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Rethinking the Foundations of Statistics

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Overview

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.

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Editorial Reviews

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"The material is well presented, and the authors themselves have made significant contributions to this area...should greatly appeal to philosophers, advanced graduate students, and researchers interested in exploring and researching the foundations of Bayesian statistics." CHOICE
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Product Details

Table of Contents

Introduction 1
Pt. 1 Decision Theory for Cooperative Decision Making
1.1 On the Shared Preferences of Two Bayesian Decision Makers 17
1.2 Decisions Without Ordering 40
1.3 A Representation of Partially Ordered Preferences 69
Pt. 2 The Truth about Consequences
2.1 Separating Probability Elicitation from Utilities 133
2.2 State-dependent Utilities 149
2.3 Shared Preferences and State-dependent Utilities 169
2.4 A Conflict Between Finite Additivity and Avoiding Dutch Book 194
2.5 Statistical Implications of Finitely Additive Probability 211
Pt. 3 Non-Cooperative Decision Making, Inference, and Learning with Shared Evidence
3.1 Subjective Probability and the Theory of Games 235
3.2 Equilibrium, Common Knowledge, and Optimal Sequential Decisions 246
3.3 A Fair Minimax Theorem for Two-Person (Zero-Sum) Games Involving Finitely Additive Strategies 267
3.4 Randomization in a Bayesian Perspective 293
3.5 Characterization of Externally Bayesian Pooling Operators 314
3.6 An Approach to Consensus and Certainty with Increasing Evidence 333
3.7 Reasoning to a Foregone Conclusion 349
3.8 When Several Bayesians Agree That There Will Be No Reasoning to a Foregone Conclusion 369
Index of Names 383
Subject Index 386
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