Optimal Statistical Decisions

Morris DeGroot (now deceased) was a great statistician and gentleman of the 20th Century. Says friend and coworker Joseph B. ("Jay") Kadane of DeGroot in the Foreword. He was an institutional builder, as founder of the Statistics Department at Carnegie Mellon University and as first Executive Editor of Statistical Science. He was a wonderful colleague and friend, always ready for a chat about principles, a research problem, a departmental problem, a reference, or personal advice.

Foreword vii

Preface ix

Part One. Survey of Probability Theory

Chapter 1. Introduction 3

Chapter 2. Experiments, Sample Spaces, and Probability 6

Chapter 3. Random Variables, Random Vectors, and Distribution Functions 16

Chapter 4. Some Special Univariate Distributions 33

Chapter 5. Some Special Multivariate Distributions 48

Part Two. Subjective Probability and Utility

Chapter 6. Subjective Probability 69

Chapter 7. Utility 86

Part Three. Statistical Decision Problems

Chapter 8. Decision Problems 121

Chapter 9. Conjugate Prior Distributions 155

Chapter 10. Limiting Posterior Distributions 190

Chapter 11. Estimation, Testing Hypotheses, and linear Statistical Models 226

Part Four. Sequential Decisions

Chapter 12. Sequential Sampling 267

Chapter 13. Optimal Stopping 324

Chapter 14. Sequential Choice of Experiments 385

References 447

Supplementary Bibliography 466

Name Index 475

Subject Index 481