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Bayes and empirical Bayes methods for data analysis. (English) Zbl 0871.62012
Monographs on Statistics and Applied Probability. 69. London: Chapman and Hall. xi, 399 p. £32.50 (1996).

The book under review deals with Bayes and Empirical Bayes (EB) methods for data analysis. The intention is to have a very practical focus, offering real solution methods to researchers with challenging problems. The book consists of 8 chapters and 3 appendices. Here is the list of the titles:

Chapter 1. Procedures and their properties; Chapter 2. The Bayes approach; Chapter 3. The empirical Bayes approach; Chapter 4. Performance of Bayes procedures; Chapter 5. Bayesian computation; Chapter 6. Model criticism and selection; Chapter 7. Special methods and models; Chapter 8. Case studies; Appendix A. Distributional catalog; Appendix B. Software guide; Appendix C. Answers to selected exercises.

Now let us discuss the book contents in more detail. The authors remind the reader that effective statistical procedures strike a balance between variance and bias, and that Bayesian formalism in a properly robust form produces procedures that achieve this balance. With this in mind they outline in Chapter 1 the decision-theoretical tools needed to compare procedures, and present the basics of the Bayes and EB approaches in Chapters 2 and 3, respectively. Chapter 4 evaluates the frequentist and empirical Bayes performance of these approaches in a variety of settings. Since no single approach can be universally best, the authors identify both virtues and drawbacks. The book’s second half begins with an extensive discussion of modern Bayesian computational methods in Chapter 5. These methods figure prominently in modern tools for such data analytic tasks as model criticism and selection, which are described in Chapter 6. Guidance on the Bayes/EB implementation of a collection of special methods and models is given in Chapter 7. Chapter 8 presents three fully worked case studies of real data sets. These studies incorporate tools from a variety of statistical subfields.

Appendix A contains a brief summary of the distributions used in the book, highlighting the typical Bayes/EB role of each. Appendix B provides a guide to the software available for performing Bayesian analysis, indicating the level of model complexity each is capable of handling. Finally, Appendix C contains solutions to several of the exercises in each of the book’s chapters.

62C10Bayesian problems; characterization of Bayes procedures
62-02Research monographs (statistics)
62-01Textbooks (statistics)
62C12Empirical decision procedures; empirical Bayes procedures
62F15Bayesian inference
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)