Objective Bayesian Inference

Author : James O Berger,Jose-miguel Bernardo,Dongchu Sun
Publisher : World Scientific
Page : 381 pages
File Size : 44,5 Mb
Release : 2024-03-06
Category : Mathematics
ISBN : 9789811284922

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Objective Bayesian Inference by James O Berger,Jose-miguel Bernardo,Dongchu Sun Pdf

Bayesian analysis is today understood to be an extremely powerful method of statistical analysis, as well an approach to statistics that is particularly transparent and intuitive. It is thus being extensively and increasingly utilized in virtually every area of science and society that involves analysis of data.A widespread misconception is that Bayesian analysis is a more subjective theory of statistical inference than what is now called classical statistics. This is true neither historically nor in practice. Indeed, objective Bayesian analysis dominated the statistical landscape from roughly 1780 to 1930, long before 'classical' statistics or subjective Bayesian analysis were developed. It has been a subject of intense interest to a multitude of statisticians, mathematicians, philosophers, and scientists. The book, while primarily focusing on the latest and most prominent objective Bayesian methodology, does present much of this fascinating history.The book is written for four different audiences. First, it provides an introduction to objective Bayesian inference for non-statisticians; no previous exposure to Bayesian analysis is needed. Second, the book provides an overview of the development and current state of objective Bayesian analysis and its relationship to other statistical approaches, for those with interest in the philosophy of learning from data. Third, the book presents a careful development of the particular objective Bayesian approach that we recommend, the reference prior approach. Finally, the book presents as much practical objective Bayesian methodology as possible for statisticians and scientists primarily interested in practical applications.

Author : S. James Press
Publisher : John Wiley & Sons
Page : 591 pages
File Size : 47,8 Mb
Release : 2009-09-25
Category : Mathematics
ISBN : 9780470317945

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Subjective and Objective Bayesian Statistics by S. James Press Pdf

Ein Wiley-Klassiker über Bayes-Statistik, jetzt in durchgesehener und erweiterter Neuauflage! - Werk spiegelt die stürmische Entwicklung dieses Gebietes innerhalb der letzten Jahre wider - vollständige Darstellung der theoretischen Grundlagen - jetzt ergänzt durch unzählige Anwendungsbeispiele - die wichtigsten modernen Methoden (u. a. hierarchische Modellierung, linear-dynamische Modellierung, Metaanalyse, MCMC-Simulationen) - einzigartige Diskussion der Finetti-Transformierten und anderer Themen, über die man ansonsten nur spärliche Informationen findet - Lösungen zu den Übungsaufgaben sind enthalten

Author : Ming-Hui Chen,Peter Müller,Dongchu Sun,Keying Ye,Dipak K. Dey
Publisher : Springer Science & Business Media
Page : 631 pages
File Size : 41,6 Mb
Release : 2010-07-24
Category : Mathematics
ISBN : 9781441969446

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Frontiers of Statistical Decision Making and Bayesian Analysis by Ming-Hui Chen,Peter Müller,Dongchu Sun,Keying Ye,Dipak K. Dey Pdf

Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

Author : Xin Zhao
Publisher : Unknown
Page : 204 pages
File Size : 54,7 Mb
Release : 2005
Category : Electronic
ISBN : CORNELL:31924102826546

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Objective Bayesian Inference in General (generalized) Linear Mixed Models Using Reference Priors by Xin Zhao Pdf

Author : S. James Press
Publisher : Unknown
Page : 264 pages
File Size : 45,6 Mb
Release : 1989-05-10
Category : Mathematics
ISBN : UOM:39015015723250

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Bayesian Statistics by S. James Press Pdf

An introduction to Bayesian statistics, with emphasis on interpretation of theory, and application of Bayesian ideas to practical problems. First part covers basic issues and principles, such as subjective probability, Bayesian inference and decision making, the likelihood principle, predictivism, and numerical methods of approximating posterior distributions, and includes a listing of Bayesian computer programs. Second part is devoted to models and applications, including univariate and multivariate regression models, the general linear model, Bayesian classification and discrimination, and a case study of how disputed authorship of some of the Federalist Papers was resolved via Bayesian analysis. Includes biographical material on Thomas Bayes, and a reproduction of Bayes's original essay. Contains exercises.

