Decision Theory / Wiley Series in Probability and Statistics (PDF)

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 of probabilities. 2.4 Exercises. 3 Utility. 3.1 St. Petersburg paradox. 3.2 Expected utility theory and the theory of means. 3.3 The expected utility principle. 3.4 The von Neumann-Morgenstern representation theorem. 3.5 Allais' criticism. 3.6 Extensions. 3.7 Exercises. 4 Utility in action. 4.1 The "standard gamble". 4.2 Utility of money. 4.3 Utility functions for medical decisions. 4.4 Exercises. 5 Ramsey and Savage. 5.1 Ramsey's theory. 5.2 Savage's theory. 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. 7 Decision functions. 7.1 Basic concepts. 7.2 Data-based decisions. 7.3 The travel insurance example. 7.4 Randomized decision rules. 7.5 Classification and hypothesis tests. 7.6 Estimation. 7.7 Minimax-Bayes connections. 7.8 Exercises. 8 Admissibility. 8.1 Admissibility and completeness. 8.2 Admissibility and minimax. 8.3 Admissibility and Bayes. 8.4 Complete classes. 8.5 Using the same alpha 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. 9.3 General shrinkage functions. 9.4 Shrinkage with different likelihood and losses. 9.5 Exercises. 10 Scoring rules. 10.1 Betting and forecasting. 10.2 Scoring rules. 10.3 Local scoring rules. 10.4 Calibration and refinement. 10.5 Exercises. 11 Choosing models. 11.1 The "true model" perspective. 11.2 Model elaborations. 11.3 Exercises. Part Three Optimal Design. 12 Dynamic programming. 12.1 History. 12.2 The travel insurance example revisited. 12.3 Dynamic programming. 12.4 Trading off

Giovanni Parmigiani is the author of Decision Theory: Principles and Approaches, published by Wiley.

Lurdes Yoshiko Tani Inoue is a Brazilian-born statistician of Japanese descent, who specializes in Bayesian inference. She works as a professor of biostatistics in the University of Washington School of Public Health.

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