1. INTRODUCTION
_ 1. The role of foundations
_ 2. Historical background
_ 3. General outline of this book
2. PRELIMINARY CONSIDERATIONS ON DECISION IN THE FACE OF UNCERTAINTY
_ 1. Introduction
_ 2. The person
_ 3. "The world, and states of the world"
_ 4. Events
_ 5. "Consequences, acts, and decisions"
_ 6. The simple ordering of acts with respect to preference
_ 7. The sure-thing principle
3. PERSONAL PROBABILITY
_ 1. Introduction
_ 2. Qualitative personal probability
_ 3. Quantitative personal probability
_ 4. Some mathematical details
_ 5. "Conditional probability, qualitative and quantitative"
_ 6. The approach to certainty through experience
_ 7. Symmetric sequences of events
4. CRITICAL COMMENTS ON PERSONAL PROBABILITY
_ 1. Introduction
_ 2. Some shortcomings of the personalistic view
_ 3. Connection with other views
_ 4. Criticism of other views
_ 5. The role of symmetry in probability
_ 6. How can science use a personalistic view of probability?
5. UTILITY
_ 1. Introduction
_ 2. Gambles
_ 3. "Utility, and preference among gambles"
_ 4. The extension of utility to more general acts
_ 5. Small worlds
_ 6. Historical and critical comments on utility
6. OBSERVATION
_ 1. Introduction
_ 2. What an observation is
_ 3. "Multiple observations, and extensions of observations and of sets of acts"
_ 4. Dominance and admissibility
_ 5. Outline of the design of experiments
7. PARTITION PROBLEMS
_ 1. Introduction
_ 2. Structure of (twofold) partition problems
_ 3. The value of observation
_ 4. "Extension of observations, and sufficient statistics"
_ 5. Likelihood ratios
_ 6. Repeated observations
_ 7. Sequential probability ratio procedures
_ 8. "Standard form, and absolute comparison between observations"
8. STATISTICS PROPER
_ 1. Introduction
_ 2. What is statistics proper?
_ 3. Multipersonal problems
_ 4. The minimax theory
9. INTRODUCTION TO THE MINIMAX THEORY
_ 1. Introduction
_ 2. The behavioralistic outlook
_ 3. Mixed acts
_ 4. Income and loss
_ 5. "The minimax rule, and the principle of admissibility"
_ 6. Illustrations of the minimax rule
_ 7. Objectivistic motivation of the minimax rule
_ 8. Loss as opposed to negative income in the minimax rule
10. A PERSONALISTIC REINTERPRETATION OF THE MINIMAX THEORY
_ 1. Introduction
_ 2. A model of group decision
_ 3. "The group minimax rule, and the group principle of admissibility"
_ 4. Critique of the group minimax rule
11. THE PARALLELISM BETWEEN THE MINIMAX THEORY AND THE THEORY OF TWO-PERSON GAMES
_ 1. Introduction
_ 2. Standard games
_ 3. Minimax play
_ 4. Parallelism and contrast with the minimax theories
12. THE MATHEMATICS OF MINIMAX PROBLEMS
_ 1. Introduction
_ 2. Abstract games
_ 3. Bilinear games
_ 4. An example of a bilinear game
_ 5. Bilinear games exhibiting symmetry
13. OJBECTIONS TO THE MINIMAX RULES
_ 1. Introduction
_ 2. A confusion between loss and negative income
_ 3. Utility and the minimax rule
_ 4. Almost sub-minimax acts
_ 5. The minimax rule does not generate a simple ordering
14. THE MINIMAX THEORY APPLIED TO OBSERVATIONS
_ 1. Introduction
_ 2. Recapitulation of partition problems
_ 3. Sufficient statistics
_ 4. "Simple dichotomy, an example"
_ 5. The approach to certainty
_ 6. Cost of observation
_ 7. Sequential probability ratio procedures
_ 8. Randomization
_ 9. Mixed acts in statistics
15. POINT ESTIMATION
_ 1. Introduction
_ 2. The verbalistic concept of point estimation
_ 3. Examples of problems of point estimation
_ 4. Criteria that have been proposed for point estimates
_ 5. A behavioralistic review of the criteria for point estimation
_ 6. "A behavioralistic review, continued"
_ 7. "A behavioralistic review, concluded"
16. TESTING
_ 1. Introduction
_ 2. A theory of testing
_ 3. Testing in practice
17. INTERVAL ESTIMATION AND RELATED TOPICS
_ 1. Estimates of the accuracy of estimates
_ 2. Interval estimation and confidence intervals
_ 3. Tolerance intervals
_ 4. Fiducial probability
_ APPENDIX 1. EXPECTED VALUE
_ APPENDIX 2. CONVEX FUNCTIONS
_ APPENDIX 3. BIBLIOGRAPHIC MATERIAL
_ APPENDIX 4. BIBLIOGRAPHIC SUPPLEMENT
_ TECHNICAL SYMBOLS
_ AUTHOR INDEX
_ GENERAL INDEX