Author : Jon Williamson
Publisher : Oxford University Press
Page : 192 pages
File Size : 45,8 Mb
Release : 2010-05-13
Category : Computers
ISBN : 9780199228003

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In Defence of Objective Bayesianism by Jon Williamson Pdf

Objective Bayesianism is a methodological theory that is currently applied in statistics, philosophy, artificial intelligence, physics and other sciences. This book develops the formal and philosophical foundations of the theory, at a level accessible to a graduate student with some familiarity with mathematical notation.

Author : Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin
Publisher : CRC Press
Page : 663 pages
File Size : 41,7 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781439898208

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Bayesian Data Analysis by Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin Pdf

Winner of the 2016 De Groot Prize from the International Society for Bayesian AnalysisNow 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

Author : David Rios Insua,Fabrizio Ruggeri
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461213062

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Robust Bayesian Analysis by David Rios Insua,Fabrizio Ruggeri Pdf

Robust Bayesian analysis aims at overcoming the traditional objection to Bayesian analysis of its dependence on subjective inputs, mainly the prior and the loss. Its purpose is the determination of the impact of the inputs to a Bayesian analysis (the prior, the loss and the model) on its output when the inputs range in certain classes. If the impact is considerable, there is sensitivity and we should attempt to further refine the information the incumbent classes available, perhaps through additional constraints on and/ or obtaining additional data; if the impact is not important, robustness holds and no further analysis and refinement would be required. Robust Bayesian analysis has been widely accepted by Bayesian statisticians; for a while it was even a main research topic in the field. However, to a great extent, their impact is yet to be seen in applied settings. This volume, therefore, presents an overview of the current state of robust Bayesian methods and their applications and identifies topics of further in terest in the area. The papers in the volume are divided into nine parts covering the main aspects of the field. The first one provides an overview of Bayesian robustness at a non-technical level. The paper in Part II con cerns foundational aspects and describes decision-theoretical axiomatisa tions leading to the robust Bayesian paradigm, motivating reasons for which robust analysis is practically unavoidable within Bayesian analysis.

Author : Kathryn Jo-Anne Barger
Publisher : Unknown
Page : 166 pages
File Size : 40,8 Mb
Release : 2008
Category : Electronic
ISBN : 0549969888

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Objective Bayesian Estimation for the Number of Classes in a Population Using Jeffreys and Reference Priors by Kathryn Jo-Anne Barger Pdf

Estimation of the number of classes in a closed population is a problem that arises in many different subject areas. A common application occurs in animal populations where there is interest in determining the number of different species, also the diversity or species richness, of the population.

Author : National Research Council,Division on Engineering and Physical Sciences,Board on Mathematical Sciences and Their Applications,Committee on the Mathematical Sciences in 2025
Publisher : National Academies Press
Page : 64 pages
File Size : 41,7 Mb
Release : 2012-08-02
Category : Mathematics
ISBN : 9780309254731

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Fueling Innovation and Discovery by National Research Council,Division on Engineering and Physical Sciences,Board on Mathematical Sciences and Their Applications,Committee on the Mathematical Sciences in 2025 Pdf

