05714nam 2200733Ia 450 991084074930332120170809170514.00-470-74668-81-282-13828-697866121382870-470-74667-X(CKB)1000000000719728(EBL)427978(SSID)ssj0000336547(PQKBManifestationID)11244456(PQKBTitleCode)TC0000336547(PQKBWorkID)10281971(PQKB)10803978(MiAaPQ)EBC427978(CaSebORM)9780471496571(OCoLC)695561337(PPN)18342719X(EXLCZ)99100000000071972820090224d2009 uy 0engur|n|---|||||txtccrDecision theory[electronic resource] principles and approaches /Giovanni Parmigiani, Lurdes Y.T. Inoue, Hedibert F. Lopes1st editionChichester, West Sussex John Wiley & Sonsc20091 online resource (404 p.)Wiley Series in Probability and Statistics ;v.812Description based upon print version of record.0-471-49657-X Includes bibliographical references and index.Decision 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 means3.2.3 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 utilities4.3.5 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 Theory7 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 Exercises8 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 α 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 θ?; 9.2.2 Empirical Bayes shrinkage; 9.3 General shrinkage functions9.3.1 Unbiased estimation of the risk of x + g(x)Decision 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 decisiWiley Series in Probability and StatisticsStatistical decisionAxiomatic set theoryExperimental designStatistical decision.Axiomatic set theory.Experimental design.519.5519.5/42519.542Parmigiani G(Giovanni)151641Inoue Lurdes Y. T(Lurdes Yoshiko Tani),1970-1728280Lopez Hedibert Freitas1728281MiAaPQMiAaPQMiAaPQBOOK9910840749303321Decision theory4136792UNINA