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Theory of Games and Statistical Decisions

David A. Blackwell and M. A. Girshick
Dover Publications
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Adam Gilbert
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As the title implies, this text develops the theory of statistical decisions within the framework of a game played between the statistician and nature. While the focus of the text is certainly on the rigorous development of the theory, the examples included cover a broad range of applications, and are expertly placed to reinforce the reader’s grasp of the content.

The first two chapters of the text provide the framework upon which the content will be built, while the third chapter exposes the reader to the general structure of statistical games. The remainder of the text is truly a treat for the reader. In chapter 4 the authors introduce the notion of utility as a measure of satisfaction with the outcome of a game. In chapter 5 the reader is exposed to the different classes of optimal strategies for games. The remaining chapters of the text provide rigorous development, discussion, and exploration of different classes of statistical games.

This graduate level text is suitable for use in a master’s level statistics course. The reader with a strong background in analysis and some exposure to point-set topology will be best-prepared for the book’s content. It is recommended that any reader maintain a well-organized list of the symbols used throughout the text, as there are many.

This advanced text is well-written and provides a very interesting perspective on statistical decisions. The book is a recommended read for any instructor or practitioner with the requisite background knowledge. Practitioners will benefit from the formalization of the practical goals of the statistician and decision maker, while instructors will gain deeper understanding of the content (particularly risk-reward analysis and hypothesis testing) that they teach in their own statistics courses.

Adam Gilbert is an Assistant Professor of Mathematics at Southern New Hampshire University in Manchester, NH. His research interests are in graph theory and combinatorial games.

The table of contents is not available.