Rethinking the Foundations of Statistics

Joseph B. Kadane; Mark J. Schervish; Teddy Seidenfeld

doi:10.1017/CBO9781139173230

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. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists.

"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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Contents

Frontmatter
pp i-viii
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Contents
pp ix-x
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Introduction
pp 1-14
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PART 1 - DECISION THEORY FOR COOPERATIVE DECISION MAKING
pp 15-16
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1.1 - On the Shared Preferences of Two Bayesian Decision Makers
pp 17-39
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1.2 - Decisions Without Ordering
pp 40-68
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1.3 - A Representation of Partially Ordered Preferences
pp 69-130
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PART 2 - THE TRUTH ABOUT CONSEQUENCES
pp 131-132
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2.1 - Separating Probability Elicitation from Utilities
pp 133-148
- By Robert L. Winkler
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2.2 - State-dependent Utilities
pp 149-168
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2.3 - Shared Preferences and State-dependent Utilities
pp 169-193
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2.4 - A Conflict Between Finite Additivity and Avoiding Dutch Book
pp 194-210
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2.5 - Statistical Implications of Finitely Additive Probability
pp 211-232
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PART 3 - NON-COOPERATIVE DECISION MAKING, INFERENCE, AND LEARNING WITH SHARED EVIDENCE
pp 233-234
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3.1 - Subjective Probability and the Theory of Games
pp 235-245
- By Patrick D. Larkey
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3.2 - Equilibrium, Common Knowledge, and Optimal Sequential Decisions
pp 246-266
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3.3 - A Fair Minimax Theorem for Two-Person (Zero-Sum) Games Involving Finitely Additive Strategies
pp 267-292
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3.4 - Randomization in a Bayesian Perspective
pp 293-313
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3.5 - Characterization of Externally Bayesian Pooling Operators
pp 314-332
- By Christian Genest, Kevin J. McConway
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3.6 - An Approach to Consensus and Certainty with Increasing Evidence
pp 333-348
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3.7 - Reasoning to a Foregone Conclusion
pp 349-368
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3.8 - When Several Bayesians Agree That There Will Be No Reasoning to a Foregone Conclusion
pp 369-382
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Index of Names
pp 383-385
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Subject Index
pp 386-388
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Rethinking the Foundations of Statistics

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Contents

Frontmatter
pp i-viii

Contents
pp ix-x

Introduction
pp 1-14

PART 1 - DECISION THEORY FOR COOPERATIVE DECISION MAKING
pp 15-16

1.1 - On the Shared Preferences of Two Bayesian Decision Makers
pp 17-39

1.2 - Decisions Without Ordering
pp 40-68

1.3 - A Representation of Partially Ordered Preferences
pp 69-130

PART 2 - THE TRUTH ABOUT CONSEQUENCES
pp 131-132

2.1 - Separating Probability Elicitation from Utilities
pp 133-148

2.2 - State-dependent Utilities
pp 149-168

2.3 - Shared Preferences and State-dependent Utilities
pp 169-193

2.4 - A Conflict Between Finite Additivity and Avoiding Dutch Book
pp 194-210

2.5 - Statistical Implications of Finitely Additive Probability
pp 211-232

PART 3 - NON-COOPERATIVE DECISION MAKING, INFERENCE, AND LEARNING WITH SHARED EVIDENCE
pp 233-234

3.1 - Subjective Probability and the Theory of Games
pp 235-245

3.2 - Equilibrium, Common Knowledge, and Optimal Sequential Decisions
pp 246-266

3.3 - A Fair Minimax Theorem for Two-Person (Zero-Sum) Games Involving Finitely Additive Strategies
pp 267-292

3.4 - Randomization in a Bayesian Perspective
pp 293-313

3.5 - Characterization of Externally Bayesian Pooling Operators
pp 314-332

3.6 - An Approach to Consensus and Certainty with Increasing Evidence
pp 333-348

3.7 - Reasoning to a Foregone Conclusion
pp 349-368

3.8 - When Several Bayesians Agree That There Will Be No Reasoning to a Foregone Conclusion
pp 369-382

Index of Names
pp 383-385

Subject Index
pp 386-388

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