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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action actually admissible analysis apply approach approximation Assume Bayes risk Bayesian Bayesian analysis bounded calculation called Chapter choice choose classical clear clearly closed complete concerning conclusion conditional consider consideration constant continued convex corresponding course decide decision rule defined Definition denote density depend desired determine developed difficult discussed distribution easy equal error estimate Example Exercise exists expected finite frequentist function given gives Hence important independent indicated instance interest invariant involving known likelihood loss matrix mean measure method minimax minimizes natural noninformative prior normal Note observed obtained optimal parameter possible posterior principle probability problem procedure proof providing random reasonable respect result robustness sample satisfied sequential shown simple situation specific standard statistical stopping rule strategy Subsection Suppose Theorem theory transformations true usually utility variance versus zero