us to say about the DUT will be discussed. In addition, how to use other sources of data such as historical, heritage, and similar part and how to apply experience, physics, and expert opinion to the analysis will be covered. Also included will be concepts of Bayesian statistics, data fitting, and bounding rates.

Analyzing Genome-Wide Association Studies with an FDR Controlling Modification of the Bayesian Information Criterion

PubMed Central

Dolejsi, Erich; Bodenstorfer, Bernhard; Frommlet, Florian

2014-01-01

The prevailing method of analyzing GWAS data is still to test each marker individually, although from a statistical point of view it is quite obvious that in case of complex traits such single marker tests are not ideal. Recently several model selection approaches for GWAS have been suggested, most of them based on LASSO-type procedures. Here we will discuss an alternative model selection approach which is based on a modification of the Bayesian Information Criterion (mBIC2) which was previously shown to have certain asymptotic optimality properties in terms of minimizing the misclassification error. Heuristic search strategies are introduced which attempt to find the model which minimizes mBIC2, and which are efficient enough to allow the analysis of GWAS data. Our approach is implemented in a software package called MOSGWA. Its performance in case control GWAS is compared with the two algorithms HLASSO and d-GWASelect, as well as with single marker tests, where we performed a simulation study based on real SNP data from the POPRES sample. Our results show that MOSGWA performs slightly better than HLASSO, where specifically for more complex models MOSGWA is more powerful with only a slight increase in Type I error. On the other hand according to our simulations GWASelect does not at all control the type I error when used to automatically determine the number of important SNPs. We also reanalyze the GWAS data from the Wellcome Trust Case-Control Consortium and compare the findings of the different procedures, where MOSGWA detects for complex diseases a number of interesting SNPs which are not found by other methods. PMID:25061809

Planning for community resilience to future United States domestic water demand

EPA Science Inventory

Costs of repairing and expanding aging infrastructure and competing demands for water from other sectors such as industry and agriculture are stretching water managers’ abilities to meet essential domestic drinking water needs for future generations. Using Bayesian statistical mo...

Transportation safety data and analysis : Volume 1, Analyzing the effectiveness of safety measures using Bayesian methods.

DOT National Transportation Integrated Search

2010-12-01

Recent research suggests that traditional safety evaluation methods may be inadequate in accurately determining the effectiveness of roadway safety measures. In recent years, advanced statistical methods are being utilized in traffic safety studies t...

Predicting Football Matches Results using Bayesian Networks for English Premier League (EPL)

NASA Astrophysics Data System (ADS)

Razali, Nazim; Mustapha, Aida; Yatim, Faiz Ahmad; Aziz, Ruhaya Ab

2017-08-01

The issues of modeling asscoiation football prediction model has become increasingly popular in the last few years and many different approaches of prediction models have been proposed with the point of evaluating the attributes that lead a football team to lose, draw or win the match. There are three types of approaches has been considered for predicting football matches results which include statistical approaches, machine learning approaches and Bayesian approaches. Lately, many studies regarding football prediction models has been produced using Bayesian approaches. This paper proposes a Bayesian Networks (BNs) to predict the results of football matches in term of home win (H), away win (A) and draw (D). The English Premier League (EPL) for three seasons of 2010-2011, 2011-2012 and 2012-2013 has been selected and reviewed. K-fold cross validation has been used for testing the accuracy of prediction model. The required information about the football data is sourced from a legitimate site at http://www.football-data.co.uk. BNs achieved predictive accuracy of 75.09% in average across three seasons. It is hoped that the results could be used as the benchmark output for future research in predicting football matches results.

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.

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

PubMed Central

2010-01-01

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

Climatic Models Ensemble-based Mid-21st Century Runoff Projections: A Bayesian Framework

NASA Astrophysics Data System (ADS)

Achieng, K. O.; Zhu, J.

2017-12-01

There are a number of North American Regional Climate Change Assessment Program (NARCCAP) climatic models that have been used to project surface runoff in the mid-21st century. Statistical model selection techniques are often used to select the model that best fits data. However, model selection techniques often lead to different conclusions. In this study, ten models are averaged in Bayesian paradigm to project runoff. Bayesian Model Averaging (BMA) is used to project and identify effect of model uncertainty on future runoff projections. Baseflow separation - a two-digital filter which is also called Eckhardt filter - is used to separate USGS streamflow (total runoff) into two components: baseflow and surface runoff. We use this surface runoff as the a priori runoff when conducting BMA of runoff simulated from the ten RCM models. The primary objective of this study is to evaluate how well RCM multi-model ensembles simulate surface runoff, in a Bayesian framework. Specifically, we investigate and discuss the following questions: How well do ten RCM models ensemble jointly simulate surface runoff by averaging over all the models using BMA, given a priori surface runoff? What are the effects of model uncertainty on surface runoff simulation?

