The Bayesian choice: a decision-theoretic motivation.

*(English)*Zbl 0808.62005
Springer Texts in Statistics. New York, NY: Springer-Verlag. xiv, 436 p. (1994).

This is a graduate level textbook on Bayesian statistics. The book focuses on the decision-oriented aspects of statistical inference. It starts from an introductory level but goes further and keeps up with most of the recent advances in Bayesian statistics. The material is covered in ten chapters in addition to a comprehensive list of references, author index and subject index.

From an introduction to statistical models including the Bayesian model, the book proceeds with Chapter 2 on decision theory, considered from a classical point of view. Chapter 3 gives the corresponding analysis for prior distributions, dealing with conjugate priors, mixtures of conjugate priors and noninformative priors, and includes a section on prior robustness. Classical models are studied in Chapter 4. Tests and confidence regions are considered in Chapter 5. Chapter 6 covers complete class results and sufficient/necessary admissibility conditions. Chapter 7 introduces the notion of invariance and its relations with Bayesian statistics. Hierarchical and empirical extensions of the Bayesian approach are treated in Chapter 8. An introduction to the state-of-the- art computational methods is given in Chapter 9. Chapter 10 is a discussion on the advantages of Bayesian theory and the most common criticisms of the Bayesian approach.

From an introduction to statistical models including the Bayesian model, the book proceeds with Chapter 2 on decision theory, considered from a classical point of view. Chapter 3 gives the corresponding analysis for prior distributions, dealing with conjugate priors, mixtures of conjugate priors and noninformative priors, and includes a section on prior robustness. Classical models are studied in Chapter 4. Tests and confidence regions are considered in Chapter 5. Chapter 6 covers complete class results and sufficient/necessary admissibility conditions. Chapter 7 introduces the notion of invariance and its relations with Bayesian statistics. Hierarchical and empirical extensions of the Bayesian approach are treated in Chapter 8. An introduction to the state-of-the- art computational methods is given in Chapter 9. Chapter 10 is a discussion on the advantages of Bayesian theory and the most common criticisms of the Bayesian approach.

Reviewer: K.Alam (Clemson)

##### MSC:

62C10 | Bayesian problems; characterization of Bayes procedures |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62Cxx | Statistical decision theory |

62F15 | Bayesian inference |