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John Winsor Pratt - Introduction to statistical decision theory

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The Bayesian revolution in statisticswhere statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicineis 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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title Introduction to Statistical Decision Theory author Pratt - photo 1

title:Introduction to Statistical Decision Theory
author:Pratt, John W.; Raiffa, Howard; Schlaifer, Robert.
publisher:MIT Press
isbn10 | asin:
print isbn13:9780262161442
ebook isbn13:9780585223148
language:English
subjectStatistical decision.
publication date:1995
lcc:QA279.4.P73 1995eb
ddc:519.5/42
subject:Statistical decision.
Page iii
Introduction to Statistical Decision Theory
John W. Pratt, Howard Raiffa, and Robert Schlaifer
Page iv Second printing 1996 1995 Massachusetts Institute of - photo 2
Page iv
Second printing, 1996
1995 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.
This book was set in Times Roman by Asco Trade Typesetting Ltd., Hong Kong, and was printed and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Pratt, John W. (John Winsor), 1931
Introduction to statistical decision theory/John Pratt, Howard
Raiffa, and Robert Schlaifer.
p. cm.
Includes bibliographical references and index.
ISBN 0-262-16144-3
1. Statistical decision. I. Raiffa, Howard, 1924-. II. Schlaifer, Robert. III. Title.
QA279.4.P73 1994
519.'42dc20 94-7958
CIP
Page v
Dedicated to
Robert O. Schlaifer (1915-1994): An original, deep, creative, indefatigable,
persistent, versatile, demanding, sometimes irascible scholar, who always
was an inspiration to us both.
John Pratt and Howard Raiffa
Page vii
Contents
Preface
xv
1
Introduction
1
Picture 3
1.1 The Problem of Decision under Uncertainty
1
Picture 4
1.2 Decision Trees
3
Picture 5
1.3 The Problem of Analysis
6
2
An Informal Treatment of Foundations
11
Picture 6
2.1 Introduction
11
Picture 7
2.2 Canonical Probability
12
Picture 8
2.3 Basic Assumptions
14
Picture 9
2.4 Comparison of Simple Canonical Lotteries
19
Picture 10
2.5 Comparison of Simple "Real" Lotteries: An Introduction
24
Picture 11
2.6 Consistency Requirements for Evaluations of Events
26
Picture 12
2.7 Reduction of Acts to Reference Lotteries
32
Picture 13
2.8 Conditional Utility and Conditional Probability
36
Picture 14
Exercises
42
3
A Formal Treatment of Foundations
47
Picture 15
3.1 Introduction
47
Picture 16
3.2 The Canonical Basis
49
Picture 17
3.3 Lotteries and Prizes
51
Picture 18
3.4 Formal Notation and Definitions
54
Picture 19
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