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

Vrugt, Jasper A; Robinson, Bruce A; Ter Braak, Cajo J F

In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented usingmore » the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.« less

Bayesian Integrated Microbial Forensics

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

Jarman, Kristin H.; Kreuzer-Martin, Helen W.; Wunschel, David S.

2008-06-01

In the aftermath of the 2001 anthrax letters, researchers have been exploring ways to predict the production environment of unknown source microorganisms. Different mass spectral techniques are being developed to characterize components of a microbe’s culture medium including water, carbon and nitrogen sources, metal ions added, and the presence of agar. Individually, each technique has the potential to identify one or two ingredients in a culture medium recipe. However, by integrating data from multiple mass spectral techniques, a more complete characterization is possible. We present a Bayesian statistical approach to integrated microbial forensics and illustrate its application on spores grownmore » in different culture media.« less

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.

IMAGINE: Interstellar MAGnetic field INference Engine

NASA Astrophysics Data System (ADS)

Steininger, Theo

2018-03-01

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

Bayesian 2-Stage Space-Time Mixture Modeling With Spatial Misalignment of the Exposure in Small Area Health Data.

PubMed

Lawson, Andrew B; Choi, Jungsoon; Cai, Bo; Hossain, Monir; Kirby, Russell S; Liu, Jihong

2012-09-01

We develop a new Bayesian two-stage space-time mixture model to investigate the effects of air pollution on asthma. The two-stage mixture model proposed allows for the identification of temporal latent structure as well as the estimation of the effects of covariates on health outcomes. In the paper, we also consider spatial misalignment of exposure and health data. A simulation study is conducted to assess the performance of the 2-stage mixture model. We apply our statistical framework to a county-level ambulatory care asthma data set in the US state of Georgia for the years 1999-2008.

On the limitations of standard statistical modeling in biological systems: a full Bayesian approach for biology.

PubMed

Gomez-Ramirez, Jaime; Sanz, Ricardo

2013-09-01

One of the most important scientific challenges today is the quantitative and predictive understanding of biological function. Classical mathematical and computational approaches have been enormously successful in modeling inert matter, but they may be inadequate to address inherent features of biological systems. We address the conceptual and methodological obstacles that lie in the inverse problem in biological systems modeling. We introduce a full Bayesian approach (FBA), a theoretical framework to study biological function, in which probability distributions are conditional on biophysical information that physically resides in the biological system that is studied by the scientist. Copyright © 2013 Elsevier Ltd. All rights reserved.

Quantifying Trace Amounts of Aggregates in Biopharmaceuticals Using Analytical Ultracentrifugation Sedimentation Velocity: Bayesian Analyses and F Statistics.

PubMed

Wafer, Lucas; Kloczewiak, Marek; Luo, Yin

2016-07-01

Analytical ultracentrifugation-sedimentation velocity (AUC-SV) is often used to quantify high molar mass species (HMMS) present in biopharmaceuticals. Although these species are often present in trace quantities, they have received significant attention due to their potential immunogenicity. Commonly, AUC-SV data is analyzed as a diffusion-corrected, sedimentation coefficient distribution, or c(s), using SEDFIT to numerically solve Lamm-type equations. SEDFIT also utilizes maximum entropy or Tikhonov-Phillips regularization to further allow the user to determine relevant sample information, including the number of species present, their sedimentation coefficients, and their relative abundance. However, this methodology has several, often unstated, limitations, which may impact the final analysis of protein therapeutics. These include regularization-specific effects, artificial "ripple peaks," and spurious shifts in the sedimentation coefficients. In this investigation, we experimentally verified that an explicit Bayesian approach, as implemented in SEDFIT, can largely correct for these effects. Clear guidelines on how to implement this technique and interpret the resulting data, especially for samples containing micro-heterogeneity (e.g., differential glycosylation), are also provided. In addition, we demonstrated how the Bayesian approach can be combined with F statistics to draw more accurate conclusions and rigorously exclude artifactual peaks. Numerous examples with an antibody and an antibody-drug conjugate were used to illustrate the strengths and drawbacks of each technique.

Simple summation rule for optimal fixation selection in visual search.

PubMed

Najemnik, Jiri; Geisler, Wilson S

2009-06-01

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

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.

Causal modelling applied to the risk assessment of a wastewater discharge.

