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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

Library of Congress subject headings for this publication:

Statistics.