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Author : Hada Moshonov
Publisher :
ISBN 13 :
Total Pages : 396 pages
Book Rating : 4.:/5 (234 download)
Download or read book Bayesian Model Chekcing - Prior-data Conflict written by Hada Moshonov and published by . This book was released on 2007 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Procedures for Model Checking, Checking for Prior-Data Conflict and Bayesian Inference written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a statistical theory as being invariant when the results of two statisticians' independent data analyses, based upon the same statistical theory and using effectively the same statistical ingredients, are the same. We discuss three aspects of invariant statistical theories. Both model checking and checking for prior-data conflict are assessments of single null hypothesis without any specific alternative hypothesis. Hence, we conduct these assessments using a measure of surprise based on a discrepancy statistic. For the discrete case, it is natural to use the probability of obtaining a data point that is less probable than the observed data. For the continuous case, the natural analog of this is not invariant under equivalent choices of discrepancies. A new method is developed to obtain an invariant assessment. This approach also allows several discrepancies to be combined into one discrepancy via a single P-value. Second, Bayesians developed many noninformative priors that are supposed to contain no information concerning the true parameter value. Any of these are data dependent or improper which can lead to a variety of difficulties. Gelman (2006) introduced the notion of the weak informativity as a comprimise between informative and noninformative priors without a precise definition. We give a precise definition of weak informativity using a measure of prior-data conflict that assesses whether or not a prior places its mass around the parameter values having relatively high likelihood. In particular, we say a prior Pi_2 is weakly informative relative to another prior Pi_1 whenever Pi_2 leads to fewer prior-data conflicts a priori than Pi_1. This leads to a precise quantitative measure of how much less informative a weakly informative prior is. In Bayesian data analysis, highest posterior density inference is a commonly used method. This approach is not invariant to the choice of dominating measure or reparametrizations. We explore properties of relativ.
Author : Gun Ho Jang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (133 download)
Download or read book Invariant Procedures for Model Checking, Checking for Prior-Data Conflict and Bayesian Inference written by Gun Ho Jang and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a statistical theory as being invariant when the results of two statisticians' independent data analyses, based upon the same statistical theory and using effectively the same statistical ingredients, are the same. We discuss three aspects of invariant statistical theories. Both model checking and checking for prior-data conflict are assessments of single null hypothesis without any specific alternative hypothesis. Hence, we conduct these assessments using a measure of surprise based on a discrepancy statistic. For the discrete case, it is natural to use the probability of obtaining a data point that is less probable than the observed data. For the continuous case, the natural analog of this is not invariant under equivalent choices of discrepancies. A new method is developed to obtain an invariant assessment. This approach also allows several discrepancies to be combined into one discrepancy via a single P-value. Second, Bayesians developed many noninformative priors that are supposed to contain no information concerning the true parameter value. Any of these are data dependent or improper which can lead to a variety of difficulties. Gelman (2006) introduced the notion of the weak informativity as a comprimise between informative and noninformative priors without a precise definition. We give a precise definition of weak informativity using a measure of prior-data conflict that assesses whether or not a prior places its mass around the parameter values having relatively high likelihood. In particular, we say a prior Pi_2 is weakly informative relative to another prior Pi_1 whenever Pi_2 leads to fewer prior-data conflicts a priori than Pi_1. This leads to a precise quantitative measure of how much less informative a weakly informative prior is. In Bayesian data analysis, highest posterior density inference is a commonly used method. This approach is not invariant to the choice of dominating measure or reparametrizations. We explore properties of relative surprise inferences suggested by Evans (1997). Relative surprise inferences which compare the belief changes from a priori to a posteriori are invariant under reparametrizations. We mainly focus on the connection of relative surprise inferences to classical Bayesian decision theory as well as important optimalities.
Author : Andrew Gelman
Publisher : CRC Press
ISBN 13 : 1439840954
Total Pages : 677 pages
Book Rating : 4.4/5 (398 download)
Download or read book Bayesian Data Analysis, Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Author : Michael J. Evans
Publisher : Macmillan
ISBN 13 : 9780716747420
Total Pages : 704 pages
Book Rating : 4.7/5 (474 download)
Download or read book Probability and Statistics written by Michael J. Evans and published by Macmillan. This book was released on 2004 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.