PubMed

Paul, Warren L; Rokahr, Pat A; Webb, Jeff M; Rees, Gavin N; Clune, Tim S

2016-03-01

Bayesian networks (BNs), or causal Bayesian networks, have become quite popular in ecological risk assessment and natural resource management because of their utility as a communication and decision-support tool. Since their development in the field of artificial intelligence in the 1980s, however, Bayesian networks have evolved and merged with structural equation modelling (SEM). Unlike BNs, which are constrained to encode causal knowledge in conditional probability tables, SEMs encode this knowledge in structural equations, which is thought to be a more natural language for expressing causal information. This merger has clarified the causal content of SEMs and generalised the method such that it can now be performed using standard statistical techniques. As it was with BNs, the utility of this new generation of SEM in ecological risk assessment will need to be demonstrated with examples to foster an understanding and acceptance of the method. Here, we applied SEM to the risk assessment of a wastewater discharge to a stream, with a particular focus on the process of translating a causal diagram (conceptual model) into a statistical model which might then be used in the decision-making and evaluation stages of the risk assessment. The process of building and testing a spatial causal model is demonstrated using data from a spatial sampling design, and the implications of the resulting model are discussed in terms of the risk assessment. It is argued that a spatiotemporal causal model would have greater external validity than the spatial model, enabling broader generalisations to be made regarding the impact of a discharge, and greater value as a tool for evaluating the effects of potential treatment plant upgrades. Suggestions are made on how the causal model could be augmented to include temporal as well as spatial information, including suggestions for appropriate statistical models and analyses.

Adaptive statistical pattern classifiers for remotely sensed data

NASA Technical Reports Server (NTRS)

Gonzalez, R. C.; Pace, M. O.; Raulston, H. S.

1975-01-01

A technique for the adaptive estimation of nonstationary statistics necessary for Bayesian classification is developed. The basic approach to the adaptive estimation procedure consists of two steps: (1) an optimal stochastic approximation of the parameters of interest and (2) a projection of the parameters in time or position. A divergence criterion is developed to monitor algorithm performance. Comparative results of adaptive and nonadaptive classifier tests are presented for simulated four dimensional spectral scan data.

Statistical distribution of time to crack initiation and initial crack size using service data

NASA Technical Reports Server (NTRS)

Heller, R. A.; Yang, J. N.

1977-01-01

Crack growth inspection data gathered during the service life of the C-130 Hercules airplane were used in conjunction with a crack propagation rule to estimate the distribution of crack initiation times and of initial crack sizes. A Bayesian statistical approach was used to calculate the fraction of undetected initiation times as a function of the inspection time and the reliability of the inspection procedure used.

Logistic random effects regression models: a comparison of statistical packages for binary and ordinal outcomes.

PubMed

Li, Baoyue; Lingsma, Hester F; Steyerberg, Ewout W; Lesaffre, Emmanuel

2011-05-23

Logistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models. We used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI) enrolled in eight Randomized Controlled Trials (RCTs) and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS) as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4), Stata (GLLAMM), SAS (GLIMMIX and NLMIXED), MLwiN ([R]IGLS) and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC), R package MCMCglmm and SAS experimental procedure MCMC.Three data sets (the full data set and two sub-datasets) were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted. The packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal) models for the main study and when based on a relatively large number of level-1 (patient level) data compared to the number of level-2 (hospital level) data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in the availability of additional tools for model evaluation, such as diagnostic plots. The experimental SAS (version 9.2) procedure MCMC appeared to be inefficient. On relatively large data sets, the different software implementations of logistic random effects regression models produced similar results. Thus, for a large data set there seems to be no explicit preference (of course if there is no preference from a philosophical point of view) for either a frequentist or Bayesian approach (if based on vague priors). The choice for a particular implementation may largely depend on the desired flexibility, and the usability of the package. For small data sets the random effects variances are difficult to estimate. In the frequentist approaches the MLE of this variance was often estimated zero with a standard error that is either zero or could not be determined, while for Bayesian methods the estimates could depend on the chosen "non-informative" prior of the variance parameter. The starting value for the variance parameter may be also critical for the convergence of the Markov chain.

Quantification of model uncertainty in aerosol optical thickness retrieval from Ozone Monitoring Instrument (OMI) measurements

NASA Astrophysics Data System (ADS)

Määttä, A.; Laine, M.; Tamminen, J.; Veefkind, J. P.

2013-09-01

We study uncertainty quantification in remote sensing of aerosols in the atmosphere with top of the atmosphere reflectance measurements from the nadir-viewing Ozone Monitoring Instrument (OMI). Focus is on the uncertainty in aerosol model selection of pre-calculated aerosol models and on the statistical modelling of the model inadequacies. The aim is to apply statistical methodologies that improve the uncertainty estimates of the aerosol optical thickness (AOT) retrieval by propagating model selection and model error related uncertainties more realistically. We utilise Bayesian model selection and model averaging methods for the model selection problem and use Gaussian processes to model the smooth systematic discrepancies from the modelled to observed reflectance. The systematic model error is learned from an ensemble of operational retrievals. The operational OMI multi-wavelength aerosol retrieval algorithm OMAERO is used for cloud free, over land pixels of the OMI instrument with the additional Bayesian model selection and model discrepancy techniques. The method is demonstrated with four examples with different aerosol properties: weakly absorbing aerosols, forest fires over Greece and Russia, and Sahara dessert dust. The presented statistical methodology is general; it is not restricted to this particular satellite retrieval application.

