- Paperback: 610 pages
- Publisher: Wiley; 1 edition (May 18, 2000)
- Language: English
- ISBN-10: 047149464X
- ISBN-13: 978-0471494645
- Product Dimensions: 6 x 1.4 x 9.1 inches
- Shipping Weight: 2.4 pounds (View shipping rates and policies)
- Average Customer Review: 8 customer reviews
- Amazon Best Sellers Rank: #1,563,899 in Books (See Top 100 in Books)
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Bayesian Theory 1st Edition
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"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. --This text refers to the Hardcover edition.
Top customer reviews
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The basic point made by BS is that all probabilities are precise,single number, point estimates or that they can be treated "as if" they were.Unfortunately,this is not the case.The subjectivist approach is applicable only in those situations where the purely deductive,mathematical laws of probability(the addition and multiplication rules for conjunction and disjunction)apply.This requires that a)there exists a complete sample space of all possible outcomes representing the choice problem before any probability is calculated;b)a complete preference ordering of all possible outcomes exists for the problem or c)a single,unique probability distribution is defined for the problem.Under these conditions,the probability calculus serves as a consistency and coherence check for the rational decision maker who is willing to bet on one side or another of all propositions.The subjectivist approach is a special theory with limited applicability.
It is this failure to recognize that the subjective approach is a limiting case, that conflates the concepts of probability,logical probability,inductive probability,and degree of belief with mathematical probability, that is the source of much of the criticism of the subjectivist approach.There are many assertions made throughout the book that are highly dubious and/or unsupported.
The rest of the review will be devoted to correcting these assertions.First,it is not the case that the Allais paradox choices are mistaken.It is strange to see it argued that such choices are similar to"...individuals(who)can often be shown to perform badly at deduction or long division"(BS,P.97).The real problem is that many/some decision makers have nonlinear probability preferences,as opposed to the linear probability preferences axiomatised by the subjectivists.The BS claim is similar to the claim made by many proponents of Euclidean geometry in the 18th and 19th centuries that non Euclidean geometries were erroneous and/or could not exist.Second,it is not the case that the Raiffa(1961) and Roberts(1963)replies to Ellsberg provide"...clear and convincing rejoinders to the Ellsberg criticisms"(BS,P.98).Both Raiffa and Roberts,like Savage in his belated reply to Allais,simply restructured and changed the problem on which they commented.Third,the claim that the Ellsberg problems and/or examples(the two color and three color urn ball problems)are"...optical or magical illusions..." makes no sense.Fourth,the claim that "The logical(emphasis added)view is entirely lacking in operational content." (BS,p.100),has no support at all.It is impossible to even talk about scientific theories unless an underlying logical conceptualization of probability is already in place beforehand.Fifth,the claim that John Maynard Keynes changed his view in 1931 and accepted the primacy of the subjectivist interpretation of F.Ramsey is erroneous.Keynes accepted Ramsey's dutch book argument claim only if the deductive,purely mathematical laws of probability("...the calculus of probability...") were completely operational.Keynes completely rejected Ramsey's assertions that habits and memory alone were the only foundations for induction and analogy.Sixth,BS are completely and totally ignorant about Keynes's establishment of the interval estimate approach to probability in this century.
It is a widespread misbelief on the part of many economists,philosophers,psychologists,etc.,that only partial, ordinal rankings,that could be made only part of the time,represents the main outcome of Keynes's 16 years of study of probability.Nothing could be further from the truth.In fact,this misbelief is due to the acceptance by most scholars of the conclusions arrived at in the horrible mess made of Keynes's book by Ramsey in both his 1922 and 1926 reviews,respectively.Ramsey's unsupported claims about Keynes's strange nonnumerical probabilities and mysterious logical relations are just that,unsupported.Most Keynesian probabilities have an upper and a lower bound or limit. It is in chapters 15 and 17 of Keynes's 1921 A Treatise on Probability(TP) that BS can find Keynes's "approximation" approach worked out in great detail.A number of problems are worked out by Keynes on pp.161-163 and pp.186-194 of the TP.All of these problems can now be solved using easier integer-mixed integer linear programming techniques.Keynes's approach is fully operational.Seventh,the claim that Keynes's logical approach provides "...no operational guidance as to how to choose..."(BS,p.99)makes it crystal clear to this reviewer that BS have never read Keynes's TP.It is a great tragedy that books can be written on probability by authors that are grossly ignorant of basic literature.
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.