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Zbl 0796.62002
Bernardo, José M.; Smith, Adrian F.M.
Bayesian theory. (English)
[B] Wiley Series in Probability and Mathematical Statistics. Chichester: John Wiley \& Sons. xiv, 586 p. \sterling 60.00 (1994). ISBN 0-471-92416-4/hbk

This textbook is the first volume of a related series of three volumes -- Bayesian Theory, Bayesian Computation and Bayesian Methods -- which are set to provide an up-to-date overview of the Why? How? and What? of Bayesian Statistics, as perceived by the authors. This volume focuses on the basic concepts and theory of Bayesian statistics, which cover elementary foundations, mathematical generalizations of foundations, modelling, inference and remodelling. Here, the primary emphasis is placed on general ideas. The material of the book is covered in nine chapters followed by two Appendices, References, Subject Index and Author Index.\par In Chapter 2, the concept of rationality is explored in the context of representing beliefs or choosing actions in situations of uncertainty. The importance of a decision-oriented framework is stressed with the approach that statistical inference should be viewed simply as a particular form of decision problem. The dual concepts of probability and utility are formally defined and analyzed within the decision making context. In Chapter 3, the ideas and results of Chapter 2 are extended to more general mathematical setting.\par The role of familiar mathematical forms of statistical models and the possible justifications, from a subjective perspective, is examined in Chapter 4. The key role of Bayes' theorem in the updating of beliefs about observables in the light of new information is identified and related to conventional mechanisms of predictive and parametric inference, in Chapter 5. The prospect of systematically entertaining a range of possible model beliefs, rather than predicating all analysis on a single assumed model, is examined in Chapter 6.\par Summaries of main univariate and multivariate distributions that appear in the text, are collected in Appendix A with the summaries of the prior/posterior and predictive forms. Classical decision theory, frequentist procedures, likelihood theory and fiducial and related theories are reviewed in Appendix B.
[K.Alam (Clemson)]

MSC 2000:: *62A01 Foundational and philosophical topics
62-02 Research monographs (statistics)
62C10 Bayesian problems
62C12 Empirical statistical decision procedures
62-01 Textbooks (statistics)

Keywords: predictive inference; fiducial theory; rationality; representing beliefs; choosing actions; uncertainty; utility; Bayes' theorem; updating of beliefs; model beliefs; frequentist procedures; likelihood theory

Cited in: Zbl 1071.62027 Zbl 1072.62537

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