"Magnitude-based inference": a statistical review.

PubMed

Welsh, Alan H; Knight, Emma J

2015-04-01

We consider "magnitude-based inference" and its interpretation by examining in detail its use in the problem of comparing two means. We extract from the spreadsheets, which are provided to users of the analysis (http://www.sportsci.org/), a precise description of how "magnitude-based inference" is implemented. We compare the implemented version of the method with general descriptions of it and interpret the method in familiar statistical terms. We show that "magnitude-based inference" is not a progressive improvement on modern statistics. The additional probabilities introduced are not directly related to the confidence interval but, rather, are interpretable either as P values for two different nonstandard tests (for different null hypotheses) or as approximate Bayesian calculations, which also lead to a type of test. We also discuss sample size calculations associated with "magnitude-based inference" and show that the substantial reduction in sample sizes claimed for the method (30% of the sample size obtained from standard frequentist calculations) is not justifiable so the sample size calculations should not be used. Rather than using "magnitude-based inference," a better solution is to be realistic about the limitations of the data and use either confidence intervals or a fully Bayesian analysis.

Statistical modelling of networked human-automation performance using working memory capacity.

PubMed

Ahmed, Nisar; de Visser, Ewart; Shaw, Tyler; Mohamed-Ameen, Amira; Campbell, Mark; Parasuraman, Raja

2014-01-01

This study examines the challenging problem of modelling the interaction between individual attentional limitations and decision-making performance in networked human-automation system tasks. Analysis of real experimental data from a task involving networked supervision of multiple unmanned aerial vehicles by human participants shows that both task load and network message quality affect performance, but that these effects are modulated by individual differences in working memory (WM) capacity. These insights were used to assess three statistical approaches for modelling and making predictions with real experimental networked supervisory performance data: classical linear regression, non-parametric Gaussian processes and probabilistic Bayesian networks. It is shown that each of these approaches can help designers of networked human-automated systems cope with various uncertainties in order to accommodate future users by linking expected operating conditions and performance from real experimental data to observable cognitive traits like WM capacity. Practitioner Summary: Working memory (WM) capacity helps account for inter-individual variability in operator performance in networked unmanned aerial vehicle supervisory tasks. This is useful for reliable performance prediction near experimental conditions via linear models; robust statistical prediction beyond experimental conditions via Gaussian process models and probabilistic inference about unknown task conditions/WM capacities via Bayesian network models.

Spiritual and ceremonial plants in North America: an assessment of Moerman's ethnobotanical database comparing Residual, Binomial, Bayesian and Imprecise Dirichlet Model (IDM) analysis.

PubMed

Turi, Christina E; Murch, Susan J

2013-07-09

Ethnobotanical research and the study of plants used for rituals, ceremonies and to connect with the spirit world have led to the discovery of many novel psychoactive compounds such as nicotine, caffeine, and cocaine. In North America, spiritual and ceremonial uses of plants are well documented and can be accessed online via the University of Michigan's Native American Ethnobotany Database. The objective of the study was to compare Residual, Bayesian, Binomial and Imprecise Dirichlet Model (IDM) analyses of ritual, ceremonial and spiritual plants in Moerman's ethnobotanical database and to identify genera that may be good candidates for the discovery of novel psychoactive compounds. The database was queried with the following format "Family Name AND Ceremonial OR Spiritual" for 263 North American botanical families. Spiritual and ceremonial flora consisted of 86 families with 517 species belonging to 292 genera. Spiritual taxa were then grouped further into ceremonial medicines and items categories. Residual, Bayesian, Binomial and IDM analysis were performed to identify over and under-utilized families. The 4 statistical approaches were in good agreement when identifying under-utilized families but large families (>393 species) were underemphasized by Binomial, Bayesian and IDM approaches for over-utilization. Residual, Binomial, and IDM analysis identified similar families as over-utilized in the medium (92-392 species) and small (<92 species) classes. The families Apiaceae, Asteraceae, Ericacea, Pinaceae and Salicaceae were identified as significantly over-utilized as ceremonial medicines in medium and large sized families. Analysis of genera within the Apiaceae and Asteraceae suggest that the genus Ligusticum and Artemisia are good candidates for facilitating the discovery of novel psychoactive compounds. The 4 statistical approaches were not consistent in the selection of over-utilization of flora. Residual analysis revealed overall trends that were supported by Binomial analysis when separated into small, medium and large families. The Bayesian, Binomial and IDM approaches identified different genera as potentially important. Species belonging to the genus Artemisia and Ligusticum were most consistently identified and may be valuable in future studies of the ethnopharmacology. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Consensus in the Wasserstein Metric Space of Probability Measures