Author : Thomas William Lucas
Publisher :
ISBN 13 :
Total Pages : 490 pages
Book Rating : 4.3/5 (121 download)
Download or read book Robust Bayesian Inference when the Data Conflicts with the Prior written by Thomas William Lucas and published by . This book was released on 1991 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Evans
Publisher : CRC Press
ISBN 13 : 148224280X
Total Pages : 252 pages
Book Rating : 4.4/5 (822 download)
Download or read book Measuring Statistical Evidence Using Relative Belief written by Michael Evans and published by CRC Press. This book was released on 2015-06-23 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of recent work on developing a theory of statistical inference based on measuring statistical evidence. It attempts to establish a gold standard for how a statistical analysis should proceed. The book illustrates relative belief theory using many examples and describes the strengths and weaknesses of the theory. The author also addresses fundamental statistical issues, including the meaning of probability, the role of subjectivity, the meaning of objectivity, and the role of infinity and continuity.
Author : Satyanshu K. Upadhyay
Publisher : Anshan Pub
ISBN 13 :
Total Pages : 528 pages
Book Rating : 4.F/5 ( download)
Download or read book Bayesian Statistics and Its Applications written by Satyanshu K. Upadhyay and published by Anshan Pub. This book was released on 2007 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades, Bayesian Statistics has acquired immense importance and has penetrated almost every area including those where the application of statistics appeared to be a remote possibility. This volume provides both theoretical and practical insights into the subject with detailed up-to-date material on various aspects. It serves two important objectives - to offer a thorough background material for theoreticians and gives a variety of applications for applied statisticians and practitioners. Consisting of 33 chapters, it covers topics on biostatistics, econometrics, reliability, image analysis, Bayesian computation, neural networks, prior elicitation, objective Bayesian methodologies, role of randomisation in Bayesian analysis, spatial data analysis, nonparametrics and a lot more. The book will serve as an excellent reference work for updating knowledge and for developing new methodologies in a wide variety of areas. It will become an invaluable tool for statisticians and the practitioners of Bayesian paradigm.
Author : Christoph Koenig
Publisher : Frontiers Media SA
ISBN 13 : 2889742148
Total Pages : 197 pages
Book Rating : 4.8/5 (897 download)
Download or read book Moving Beyond Non-Informative Prior Distributions: Achieving the Full Potential of Bayesian Methods for Psychological Research written by Christoph Koenig and published by Frontiers Media SA. This book was released on 2022-02-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ian L. Dryden
Publisher : John Wiley & Sons
ISBN 13 : 1118866614
Total Pages : 432 pages
Book Rating : 4.1/5 (188 download)
Download or read book Geometry Driven Statistics written by Ian L. Dryden and published by John Wiley & Sons. This book was released on 2015-07-22 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia's long and influential career in statistics. A common theme unifying much of Mardia’s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high-profile researchers in the field. Geometry Driven Statistics covers a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations. Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia.
Author : Jim Albert
Publisher : CRC Press
ISBN 13 : 1351030132
Total Pages : 553 pages
Book Rating : 4.3/5 (51 download)
Download or read book Probability and Bayesian Modeling written by Jim Albert and published by CRC Press. This book was released on 2019-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.
Author : Sarah Depaoli
Publisher : Guilford Publications
ISBN 13 : 1462547796
Total Pages : 550 pages
Book Rating : 4.4/5 (625 download)
Download or read book Bayesian Structural Equation Modeling written by Sarah Depaoli and published by Guilford Publications. This book was released on 2021-07-01 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers researchers a systematic and accessible introduction to using a Bayesian framework in structural equation modeling (SEM). Stand-alone chapters on each SEM model clearly explain the Bayesian form of the model and walk the reader through implementation. Engaging worked-through examples from diverse social science subfields illustrate the various modeling techniques, highlighting statistical or estimation problems that are likely to arise and describing potential solutions. For each model, instructions are provided for writing up findings for publication, including annotated sample data analysis plans and results sections. Other user-friendly features in every chapter include "Major Take-Home Points," notation glossaries, annotated suggestions for further reading, and sample code in both Mplus and R. The companion website (www.guilford.com/depaoli-materials) supplies data sets; annotated code for implementation in both Mplus and R, so that users can work within their preferred platform; and output for all of the book’s examples.
