# Introduction to Statistical Decision Theory

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

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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.

## Product Details

ISBN-13:
9780262662062
Publisher:
MIT Press
Publication date:
03/31/2008
Edition description:
New Edition
Pages:
896
Product dimensions:
7.00(w) x 10.00(h) x 1.50(d)
Age Range:
18 Years

## Related Subjects

 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