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Bayesian Theory, by José M. Bernardo, Adrian F. M. Smith
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This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics
- Sales Rank: #1202381 in Books
- Published on: 2000-05-18
- Released on: 2000-04-24
- Original language: English
- Number of items: 1
- Dimensions: 9.13" h x 1.39" w x 6.04" l, 1.94 pounds
- Binding: Paperback
- 610 pages
Review
"an excellent primary source for those who wish to learn about the learning and decision process in a situation of uncertainty..." (Measurement Science Technology, February 2001)
"an ideal source for all students and researchers in statistics mathematics, decision analysis, economic and business studies and all branches of science and engineering who wish to further their understanding of Bayesian statistics." (Zentralblatt Fur Didaktik der Mathematik)
"...Bayesians will find it indispensable: non-Bayesians will find, and enjoy, much thought-provoking material to challenge their orthodoxy...." (The Statistician, Vol.51, No.2, 2002)
From the Publisher
Provides a thorough account of key basic concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Presents a novel discussion of model comparison and choice from a Bayesian perspective. An overview of non-Bayesian theories is provided and each chapter contains a wide-ranging critical re-examination of controversial issues.
From the Inside Flap
Bayesian Theory José M. Bernardo Universidad de Valencia, Valencia, Spain Adrian F. M. Smith Imperial College of Science, Technology and Medicine, London, UK Bayesian Theory is the first volume of a related series of three and will be followed by Bayesian Computation, and Bayesian Methods. The series aims to provide an up-to-date overview of the why?, how? and what? of Bayesian statistics. This volume provides a thorough account of key basic concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development, which provides, in particular, a detailed treatment of the problem of specification of so-called "prior ignorance". The work is written from the authors’ committed Bayesian perspective, but an overview of non-Bayesian theories is provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material should be accessible to readers with a knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics. Contents Preface Chapter 1 Introduction Chapter 2 Foundations Chapter 3 Generalisations Chapter 4 Modelling Chapter 5 Inference Chapter 6 Remodelling Appendix A Summary of Basic Formulae Appendix B Non-Bayesian Theories References Subject index Author Index
Most helpful customer reviews
32 of 33 people found the following review helpful.
bayesian theory bible
By Michael R. Chernick
Recently there have been a wealth of good books published on Bayesian methods and the Markov chain Monte Carlo approach to its implementation. For the beginner Berry's introductory book is a good place to start.
Bernardo and Smith are experts in the field who have participated in many of the Bayesian conferences held in Valencia and much of that lterature is contained in this book. They originally wrote the book in 1993 (with a publication date of January 1994). This paperback edition is not a revision but rather a reprinting with corrections. The original hardcover edition was very expensive and this paperback edition makes the text more affordable and should greatly expand the list of Bayesian specialists and other statisticians and practitioners that read it.
The authors intent was to extend the classical work of Bruno deFinetti who popularized the Bayesian approach with his two classic probability books. One of the authors was involved in translating deFinetti's books into English and they are both well familiar with it. In this book they offer an extension to the area of statistical inference.
The beauty of deFinetti is the logical and systematic nature of the presentation but he did not extend this to statistical practice. These authors maintain the systematic approach and review the probability axioms but then go on to cover statistical modelling including how models are approached through concepts of exchangeability, invariance, sufficency and partial exchangeability. The chapter on inference covers the Bayesian paradigm, the use of conjugate families, asymptotic methods, multiparameter problems and the thorny issues with nuisance parameters. It also includes a number of methods of numerical approximation including Markov chain Monte Carlo (MCMC) methods.
The authors deliberately left the coverage of computational methods brief as they planned a second volume to cover it in detail. But in the preface to the new paperback edition they admit that they have abandon this plan due to the evolution of MCMC methods as the dominant numerical approach and the wealth of new texts that adequately cover the topic.
I suggest that this text is the new bible for Bayesian statistics because I think it replaces the old bibles, Lindley's two volumes (some may argue for Savage's book). This is fitting as both authors attest to being students and disciples of Dennis Lindley. The reason I think it is worthy of bible status is because it covers the foundations in systematic detail, is current and very complete. The text contains references from 1763 (Bayes' original treatise) to 1993 covering an incredible 66 pages of the text. With 20 plus references per page that means over 1320 references!
This is an intermediate level text that requires advanced calculus but not measure theory. Emphasis is on concepts and not mathematical proofs. The authors also provide an overview of the non-Bayesian forms of statistical inference in Appendix B. The authors confront the controversial issues in each chapter. Bayesian statistical methods are treated in the framework of decision theory and ideas from information theory take on a central role.
11 of 11 people found the following review helpful.
The Standard First Text To Begin Studying Bayesian Methods
By Craig Matteson
This is an extremely nice introduction to Bayesian statistical methods. It takes you from the very basics - even who Thomas Bayes was (who happens to be buried in Bunhill Fields cemetery in London with William Blake (Songs of Innocence and Experience, Jerusalem), Daniel Defoe (Robinson Crusoe), John Bunyan (Pilgrim's Progress)).
Its chapters are divided into sections forming an Introduction, Foundations, Generalizations, Modeling, Inference, and Remodeling. There is also a section summarizing the basic formulae and alternative non-Bayesian approaches. A rich reference list, subject index, and author index are also provided.
If you are familiar with the math of undergraduate statistics you should not have a problem with the math notation in this book. This really is the standard text you find on most shelves of folks who are familiar with this subject. There are many books to read beyond this one, but this is a fine place to start.
26 of 26 people found the following review helpful.
A complete introduction to classical Bayesian analysis
By supercutepig
[1] It is an excellent book on the classical Bayesian theory. The first author is a famous mathematician, who held several international conferences on Bayesian statistics.
[2] Similar to Berger's book, it is also built on Statistical Decision Theory. In my opinion, Berger's is a little better.
[3] The part of Bayesian foundation is heavy, maybe a topos today. But in the bookshelf, we indeed need such work.
[4] Think about the thickness of the bibliography --- the reference is awesome!
[5] The history of Bayesian statistics is well overviewed.
[6] To learn more about the Bayesian computation, you need some complement books, such as Liu's, Tanner's, Gelman's, etc.
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