Author : Gero Walter
Publisher :
ISBN 13 : 9783897914230
Total Pages : 0 pages
Book Rating : 4.9/5 (142 download)
Download or read book Generalized Bayesian Inference Under Prior-data Conflict written by Gero Walter and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 800 pages
Book Rating : 4.F/5 ( download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James Berger
Publisher : CRC Press
ISBN 13 : 1003837697
Total Pages : 564 pages
Book Rating : 4.0/5 (38 download)
Download or read book Handbook of Bayesian, Fiducial, and Frequentist Inference written by James Berger and published by CRC Press. This book was released on 2024-02-26 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of data science, in recent decades, has magnified the need for efficient methodology for analyzing data and highlighted the importance of statistical inference. Despite the tremendous progress that has been made, statistical science is still a young discipline and continues to have several different and competing paths in its approaches and its foundations. While the emergence of competing approaches is a natural progression of any scientific discipline, differences in the foundations of statistical inference can sometimes lead to different interpretations and conclusions from the same dataset. The increased interest in the foundations of statistical inference has led to many publications, and recent vibrant research activities in statistics, applied mathematics, philosophy and other fields of science reflect the importance of this development. The BFF approaches not only bridge foundations and scientific learning, but also facilitate objective and replicable scientific research, and provide scalable computing methodologies for the analysis of big data. Most of the published work typically focusses on a single topic or theme, and the body of work is scattered in different journals. This handbook provides a comprehensive introduction and broad overview of the key developments in the BFF schools of inference. It is intended for researchers and students who wish for an overview of foundations of inference from the BFF perspective and provides a general reference for BFF inference. Key Features: Provides a comprehensive introduction to the key developments in the BFF schools of inference Gives an overview of modern inferential methods, allowing scientists in other fields to expand their knowledge Is accessible for readers with different perspectives and backgrounds
Author : Emmanuel Lesaffre
Publisher : John Wiley & Sons
ISBN 13 : 0470018232
Total Pages : 544 pages
Book Rating : 4.4/5 (7 download)
Download or read book Bayesian Biostatistics written by Emmanuel Lesaffre and published by John Wiley & Sons. This book was released on 2012-08-13 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introductory and more advanced chapters, this book provides an invaluable understanding of the complex world of biomedical statistics illustrated via a diverse range of applications taken from epidemiology, exploratory clinical studies, health promotion studies, image analysis and clinical trials. Key Features: Provides an authoritative account of Bayesian methodology, from its most basic elements to its practical implementation, with an emphasis on healthcare techniques. Contains introductory explanations of Bayesian principles common to all areas of application. Presents clear and concise examples in biostatistics applications such as clinical trials, longitudinal studies, bioassay, survival, image analysis and bioinformatics. Illustrated throughout with examples using software including WinBUGS, OpenBUGS, SAS and various dedicated R programs. Highlights the differences between the Bayesian and classical approaches. Supported by an accompanying website hosting free software and case study guides. Bayesian Biostatistics introduces the reader smoothly into the Bayesian statistical methods with chapters that gradually increase in level of complexity. Master students in biostatistics, applied statisticians and all researchers with a good background in classical statistics who have interest in Bayesian methods will find this book useful.
Author : David J. Spiegelhalter
Publisher : John Wiley & Sons
ISBN 13 : 9780471499756
Total Pages : 416 pages
Book Rating : 4.4/5 (997 download)
Download or read book Bayesian Approaches to Clinical Trials and Health-Care Evaluation written by David J. Spiegelhalter and published by John Wiley & Sons. This book was released on 2004-01-16 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: READ ALL ABOUT IT! David Spiegelhalter has recently joined the ranks of Isaac Newton, Charles Darwin and Stephen Hawking by becoming a fellow of the Royal Society. Originating from the Medical Research Council’s biostatistics unit, David has played a leading role in the Bristol heart surgery and Harold Shipman inquiries. Order a copy of this author’s comprehensive text TODAY! The Bayesian approach involves synthesising data and judgement in order to reach conclusions about unknown quantities and make predictions. Bayesian methods have become increasingly popular in recent years, notably in medical research, and although there are a number of books on Bayesian analysis, few cover clinical trials and biostatistical applications in any detail. Bayesian Approaches to Clinical Trials and Health-Care Evaluation provides a valuable overview of this rapidly evolving field, including basic Bayesian ideas, prior distributions, clinical trials, observational studies, evidence synthesis and cost-effectiveness analysis. Covers a broad array of essential topics, building from the basics to more advanced techniques. Illustrated throughout by detailed case studies and worked examples Includes exercises in all chapters Accessible to anyone with a basic knowledge of statistics Authors are at the forefront of research into Bayesian methods in medical research Accompanied by a Web site featuring data sets and worked examples using Excel and WinBUGS - the most widely used Bayesian modelling package Bayesian Approaches to Clinical Trials and Health-Care Evaluation is suitable for students and researchers in medical statistics, statisticians in the pharmaceutical industry, and anyone involved in conducting clinical trials and assessment of health-care technology.
