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. |
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a₂ accepting H₁ action probabilities admissible strategies apply assume average loss b₁ b₂ batch Bayes risk Bayes strategy big eaters bility called Chapter coin compute confidence interval consider convex set cumulative frequency curve decision density dice distributed with mean equal Equation error curve error probabilities estimate evaluate Example 7.1 Exercise experiment falls heads Figure gamble given graph Hence hypothesis L₁ likelihood-ratio test method minimax minimax risk minimax strategy minimizes nature normally distributed number of heads obtained P₁ P₂ parameter Phiggins player points possible outcomes possible values posteriori probabilities priori probabilities proba probability density function probability distribution prospect pure strategies random variable regret function represented risk function s₁ sample mean set of possible standard deviation statistical statistician Suppose t₁ Table tion toss utility function variance versus H₂ w₁ w₂ weighted average X₁ Y₁ yield zero