Introduction To Statistical Decision Theory

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“This book is a classic.... The strengths of this text are twofold. First, it gives a general and well-motivated introduction to the principles of Bayesian decision theory that should be accessible to anyone with a good mathematical statistics background. Second, it provides a good introduction to Bayesian inference in general with particular emphasis on the use of subjective information to choose prior distributions.” Mark J. Schervish Journal of the American Statistical Association Introduction to Statistical Decision Theory integrates statistical inference with decision making and discusses real-world actions involving economic payoffs and risks. Besides developing the rationale and demonstrating the power and relevance of the subjective, decision approach, the text also examines and critiques the limitations of the objective, classical approach. Thus, in a self-contained comprehensive way, the book shows that the Bayesian approach in statistics – integration of statistics with decision making in areas such as management, engineering, public policy and clinical medicine, is operational and relevant for real-world decision making under uncertainty. Table of Contents Preface. Introduction. An Informal Treatment of Foundations. A Formal Treatment of Foundations. Assessment of Utilities for Consequences. Quantification of Judgments. Analysis of Decision Trees. Random Variables. Continuous Lotteries and Expectations. Special Univariate Distributions. Conditional Probability and Bayes’ Theorem. Bernoulli Process. Terminal Analysis: Opportunity Loss and the Value of Perfect Information. Paired Random Variables. Preposterior Analysis: The Value of Sample Information. Poisson Process. Normal Process with Known Variance. Normal Process with Known Variance. Normal Process with Unknown Variance. Large Sample Theory. Statistical Analysis in Normal Form. Classical Methods. Multivariate Random Variables. The Multivariate Normal Distribution. Choosing the Best of Several Processes. Allowance for Uncertain Bias. Stratification. The Portfolio Problem. Normal Linear Regression with Known Variance. Appendices 1: The Terminology of Sets. 2: Elements of Matrix Theory. 3: Properties of Utility Functions for Monetary Consequences. 4: Tables. Bibliography. Index.