Decision theory : principles and approaches

摘要: 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. 2.2 Temporal coherence. 2.3 Scoring rules and the axioms probabilities. 2.4 Exercises. 3 Utility. 3.1 St. Petersburg paradox. 3.2 Expected utility theory means. 3.3 expected principle. 3.4 von Neumann-Morgenstern representation 3.5 Allais' criticism. 3.6 Extensions. 3.7 4 Utility in action. 4.1 "standard gamble". 4.2 money. 4.3 functions for medical decisions. 4.4 5 Ramsey Savage. 5.1 Ramsey's 5.2 Savage's 5.3 Allais revisited. 5.4 Ellsberg 5.5 6 State independence. 6.1 Horse lotteries. 6.2 State-dependent utilities. 6.3 State-independent 6.4 Anscombe-Aumann 6.5 Two Statistical Decision Theory. 7 functions. 7.1 Basic concepts. 7.2 Data-based 7.3 travel insurance example. 7.4 Randomized rules. 7.5 Classification hypothesis tests. 7.6 Estimation. 7.7 Minimax-Bayes connections. 7.8 8 Admissibility. 8.1 Admissibility completeness. 8.2 minimax. 8.3 Bayes. 8.4 Complete classes. 8.5 Using same alpha level across studies with different sample sizes is inadmissible. 8.6 9 Shrinkage. 9.1 Stein effect. 9.2 Geometric empirical Bayes heuristics. 9.3 General shrinkage 9.4 Shrinkage likelihood losses. 9.5 10 10.1 Betting forecasting. 10.2 10.3 Local scoring 10.4 Calibration refinement. 10.5 11 Choosing models. 11.1 "true model" perspective. 11.2 Model elaborations. 11.3 Three Optimal Design. 12 Dynamic programming. 12.1 History. 12.2 example 12.3 12.4 Trading off immediate gains information. 12.5 Sequential clinical trials. 12.6 Variable selection multiple regression. 12.7 Computing. 12.8 13 Changes as 13.1 Measuring value 13.2 Examples. 13.3 Lindley 13.4 Minimax 13.5 14 Sample size. 14.1 Decision-theoretic approaches to 14.2 14.3 14.4 15 Stopping. 15.1 Historical note. 15.2 motivating 15.3 Bayesian optimal stopping. 15.4 15.5 sampling reduce uncertainty. 15.6 stopping rule 15.7 Appendix. A.1 Notation. A.2 Relations. A.3 Probability (density) some distributions. A.4 Conjugate updating. References. Index.