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.