DTIC Science & Technology

2015-07-01

this direction, potential applications/uses for the Wasser - stein barycentre (itself) have been considered previously in a number of fields...one is interested in more general empirical input measures. Applications in machine learning and Bayesian statistics have also made use of the Wasser

Bayesian Methods for Determining the Importance of Effects

USDA-ARS?s Scientific Manuscript database

Criticisms have plagued the frequentist null-hypothesis significance testing (NHST) procedure since the day it was created from the Fisher Significance Test and Hypothesis Test of Jerzy Neyman and Egon Pearson. Alternatives to NHST exist in frequentist statistics, but competing methods are also avai...

Deductive Updating Is Not Bayesian

ERIC Educational Resources Information Center

Markovits, Henry; Brisson, Janie; de Chantal, Pier-Luc

2015-01-01

One of the major debates concerning the nature of inferential reasoning is between counterexample-based theories such as mental model theory and probabilistic theories. This study looks at conclusion updating after the addition of statistical information to examine the hypothesis that deductive reasoning cannot be explained by probabilistic…

Assessing Uncertainty in the Toxicology of PFOA

EPA Science Inventory

We use an approach known as Bayesian statistics to characterize our knowledge about the behavior of a chemical prior to an experiment and make explicit our assumptions about how we think the chemical behaves. When we then analyze the results of an experiment, we determine probab...

Smile detectors correlation

NASA Astrophysics Data System (ADS)

Yuksel, Kivanc; Chang, Xin; Skarbek, Władysław

2017-08-01

The novel smile recognition algorithm is presented based on extraction of 68 facial salient points (fp68) using the ensemble of regression trees. The smile detector exploits the Support Vector Machine linear model. It is trained with few hundreds exemplar images by SVM algorithm working in 136 dimensional space. It is shown by the strict statistical data analysis that such geometric detector strongly depends on the geometry of mouth opening area, measured by triangulation of outer lip contour. To this goal two Bayesian detectors were developed and compared with SVM detector. The first uses the mouth area in 2D image, while the second refers to the mouth area in 3D animated face model. The 3D modeling is based on Candide-3 model and it is performed in real time along with three smile detectors and statistics estimators. The mouth area/Bayesian detectors exhibit high correlation with fp68/SVM detector in a range [0:8; 1:0], depending mainly on light conditions and individual features with advantage of 3D technique, especially in hard light conditions.

Learning coefficient of generalization error in Bayesian estimation and vandermonde matrix-type singularity.

PubMed

Aoyagi, Miki; Nagata, Kenji

2012-06-01

The term algebraic statistics arises from the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry (Sturmfels, 2009 ). The purpose of our study is to consider the generalization error and stochastic complexity in learning theory by using the log-canonical threshold in algebraic geometry. Such thresholds correspond to the main term of the generalization error in Bayesian estimation, which is called a learning coefficient (Watanabe, 2001a , 2001b ). The learning coefficient serves to measure the learning efficiencies in hierarchical learning models. In this letter, we consider learning coefficients for Vandermonde matrix-type singularities, by using a new approach: focusing on the generators of the ideal, which defines singularities. We give tight new bound values of learning coefficients for the Vandermonde matrix-type singularities and the explicit values with certain conditions. By applying our results, we can show the learning coefficients of three-layered neural networks and normal mixture models.

Phylogenetic relationships of South American lizards of the genus Stenocercus (Squamata: Iguania): A new approach using a general mixture model for gene sequence data.

PubMed

Torres-Carvajal, Omar; Schulte, James A; Cadle, John E

2006-04-01

The South American iguanian lizard genus Stenocercus includes 54 species occurring mostly in the Andes and adjacent lowland areas from northern Venezuela and Colombia to central Argentina at elevations of 0-4000m. Small taxon or character sampling has characterized all phylogenetic analyses of Stenocercus, which has long been recognized as sister taxon to the Tropidurus Group. In this study, we use mtDNA sequence data to perform phylogenetic analyses that include 32 species of Stenocercus and 12 outgroup taxa. Monophyly of this genus is strongly supported by maximum parsimony and Bayesian analyses. Evolutionary relationships within Stenocercus are further analyzed with a Bayesian implementation of a general mixture model, which accommodates variability in the pattern of evolution across sites. These analyses indicate a basal split of Stenocercus into two clades, one of which receives very strong statistical support. In addition, we test previous hypotheses using non-parametric and parametric statistical methods, and provide a phylogenetic classification for Stenocercus.