The mathematical sciences are part of everyday life. Modern communication, transportation, science, engineering, technology, medicine, manufacturing, security, and finance all depend on the mathematical sciences. Fueling Innovation and Discovery describes recent advances in the mathematical sciences and advances enabled by mathematical sciences research. It is geared toward general readers who would like to know more about ongoing advances in the mathematical sciences and how these advances are changing our understanding of the world, creating new technologies, and transforming industries. Although the mathematical sciences are pervasive, they are often invoked without an explicit awareness of their presence. Prepared as part of the study on the Mathematical Sciences in 2025, a broad assessment of the current state of the mathematical sciences in the United States, Fueling Innovation and Discovery presents mathematical sciences advances in an engaging way. The report describes the contributions that mathematical sciences research has made to advance our understanding of the universe and the human genome. It also explores how the mathematical sciences are contributing to healthcare and national security, and the importance of mathematical knowledge and training to a range of industries, such as information technology and entertainment. Fueling Innovation and Discovery will be of use to policy makers, researchers, business leaders, students, and others interested in learning more about the deep connections between the mathematical sciences and every other aspect of the modern world. To function well in a technologically advanced society, every educated person should be familiar with multiple aspects of the mathematical sciences.

Author : George E. P. Box,George C. Tiao
Publisher : John Wiley & Sons
Page : 610 pages
File Size : 43,6 Mb
Release : 2011-01-25
Category : Mathematics
ISBN : 9781118031445

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Bayesian Inference in Statistical Analysis by George E. P. Box,George C. Tiao Pdf

Its main objective is to examine the application and relevance of Bayes' theorem to problems that arise in scientific investigation in which inferences must be made regarding parameter values about which little is known a priori. Begins with a discussion of some important general aspects of the Bayesian approach such as the choice of prior distribution, particularly noninformative prior distribution, the problem of nuisance parameters and the role of sufficient statistics, followed by many standard problems concerned with the comparison of location and scale parameters. The main thrust is an investigation of questions with appropriate analysis of mathematical results which are illustrated with numerical examples, providing evidence of the value of the Bayesian approach.

Author : Jayanta K. Ghosh,Mohan Delampady,Tapas Samanta
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 47,8 Mb
Release : 2007-07-03
Category : Mathematics
ISBN : 9780387354330

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An Introduction to Bayesian Analysis by Jayanta K. Ghosh,Mohan Delampady,Tapas Samanta Pdf

This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing. Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques. Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping. The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.

Author : Satyanshu K. Upadhyay,Umesh Singh,Dipak K. Dey,Appaia Loganathan
Publisher : CRC Press
Page : 674 pages
File Size : 47,6 Mb
Release : 2015-05-21
Category : Mathematics
ISBN : 9781482235128

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Current Trends in Bayesian Methodology with Applications by Satyanshu K. Upadhyay,Umesh Singh,Dipak K. Dey,Appaia Loganathan Pdf

Collecting Bayesian material scattered throughout the literature, Current Trends in Bayesian Methodology with Applications examines the latest methodological and applied aspects of Bayesian statistics. The book covers biostatistics, econometrics, reliability and risk analysis, spatial statistics, image analysis, shape analysis, Bayesian computation, clustering, uncertainty assessment, high-energy astrophysics, neural networking, fuzzy information, objective Bayesian methodologies, empirical Bayes methods, small area estimation, and many more topics. Each chapter is self-contained and focuses on a Bayesian methodology. It gives an overview of the area, presents theoretical insights, and emphasizes applications through motivating examples. This book reflects the diversity of Bayesian analysis, from novel Bayesian methodology, such as nonignorable response and factor analysis, to state-of-the-art applications in economics, astrophysics, biomedicine, oceanography, and other areas. It guides readers in using Bayesian techniques for a range of statistical analyses.

Author : Ben Lambert
Publisher : SAGE
Page : 744 pages
File Size : 55,8 Mb
Release : 2018-04-20
Category : Social Science
ISBN : 9781526418265

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A Student’s Guide to Bayesian Statistics by Ben Lambert Pdf

Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics. Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers: An introduction to probability and Bayesian inference Understanding Bayes′ rule Nuts and bolts of Bayesian analytic methods Computational Bayes and real-world Bayesian analysis Regression analysis and hierarchical methods This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.

Author : James O. Berger,Robert L. Wolpert
Publisher : IMS
Page : 266 pages
File Size : 49,7 Mb
Release : 1988
Category : Mathematics
ISBN : 0940600137

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The Likelihood Principle by James O. Berger,Robert L. Wolpert Pdf