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Elementary Decision Theory

Herman Chernoff and Lincoln E. Moses
Publisher: 
Dover Publications
Publication Date: 
1987
Number of Pages: 
364
Format: 
Paperback
Price: 
22.95
ISBN: 
978-0486652184
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Robert W. Hayden
, on
11/19/2010
]

Shortly before this book was published, John Tukey gave a famous talk in which he warned against the takeover of statistics by decision theory. (It hasn’t happened yet.) Shortly after this book was published, Tukey’s talk appeared in print. (“Conclusions vs. decisions”, Technometrics, Vol.2, 1960, pp.424–433) In it, he distinguished two uses of statistics. In one, the goal is to make a decision. This is most common in business applications, and this is the sort of thing covered in the book at hand. Real-life decision making always involves subjective elements. There seems to be a split between statisticians who would like to keep the objective and subjective elements segregated and those who feel they can profitably be combined.

The other use of statistics Tukey discussed was in accumulating scientific evidence. Here the issue is to evaluate how much evidence a new study provides, but decisions are made only after many studies have accumulated. In these applications, no subjectivity is allowed in reporting the individual studies.

The book at hand is half an introduction to decision theory and half an application of those ideas to introductory statistics. For example, modern texts often advise against automatically setting an alpha of 0.05 for all hypothesis tests, and say that the level should be determined by context. Here subjectivity seems to creep in a bit, but if that be allowed, Chernoff and Moses have suggestions. Many similar discussions presented here are worth reading even if one does not agree with their suggestions, for in real life such questions must be answered. The discussion of mathematical modeling is especially fine.

It is hard to specify the level of this book. Not much in the way of mathematical content is needed in most places other than high school algebra, but the authors are almost belligerent in their use of symbolism, often in places where it serves no useful purpose, and can alienate a significant portion of practical decision-makers. The book also seems elementary in its use of fanciful and unreal examples of the kinds of decisions one might want to make. Whether to carry an umbrella is a favorite, for example. This can leave the reader lacking in motivation, wondering if the techniques have any real uses, and certainly lacking in any skill at applying the ideas to real life.

There are probably better textbooks in decision theory that one could adopt than this. Recommended to teachers of statistics for its discussion of many issues in applied statistics that textbooks tell you to consider but don’t say how.


After a few years in industry, Robert W. Hayden (bob@statland.org) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at statistics.com and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.

1 INTRODUCTION

2 DATA PROCESSING

3 INTRODUCTION TO PROBABILITY AND RANDOM VARIABLES

4 UTILITY AND DESCRIPITIVE STATISTICS

5 UNCERTAINTY DUE TO IGNORANCE OF THE STATE OF NATURE

6 THE COMPUTATION OF BAYES STRATEGIES

7 INTRODUCTION TO CLASSICAL STATISTICS

8 MODELS

9 TESTING HYPOTHESES

10 ESTIMATION AND CONFIDENCE INTERVALS

APPENDIX

A NOTATION

B MATHEMATICAL TABLES

C TABLES OF RANDOM DEVIATES

D TABLES OF PROBABILITY DISTRIBUTIONS

E DERIVATIONS

F MISCELLANEOUS REMARKS ABOUT GAME THEORY AND UTILITY THEORY

PARTIAL LIST OF ANSWERS TO EXERCISES

INDEX

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