Decision generation tools and Bayesian inference

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Wang, Wenjian; Forrester, Thomas; Kostrzewski, Andrew; Veeris, Christian; Nielsen, Thomas

2014-05-01

Digital Decision Generation (DDG) tools are important software sub-systems of Command and Control (C2) systems and technologies. In this paper, we present a special type of DDGs based on Bayesian Inference, related to adverse (hostile) networks, including such important applications as terrorism-related networks and organized crime ones.

A novel approach for choosing summary statistics in approximate Bayesian computation.

PubMed

Aeschbacher, Simon; Beaumont, Mark A; Futschik, Andreas

2012-11-01

The choice of summary statistics is a crucial step in approximate Bayesian computation (ABC). Since statistics are often not sufficient, this choice involves a trade-off between loss of information and reduction of dimensionality. The latter may increase the efficiency of ABC. Here, we propose an approach for choosing summary statistics based on boosting, a technique from the machine-learning literature. We consider different types of boosting and compare them to partial least-squares regression as an alternative. To mitigate the lack of sufficiency, we also propose an approach for choosing summary statistics locally, in the putative neighborhood of the true parameter value. We study a demographic model motivated by the reintroduction of Alpine ibex (Capra ibex) into the Swiss Alps. The parameters of interest are the mean and standard deviation across microsatellites of the scaled ancestral mutation rate (θ(anc) = 4N(e)u) and the proportion of males obtaining access to matings per breeding season (ω). By simulation, we assess the properties of the posterior distribution obtained with the various methods. According to our criteria, ABC with summary statistics chosen locally via boosting with the L(2)-loss performs best. Applying that method to the ibex data, we estimate θ(anc)≈ 1.288 and find that most of the variation across loci of the ancestral mutation rate u is between 7.7 × 10(-4) and 3.5 × 10(-3) per locus per generation. The proportion of males with access to matings is estimated as ω≈ 0.21, which is in good agreement with recent independent estimates.

P values in display items are ubiquitous and almost invariably significant: A survey of top science journals

PubMed Central

Cristea, Ioana Alina

2018-01-01

P values represent a widely used, but pervasively misunderstood and fiercely contested method of scientific inference. Display items, such as figures and tables, often containing the main results, are an important source of P values. We conducted a survey comparing the overall use of P values and the occurrence of significant P values in display items of a sample of articles in the three top multidisciplinary journals (Nature, Science, PNAS) in 2017 and, respectively, in 1997. We also examined the reporting of multiplicity corrections and its potential influence on the proportion of statistically significant P values. Our findings demonstrated substantial and growing reliance on P values in display items, with increases of 2.5 to 14.5 times in 2017 compared to 1997. The overwhelming majority of P values (94%, 95% confidence interval [CI] 92% to 96%) were statistically significant. Methods to adjust for multiplicity were almost non-existent in 1997, but reported in many articles relying on P values in 2017 (Nature 68%, Science 48%, PNAS 38%). In their absence, almost all reported P values were statistically significant (98%, 95% CI 96% to 99%). Conversely, when any multiplicity corrections were described, 88% (95% CI 82% to 93%) of reported P values were statistically significant. Use of Bayesian methods was scant (2.5%) and rarely (0.7%) articles relied exclusively on Bayesian statistics. Overall, wider appreciation of the need for multiplicity corrections is a welcome evolution, but the rapid growth of reliance on P values and implausibly high rates of reported statistical significance are worrisome. PMID:29763472

P values in display items are ubiquitous and almost invariably significant: A survey of top science journals.

PubMed

Cristea, Ioana Alina; Ioannidis, John P A

2018-01-01

P values represent a widely used, but pervasively misunderstood and fiercely contested method of scientific inference. Display items, such as figures and tables, often containing the main results, are an important source of P values. We conducted a survey comparing the overall use of P values and the occurrence of significant P values in display items of a sample of articles in the three top multidisciplinary journals (Nature, Science, PNAS) in 2017 and, respectively, in 1997. We also examined the reporting of multiplicity corrections and its potential influence on the proportion of statistically significant P values. Our findings demonstrated substantial and growing reliance on P values in display items, with increases of 2.5 to 14.5 times in 2017 compared to 1997. The overwhelming majority of P values (94%, 95% confidence interval [CI] 92% to 96%) were statistically significant. Methods to adjust for multiplicity were almost non-existent in 1997, but reported in many articles relying on P values in 2017 (Nature 68%, Science 48%, PNAS 38%). In their absence, almost all reported P values were statistically significant (98%, 95% CI 96% to 99%). Conversely, when any multiplicity corrections were described, 88% (95% CI 82% to 93%) of reported P values were statistically significant. Use of Bayesian methods was scant (2.5%) and rarely (0.7%) articles relied exclusively on Bayesian statistics. Overall, wider appreciation of the need for multiplicity corrections is a welcome evolution, but the rapid growth of reliance on P values and implausibly high rates of reported statistical significance are worrisome.

