LEADER 05716nam 2200733Ia 450 001 9910146132003321 005 20170809170514.0 010 $a0-470-74668-8 010 $a1-282-13828-6 010 $a9786612138287 010 $a0-470-74667-X 035 $a(CKB)1000000000719728 035 $a(EBL)427978 035 $a(OCoLC)436206119 035 $a(SSID)ssj0000336547 035 $a(PQKBManifestationID)11244456 035 $a(PQKBTitleCode)TC0000336547 035 $a(PQKBWorkID)10281971 035 $a(PQKB)10803978 035 $a(MiAaPQ)EBC427978 035 $a(CaSebORM)9780471496571 035 $a(PPN)18342719X 035 $a(EXLCZ)991000000000719728 100 $a20090224d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDecision theory$b[electronic resource] $eprinciples and approaches /$fGiovanni Parmigiani, Lurdes Y.T. Inoue, Hedibert F. Lopes 205 $a1st edition 210 $aChichester, West Sussex $cJohn Wiley & Sons$dc2009 215 $a1 online resource (404 p.) 225 1 $aWiley Series in Probability and Statistics ;$vv.812 300 $aDescription based upon print version of record. 311 $a0-471-49657-X 320 $aIncludes bibliographical references and index. 327 $aDecision Theory; Contents; Preface; Acknowledgments; 1 Introduction; 1.1 Controversies; 1.2 A guided tour of decision theory; Part One Foundations; 2 Coherence; 2.1 The "Dutch Book" theorem; 2.1.1 Betting odds; 2.1.2 Coherence and the axioms of probability; 2.1.3 Coherent conditional probabilities; 2.1.4 The implications of Dutch Book theorems; 2.2 Temporal coherence; 2.3 Scoring rules and the axioms of probabilities; 2.4 Exercises; 3 Utility; 3.1 St. Petersburg paradox; 3.2 Expected utility theory and the theory of means; 3.2.1 Utility and means; 3.2.2 Associative means 327 $a3.2.3 Functional means3.3 The expected utility principle; 3.4 The von Neumann-Morgenstern representation theorem; 3.4.1 Axioms; 3.4.2 Representation of preferences via expected utility; 3.5 Allais' criticism; 3.6 Extensions; 3.7 Exercises; 4 Utility in action; 4.1 The "standard gamble"; 4.2 Utility of money; 4.2.1 Certainty equivalents; 4.2.2 Risk aversion; 4.2.3 A measure of risk aversion; 4.3 Utility functions for medical decisions; 4.3.1 Length and quality of life; 4.3.2 Standard gamble for health states; 4.3.3 The time trade-off methods; 4.3.4 Relation between QALYs and utilities 327 $a4.3.5 Utilities for time in ill health4.3.6 Difficulties in assessing utility; 4.4 Exercises; 5 Ramsey and Savage; 5.1 Ramsey's theory; 5.2 Savage's theory; 5.2.1 Notation and overview; 5.2.2 The sure thing principle; 5.2.3 Conditional and a posteriori preferences; 5.2.4 Subjective probability; 5.2.5 Utility and expected utility; 5.3 Allais revisited; 5.4 Ellsberg paradox; 5.5 Exercises; 6 State independence; 6.1 Horse lotteries; 6.2 State-dependent utilities; 6.3 State-independent utilities; 6.4 Anscombe-Aumann representation theorem; 6.5 Exercises; Part Two Statistical Decision Theory 327 $a7 Decision functions7.1 Basic concepts; 7.1.1 The loss function; 7.1.2 Minimax; 7.1.3 Expected utility principle; 7.1.4 Illustrations; 7.2 Data-based decisions; 7.2.1 Risk; 7.2.2 Optimality principles; 7.2.3 Rationality principles and the Likelihood Principle; 7.2.4 Nuisance parameters; 7.3 The travel insurance example; 7.4 Randomized decision rules; 7.5 Classification and hypothesis tests; 7.5.1 Hypothesis testing; 7.5.2 Multiple hypothesis testing; 7.5.3 Classification; 7.6 Estimation; 7.6.1 Point estimation; 7.6.2 Interval inference; 7.7 Minimax-Bayes connections; 7.8 Exercises 327 $a8 Admissibility8.1 Admissibility and completeness; 8.2 Admissibility and minimax; 8.3 Admissibility and Bayes; 8.3.1 Proper Bayes rules; 8.3.2 Generalized Bayes rules; 8.4 Complete classes; 8.4.1 Completeness and Bayes; 8.4.2 Sufficiency and the Rao-Blackwell inequality; 8.4.3 The Neyman-Pearson lemma; 8.5 Using the same ? level across studies with different sample sizes is inadmissible; 8.6 Exercises; 9 Shrinkage; 9.1 The Stein effect; 9.2 Geometric and empirical Bayes heuristics; 9.2.1 Is x too big for ??; 9.2.2 Empirical Bayes shrinkage; 9.3 General shrinkage functions 327 $a9.3.1 Unbiased estimation of the risk of x + g(x) 330 $aDecision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice. The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decisi 410 0$aWiley Series in Probability and Statistics 606 $aStatistical decision 606 $aAxiomatic set theory 606 $aExperimental design 615 0$aStatistical decision. 615 0$aAxiomatic set theory. 615 0$aExperimental design. 676 $a519.5 676 $a519.5/42 676 $a519.542 700 $aParmigiani$b G$g(Giovanni)$0151641 701 $aInoue$b Lurdes Y. T$g(Lurdes Yoshiko Tani),$f1970-$0963198 701 $aLopez$b Hedibert Freitas$0963199 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146132003321 996 $aDecision theory$92183921 997 $aUNINA