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 viiPreface ixPart One. Survey of Probability Theory Chapter 1. Introduction 3Chapter 2. Experiments, Sample Spaces, and Probability 6Chapter 3. Random Variables, Random Vectors, and Distribution Functions 16Chapter 4. Some Special Univariate Distributions 33Chapter 5. Some Special Multivariate Distributions 48Part Two. Subjective Probability and Utility Chapter 6. Subjective Probability 69Chapter 7. Utility 86Part Three. Statistical Decision Problems Chapter 8. Decision Problems 121Chapter 9. Conjugate Prior Distributions 155Chapter 10. Limiting Posterior Distributions 190Chapter 11. Estimation, Testing Hypotheses, and linear Statistical Models 226Part Four. Sequential Decisions Chapter 12. Sequential Sampling 267Chapter 13. Optimal Stopping 324Chapter 14. Sequential Choice of Experiments 385References 447Supplementary Bibliography 466Name Index 475Subject Index 481