A Novel Approach for Choosing Summary Statistics in Approximate Bayesian Computation

PubMed Central

Aeschbacher, Simon; Beaumont, Mark A.; Futschik, Andreas

2012-01-01

The choice of summary statistics is a crucial step in approximate Bayesian computation (ABC). Since statistics are often not sufficient, this choice involves a trade-off between loss of information and reduction of dimensionality. The latter may increase the efficiency of ABC. Here, we propose an approach for choosing summary statistics based on boosting, a technique from the machine-learning literature. We consider different types of boosting and compare them to partial least-squares regression as an alternative. To mitigate the lack of sufficiency, we also propose an approach for choosing summary statistics locally, in the putative neighborhood of the true parameter value. We study a demographic model motivated by the reintroduction of Alpine ibex (Capra ibex) into the Swiss Alps. The parameters of interest are the mean and standard deviation across microsatellites of the scaled ancestral mutation rate (θanc = 4Neu) and the proportion of males obtaining access to matings per breeding season (ω). By simulation, we assess the properties of the posterior distribution obtained with the various methods. According to our criteria, ABC with summary statistics chosen locally via boosting with the L2-loss performs best. Applying that method to the ibex data, we estimate θ^anc≈1.288 and find that most of the variation across loci of the ancestral mutation rate u is between 7.7 × 10−4 and 3.5 × 10−3 per locus per generation. The proportion of males with access to matings is estimated as ω^≈0.21, which is in good agreement with recent independent estimates. PMID:22960215

Identifying Dynamic Functional Connectivity Changes in Dementia with Lewy Bodies Based on Product Hidden Markov Models.

PubMed

Sourty, Marion; Thoraval, Laurent; Roquet, Daniel; Armspach, Jean-Paul; Foucher, Jack; Blanc, Frédéric

2016-01-01

Exploring time-varying connectivity networks in neurodegenerative disorders is a recent field of research in functional MRI. Dementia with Lewy bodies (DLB) represents 20% of the neurodegenerative forms of dementia. Fluctuations of cognition and vigilance are the key symptoms of DLB. To date, no dynamic functional connectivity (DFC) investigations of this disorder have been performed. In this paper, we refer to the concept of connectivity state as a piecewise stationary configuration of functional connectivity between brain networks. From this concept, we propose a new method for group-level as well as for subject-level studies to compare and characterize connectivity state changes between a set of resting-state networks (RSNs). Dynamic Bayesian networks, statistical and graph theory-based models, enable one to learn dependencies between interacting state-based processes. Product hidden Markov models (PHMM), an instance of dynamic Bayesian networks, are introduced here to capture both statistical and temporal aspects of DFC of a set of RSNs. This analysis was based on sliding-window cross-correlations between seven RSNs extracted from a group independent component analysis performed on 20 healthy elderly subjects and 16 patients with DLB. Statistical models of DFC differed in patients compared to healthy subjects for the occipito-parieto-frontal network, the medial occipital network and the right fronto-parietal network. In addition, pairwise comparisons of DFC of RSNs revealed a decrease of dependency between these two visual networks (occipito-parieto-frontal and medial occipital networks) and the right fronto-parietal control network. The analysis of DFC state changes thus pointed out networks related to the cognitive functions that are known to be impaired in DLB: visual processing as well as attentional and executive functions. Besides this context, product HMM applied to RSNs cross-correlations offers a promising new approach to investigate structural and temporal aspects of brain DFC.

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 voxel-based investigation for MRI-only radiotherapy of the brain using ultra short echo times

NASA Astrophysics Data System (ADS)

Edmund, Jens M.; Kjer, Hans M.; Van Leemput, Koen; Hansen, Rasmus H.; Andersen, Jon AL; Andreasen, Daniel

2014-12-01

Radiotherapy (RT) based on magnetic resonance imaging (MRI) as the only modality, so-called MRI-only RT, would remove the systematic registration error between MR and computed tomography (CT), and provide co-registered MRI for assessment of treatment response and adaptive RT. Electron densities, however, need to be assigned to the MRI images for dose calculation and patient setup based on digitally reconstructed radiographs (DRRs). Here, we investigate the geometric and dosimetric performance for a number of popular voxel-based methods to generate a so-called pseudo CT (pCT). Five patients receiving cranial irradiation, each containing a co-registered MRI and CT scan, were included. An ultra short echo time MRI sequence for bone visualization was used. Six methods were investigated for three popular types of voxel-based approaches; (1) threshold-based segmentation, (2) Bayesian segmentation and (3) statistical regression. Each approach contained two methods. Approach 1 used bulk density assignment of MRI voxels into air, soft tissue and bone based on logical masks and the transverse relaxation time T2 of the bone. Approach 2 used similar bulk density assignments with Bayesian statistics including or excluding additional spatial information. Approach 3 used a statistical regression correlating MRI voxels with their corresponding CT voxels. A similar photon and proton treatment plan was generated for a target positioned between the nasal cavity and the brainstem for all patients. The CT agreement with the pCT of each method was quantified and compared with the other methods geometrically and dosimetrically using both a number of reported metrics and introducing some novel metrics. The best geometrical agreement with CT was obtained with the statistical regression methods which performed significantly better than the threshold and Bayesian segmentation methods (excluding spatial information). All methods agreed significantly better with CT than a reference water MRI comparison. The mean dosimetric deviation for photons and protons compared to the CT was about 2% and highest in the gradient dose region of the brainstem. Both the threshold based method and the statistical regression methods showed the highest dosimetrical agreement. Generation of pCTs using statistical regression seems to be the most promising candidate for MRI-only RT of the brain. Further, the total amount of different tissues needs to be taken into account for dosimetric considerations regardless of their correct geometrical position.

