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. |
Contents
I | 1 |
II | 3 |
III | 8 |
IV | 12 |
V | 16 |
VI | 20 |
VII | 35 |
VIII | 38 |
XXXIX | 388 |
XL | 391 |
XLI | 397 |
XLII | 400 |
XLIII | 402 |
XLIV | 406 |
XLV | 418 |
XLVI | 422 |
IX | 46 |
X | 47 |
XI | 53 |
XII | 57 |
XIII | 69 |
XIV | 74 |
XV | 77 |
XVI | 82 |
XVII | 90 |
XVIII | 94 |
XIX | 106 |
XX | 109 |
XXI | 113 |
XXII | 118 |
XXIII | 126 |
XXIV | 132 |
XXV | 158 |
XXVI | 167 |
XXVII | 180 |
XXVIII | 195 |
XXIX | 253 |
XXX | 262 |
XXXI | 267 |
XXXII | 271 |
XXXIII | 281 |
XXXIV | 308 |
XXXV | 310 |
XXXVI | 347 |
XXXVII | 359 |
XXXVIII | 370 |
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Common terms and phrases
a₁ a₂ admissible approach approximation Bayes estimator Bayes procedure Bayes risk Bayes rule Bayesian analysis Berger best invariant calculation choice classical complete class conditional conjugate priors consider convex decision loss decision problem decision rule decision theory defined denote desired to estimate desired to test determine discussed empirical Bayes error probabilities example Exercise expected loss exponential family finite fixed sample frequentist given Hence HPD credible set hypothesis inadmissible inference Lemma likelihood function Likelihood Principle loss function matrix maximin minimax estimators minimax rule minimizes multivariate noninformative prior nonrandomized Note observed optimal parameter posterior distribution posterior mean posterior probability prior density prior distribution prior information proof reasonable result risk function robustness Section sequential sample simple situation SPRT squared-error loss Statist stopping rule strategy Subsection Suppose Theorem utility function variance vector versus H₁ X₁ zero σ²