Statistical Decision Theory and Bayesian AnalysisSpringer Science & Business Media, 14 mar 2013 - 618 "The outstanding strengths of the book are its topic coverage, references, exposition, examples and problem sets... This book is an excellent addition to any mathematical statistician's library." -Bulletin of the American Mathematical Society In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation. |
Spis treści
| 1 | |
7 | 33 |
Exercises | 70 |
CHAPTER 4 | 118 |
CHAPTER 5 | 308 |
CHAPTER 2 | 311 |
CHAPTER 6 | 388 |
CHAPTER 7 | 432 |
CHAPTER 8 | 514 |
Complete and Essentially Complete Classes | 521 |
APPENDIX 1 | 559 |
Verification of Formula 4 123 | 565 |
Bibliography | 571 |
Notation and Abbreviations | 599 |
| 609 | |
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a₁ a₂ admissible approach approximation Assume Bayes estimator Bayes risk Bayes rule Bayesian analysis Berger best invariant calculation choice choose class of priors classical complete class conditional conjugate priors considered convex decision problem decision rule decision theory defined denote desired to estimate desired to test determine discussed empirical Bayes error probabilities Example 15 finite frequentist functional form given Hence hierarchical Bayes HPD credible set hyperparameters hypothesis inadmissible inference Lemma likelihood function Likelihood Principle loss function matrix minimax rule minimizes noninformative prior nonrandomized normal Note observed optimal parameter posterior distribution posterior mean posterior probability prior density prior distribution prior information random variables reasonable result risk function robustness sample Section sequential Show simple squared-error loss Statist stopping rule strategy Subsection Suppose Theorem utility function variance vector versus H₁ X₁ zero σ²