Evaluation of calibration efficacy under different levels of uncertainty

DOE PAGES

Heo, Yeonsook; Graziano, Diane J.; Guzowski, Leah; ...

2014-06-10

This study examines how calibration performs under different levels of uncertainty in model input data. It specifically assesses the efficacy of Bayesian calibration to enhance the reliability of EnergyPlus model predictions. A Bayesian approach can be used to update uncertain values of parameters, given measured energy-use data, and to quantify the associated uncertainty.We assess the efficacy of Bayesian calibration under a controlled virtual-reality setup, which enables rigorous validation of the accuracy of calibration results in terms of both calibrated parameter values and model predictions. Case studies demonstrate the performance of Bayesian calibration of base models developed from audit data withmore » differing levels of detail in building design, usage, and operation.« less

Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests

NASA Astrophysics Data System (ADS)

Wheeler, David C.; Waller, Lance A.

2009-03-01

In this paper, we compare and contrast a Bayesian spatially varying coefficient process (SVCP) model with a geographically weighted regression (GWR) model for the estimation of the potentially spatially varying regression effects of alcohol outlets and illegal drug activity on violent crime in Houston, Texas. In addition, we focus on the inherent coefficient shrinkage properties of the Bayesian SVCP model as a way to address increased coefficient variance that follows from collinearity in GWR models. We outline the advantages of the Bayesian model in terms of reducing inflated coefficient variance, enhanced model flexibility, and more formal measuring of model uncertainty for prediction. We find spatially varying effects for alcohol outlets and drug violations, but the amount of variation depends on the type of model used. For the Bayesian model, this variation is controllable through the amount of prior influence placed on the variance of the coefficients. For example, the spatial pattern of coefficients is similar for the GWR and Bayesian models when a relatively large prior variance is used in the Bayesian model.

Bayesian estimation and use of high-throughput remote sensing indices for quantitative genetic analyses of leaf growth.

PubMed

Baker, Robert L; Leong, Wen Fung; An, Nan; Brock, Marcus T; Rubin, Matthew J; Welch, Stephen; Weinig, Cynthia

2018-02-01

We develop Bayesian function-valued trait models that mathematically isolate genetic mechanisms underlying leaf growth trajectories by factoring out genotype-specific differences in photosynthesis. Remote sensing data can be used instead of leaf-level physiological measurements. Characterizing the genetic basis of traits that vary during ontogeny and affect plant performance is a major goal in evolutionary biology and agronomy. Describing genetic programs that specifically regulate morphological traits can be complicated by genotypic differences in physiological traits. We describe the growth trajectories of leaves using novel Bayesian function-valued trait (FVT) modeling approaches in Brassica rapa recombinant inbred lines raised in heterogeneous field settings. While frequentist approaches estimate parameter values by treating each experimental replicate discretely, Bayesian models can utilize information in the global dataset, potentially leading to more robust trait estimation. We illustrate this principle by estimating growth asymptotes in the face of missing data and comparing heritabilities of growth trajectory parameters estimated by Bayesian and frequentist approaches. Using pseudo-Bayes factors, we compare the performance of an initial Bayesian logistic growth model and a model that incorporates carbon assimilation (A max ) as a cofactor, thus statistically accounting for genotypic differences in carbon resources. We further evaluate two remotely sensed spectroradiometric indices, photochemical reflectance (pri2) and MERIS Terrestrial Chlorophyll Index (mtci) as covariates in lieu of A max , because these two indices were genetically correlated with A max across years and treatments yet allow much higher throughput compared to direct leaf-level gas-exchange measurements. For leaf lengths in uncrowded settings, including A max improves model fit over the initial model. The mtci and pri2 indices also outperform direct A max measurements. Of particular importance for evolutionary biologists and plant breeders, hierarchical Bayesian models estimating FVT parameters improve heritabilities compared to frequentist approaches.