From where we stand, the rain seems random. If we could stand somewhere else, we would see the order in it. - T. Hillerman (1990) Coyote Waits. Harper-Collins, New York. This book stemmed from a translation of a French version that was written to supplement the gap in the French statistical literature about Bayesian Analysis and Decision Theory. As a result, its scope is wide enough to cover the two years of the French graduate Statistics curriculum and, more generally, most graduate programs. This book builds on very little preยญ requisites in Statistics and only requires basic skills in calculus, measure theory, and probability. Intended as a preparation of Ph. D. students, this book goes far enough to cover advanced topics and modern developments of Bayesian Statistics (complete class theorems, the Stein effect, hierarchical and empirical modelings, Gibbs sampling, etc. ). As usual, what started as a translation eventually ended up as a deeper revision, because of the comยญ ments of French readers, of adjustments to the different needs of American programs, and also because my perception of things has slightly changed in the meantime. As a result, this new version is quite adequate for a general graduate audience of an American university
CONTENT
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
