Statistical Decision Theory and Bayesian Analysis
"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.
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admissible approach approximation Assume Bayes decision Bayes estimator Bayes procedure Bayes risk Bayes rule Bayesian analysis Berger calculation choice choose classical complete class conditional conjugate priors consider constant convex decision loss decision problem decision rule decision theory defined Definition denote desired to estimate desired to test determine discussed empirical Bayes error probabilities Example 15 finite fixed sample frequentist given Hence HPD credible set inadmissible inference Lemma likelihood function Likelihood Principle look ahead procedure loss function matrix minimax rule minimizes ML-II noninformative prior nonrandomized normal Note observed optimal parameter posterior distribution posterior mean posterior probability prior density prior distribution prior information proof random variables reasonable result risk function risk point robustness Section sequential procedure sequential sample simple SPRT squared-error loss stopping rule Subsection sufficient statistic Suppose test H0 Theorem transformations utility function variance vector versus H zero