Introduction to Statistical Decision Theory

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Overview

The Bayesian revolution in statistics - where statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicine - is here to stay. Introduction to Statistical Decision Theory states the case and in a self-contained,comprehensive way shows how the approach is operational and relevant for real-world decision making under uncertainty.Starting with an extensive account of the foundations of decision theory, the authors develop the intertwining concepts of subjective probability and utility. They then systematically and comprehensively examine the Bernoulli, Poisson, and Normal (univariate and multivariate) data generating processes. For each process they consider how prior judgments about the uncertain parameters of the process are modified given the results of statistical sampling, and they investigate typical decision problems in which the main sources of uncertainty are the population parameters. They also discuss the value of sampling information and optimal sample sizes given sampling costs and the economics of the terminal decision problems.Unlike most introductory texts in statistics, Introduction to Statistical Decision Theory integrates statistical inference with decision making and discusses real-world actions involving economic payoffs and risks. After 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.

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Editorial Reviews

From the Publisher
"An excellent introduction to Bayesian statistical theory." Frank Windmeijer Times Higher Education Supplement

"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

"This is the authoritative introductory treatise (almost 900 pages) on appliedBayesian statistical theory. It is self-contained and well-presented, developed with great care and obvious affection by the founders of the subject." James M. Dickey Mathematical Reviews

Booknews
An introduction to Bayesian statistics, i.e., to the mathematical analysis of the problems that arise when the consequence of action depends on the uncertain "state of the world," about which the decision maker either has obtained or can obtain additional information by sampling or experimentation. The exercises and case material are an integral part of the text, which is written more for classroom use than for individual study. Assumes familiarity with the basic concepts of calculus. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780262662062
  • Publisher: MIT Press
  • Publication date: 3/31/2008
  • Edition description: New Edition
  • Pages: 896
  • Sales rank: 919,714
  • Product dimensions: 7.00 (w) x 10.00 (h) x 1.50 (d)

Table of Contents

Preface
1 Introduction 1
2 An Informal Treatment of Foundations 11
3 A Formal Treatment of Foundations 47
4 Assessment of Utilities for Consequences 69
5 Quantification of Judgments 93
6 Analysis of Decision Trees 113
7 Random Variables 133
8 Continuous Lotteries and Expectations 159
9 Special Univariate Distributions 181
10 Conditional Probability and Bayes' Theorem 211
11 Bernoulli Process 225
12 Terminal Analysis: Opportunity Loss and the Value of Perfect Information 247
13 Paired Random Variables 273
14 Preposterior Analysis: The Value of Sample Information 307
15 Poisson Process 345
16 Normal Process with Known Variance 375
17 Normal Process with Unknown Variance 417
18 Large Sample Theory 437
19 Statistical Analysis in Normal Form 463
20 Classical Methods 517
21 Multivariate Random Variables 551
22 The Multivariate Normal Distribution 585
23A Choosing the Best of Several Processes 639
23B Allowance for Uncertain Bias 655
23C Stratification 689
23D The Portfolio Problem 713
24 Normal Linear Regression with Known Variance 731
Appendix 1: The Terminology of Sets 781
Appendix 2: Elements of Matrix Theory 785
Appendix 3: Properties of Utility Functions for Monetary Consequences 805
Appendix 4: Tables 819
Bibliography 861
Index 865
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