Elementary Decision Theory

"The text is very clearly written [with] many illustrative examples and exercises [and] should be considered by those instructors who would like to introduce a more modern (and a more logical) approach in a basic course in statistics." —Journal of the American Statistical Association This volume is a well-known, well-respected introduction to a lively area of statistics. Professors Chernoff and Moses bring years of professional expertise as classroom teachers to this straightforward approach to statistical problems. And happily, for beginning students, they have by-passed involved computational reasonings which would only confuse the mathematical novice. Developed from nine years of teaching statistics at Stanford, the book furnishes a simple and clear-cut method of exhibiting the fundamental aspects of a statistical problem. Beginners will find this book a motivating introduction to important mathematical notions such as set, function and convexity. Examples and exercises throughout introduce new topics and ideas. The first seven chapters are recommended for beginning courses in the basic ideas of statistics and require only a knowledge of high school math. These sections include material on data processing, probability and random variables, utility and descriptive statistics, uncertainty due to ignorance of the state of nature, computing Bayes strategies and an introduction to classical statistics. The last three chapters review mathematical models and summarize terminology and methods of testing hypotheses. Tables and appendixes provide information on notation, shortcut computational formulas, axioms of probability, properties of expectations, likelihood ratio test, game theory, and utility functions. Authoritative, yet elementary in its approach to statistics and statistical theory, this work is also concise, well-indexed and abundantly equipped with exercise material. Ideal for a beginning course, this modestly priced edition will be especially valuable to those interested in the principles of statistics and scientific method.

All of human life may be seen as a process of decision-making, but it is only in recent years and in response to the needs of the large and complex organizations characterizing our society that this process has been subjected to scientifi c scrutiny. Out of this scrutiny-undertaken by a wide range of professionals in economics, administration, management, statistics, psychology, engineering, computer science, operations research, and systems analysis-there has begun to emerge a body of theory that has profound implications for improving practical decision-making. This book is the fi rst to bring together all the various aspects of decision theory into one cohesive treatment.

A comprehensive and accessible introduction to all aspects of decision theory, now with new and updated discussions and over 140 exercises.

For advanced graduate students, this book is a one-stop shop that presents the main ideas of decision theory in an organized, balanced, and mathematically rigorous manner, while observing statistical relevance. All of the major topics are introduced at an elementary level, then developed incrementally to higher levels. The book is self-contained as it provides full proofs, worked-out examples, and problems. The authors present a rigorous account of the concepts and a broad treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory. With its broad coverage of decision theory, this book fills the gap between standard graduate texts in mathematical statistics and advanced monographs on modern asymptotic theory.

The book treats two approaches to decision theory: (1) the normative, purporting to determine how a 'perfectly rational' actor ought to choose among available alternatives; (2) the descriptive, based on observations of how people actually choose in real life and in laboratory experiments. The mathematical tools used in the normative approach range from elementary algebra to matrix and differential equations. Sections on different levels can be studied independently. Special emphasis is made on 'offshoots' of both theories to cognitive psychology, theoretical biology, and philosophy.

This monograph presents a radical rethinking of how elementary inferences should be made in statistics, implementing a comprehensive alternative to hypothesis testing in which the control of the probabilities of the errors is replaced by selecting the course of action (one of the available options) associated with the smallest expected loss. Its strength is that the inferences are responsive to the elicited or declared consequences of the erroneous decisions, and so they can be closely tailored to the client’s perspective, priorities, value judgments and other prior information, together with the uncertainty about them.