Rethinking the Foundations of Statistics

by Joseph B. Kadane , Mark J. Schervish , Teddy Seidenfeld

• ISBN13: 9780521649759
• ISBN10: 0521649757
• Format: Paperback
• Copyright: 1999-08-13
• Publisher: Cambridge University Press

Summary

This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists.

Table of Contents

Introduction	1	(16)
PART 1 DECISION THEORY FOR COOPERATIVE DECISION MAKING
On the Shared Preferences of Two Bayesian Decision Makers	17	(23)
Decisions Without Ordering	40	(29)
A Representation of Partially Ordered Preferences	69	(64)
PART 2 THE TRUTH ABOUT CONSEQUENCES
Separating Probability Elicitation from Utilities	133	(16)
State-dependent Utilities	149	(20)
Shared Preferences and State-dependent Utilities	169	(25)
A Conflict Between Finite Additivity and Avoiding Dutch Book	194	(17)
Statistical Implications of Finitely Additive Probability	211	(24)
PART 3 NON-COOPERATIVE DECISION MAKING, INFERENCE, AND LEARNING WITH SHARED EVIDENCE
Subjective Probability and the Theory of Games	235	(11)
Equilibrium, Common Knowledge, and Optimal Sequential Decisions	246	(21)
A Fair Minimax Theorem for Two-Person (Zero-Sum) Games Involving Finitely Additive Strategies	267	(26)
Randomization in a Bayesian Perspective	293	(21)
Characterization of Externally Bayesian Pooling Operators	314	(19)
An Approach to Consensus and Certainty with Increasing Evidence	333	(16)
Reasoning to a Foregone Conclusion	349	(20)
When Several Bayesians Agree That There Will Be No Reasoning to a Foregone Conclusion	369	(14)
Index of Names	383	(3)
Subject Index	386