Optimal statistical decisions

✍ Scribed by Morris H. DeGroot

• Publisher: John Wiley & Sons
• Year: 2004
• Tongue: English
• Leaves: 505
• Series: Wiley Classics Library
• Category: Library

✦ Synopsis

(foreword to the Wiley Classics Libary edition - part of the book)

Optimal Statistical Decisions is a landmark book. It is still about the clearest introduction to Bayesian Statistical Decision Theory available. Written in the late 1960’s, it does not cover the computational advances that have become so popular and well-used. But with the rapid growth of interest in computational methods, it is all too easy to neglect what purposes are served by those computations. DeGroot’s book, with its clear exposition of Bayesian principles, will be useful to help keep those purposes in mind.
The book is divided into four parts. The first, a review of probability theory, is useful as a reference and for clarifying notation. The second, a derivation of the principle of maximizing expected utility is original in that it takes two primitives: “is more likely than” for probability, and “is preferred to” for utility. This resolves the uncomfortable fact that using only "is preferred to” among gambles identifies the product of probability and utility, but does not clarify how to disentangle them. The third part, on statistical decisions, rehearses the facts about fixed-sample posterior decisions. Chapter 11 compares Bayesian answers to classical ones concerning the linear model (and goes further in compromising Bayesian ideas than I find comfortable now).
The strongest part of the book, in my mind, is the last part, on sequential decisions. This is the subject that most engaged DeGroot as a researcher, and here we see the full power of his intellect.
To appreciate a book, it is useful to understand the author. Even a reader who never knew DeGroot will appreciate what a wonderful writer he was. While some may disagree with what he writes, it is hard to imagine that anyone will be in doubt as to what he means. His papers are as clear as his books. But this is only one aspect of an extraordinary scholar and person. 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.
It is a great pleasure to me to play a role in reintroducing a great book and a great man to a new generation of Bayesian statisticians.

Joseph B. (“Jay”) Kadane
Pittsburgh, Pa.
Nov. 22, 2003

✦ Table of Contents

Copyright
Foreword to the Wiley Classics Library edition
Preface to the original edition
Contents
Part I: Survey of probability theory
1. Introduction
2. Experiments, sample spaces, and probability
3. Random variables, random vectors, and distribution functions
4. Some special univariate distributions
5. Some special multivariate distributions
Part II: Subjective probability and utility
6. Subjective probability
7. Utility
Part III: Statistical decision problems
8. Decision problems
9. Conjugate prior distributions
10. Limiting posterior distributions
11. Estimation, testing hypotheses, and linear statistical models
Part IV: Sequential decisions
12. Sequential sampling
13. Optimal stopping
14. Sequential choice of experiments
References
Supplementary bibliography
Indexes
Name index
Subject index

✦ Subjects

statistics,decision making