This graduate-level textbook covers both the basic ideas of statistical theory, and also some of the more modern and advanced topics of Bayesian statistics, such as complete class theorems, the Stein effect, hierarchical and empirical Bayes modelling, Monte Carlo integration, and Gibbs sampling. In translating the book from the original French, the author has taken the opportunity to add and update material, and to include many problems and exercises for students.

Inhalt

1. Introduction.- 2. Decision-Theoretic Foundations of Statistical Inference.- 3. From Prior Information to Prior Distributions.- 4. Bayesian Point Estimation.- 5. Tests and Confidence Regions.- 6. Admissibility and Complete Classes.- 7. Invariance, Haar Measures, and Equivariant Estimators.- 8. Hierarchical and Empirical Bayes Extensions.- 9. Bayesian Calculations.- 10. A Defense of the Bayesian Choice.- Appendix A: Usual Probability Distributions.- Appendix B: Usual Pseudorandom Generators.- Notation.- References.- Author Index.