Rethinking the Foundations of Statistics

A synthesis of foundational studies in Bayesian decision theory and statistics.

Introduction; Part I. Decision Theory for Cooperative Decision-Making: 1. Shared preferences of two Bayesian decision makers; 2. Decisions without ordering; 3. A representation of partially ordered preferences; Part II. The Truth about Consequences: 4. Separating probability elicitation from utilities; 5. State-dependent utilities; 6. Shared preferences and state-dependent utilities; 7. A conflict between finitely additive probability and avoiding Dutch book; 8. Statistical implications of finitely additive probability; Part III. Non-Cooperative Decision Making, Inference, and Learning with Shared Evidence: 9. Subjective probability and the theory of games; 10. Equilibrium, common knowledge, and optimal sequential decisions; 11. A fair minimax theorem for 2 person (zero-sum) games involving finitely additive strategies; 12. Randomization in a Bayesian perspective; 13. Characterizations of externally Bayesian pooling operators; 14. An approach to consensus and certainty with increasing evidence; 15. Reasoning to a foregone conclusion; 16. When several Bayesians agree that there will be no reasoning to a foregone conclusion.