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