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Bayesian data analysis. Repr. (English) Zbl 0914.62018
Chapman & Hall/CRC Texts in Statistical Science Series. London: Chapman & Hall (ISBN 0-412-03991-5/hbk). xix, 526 p. (1998).
The authors of this book say in the preface “This book is intended to have three roles and to serve three associated audiences: an introductory text on Bayesian inference starting from first principles, a graduate text on effective current approaches to Bayesian modeling and computation in statistics and related fields for graduate students, and a handbook of Bayesian methods in applied statistics for general users and researchers of applied statistics”. They have succeded in their efforts. The contents of the book are as follows:
Part I: Fundamentals of Bayesian inference: 1. Background; 2. Single parameter models; 3. Introduction to multiparameter models; 4. Large-sample inference and connections to standard statistical models.
Part II: Fundamentals of Bayesian data analysis: 5. Hierarchical models; 6. Model checking and sensitivity analysis; 7. Study design in Bayesian analysis; 8. Introduction to regression models.
Part III: Advanced computation: 9. Approximations based on posterior modes; 10. Posterior simulation and integration; 11. Markov chain simulation.
Part IV: Specific models; 12. Models for robust inference and sensitivity analysis; 13. Hierarchical linear models; 14. Generalized linear models; 15. Multivariate models; 16. Mixture models; 17. Models for missing data; 18. Concluding advice. Appendices: A. Standard probability distributions; B. Outline of proof of asymptotic theorems; References.
The book contains a lot of interesting examples with real statistical data analysis illustrating the theory and each chapter contains a set of exercises which involve both theoretical and computational aspects of Bayesian data analysis. It is possibly the first book which gives such a comprehensive coverage of the subject of Bayesian data analysis and it is a welcome addition to the literature in this area.

62F15 Bayesian inference
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
65C99 Probabilistic methods, stochastic differential equations