Bayesian Decision Analysis: Principles and Practice

by Jim Q. Smith

• ISBN13: 9780521764544
• ISBN10: 0521764548
• Format: Hardcover
• Copyright: 2010-11-15
• Publisher: Cambridge University Press

Summary

Bayesian decision analysis supports principled decision making in complex domains. This textbook takes the reader from a formal analysis of simple decision problems to a careful analysis of the sometimes very complex and data rich structures confronted by practitioners. The book contains basic material on subjective probability theory and multi-attribute utility theory, event and decision trees, Bayesian networks, influence diagrams and causal Bayesian networks. The author demonstrates when and how the theory can be successfully applied to a given decision problem, how data can be sampled and expert judgements elicited to support this analysis, and when and how an effective Bayesian decision analysis can be implemented. Evolving from a third-year undergraduate course taught by the author over many years, all of the material in this book will be accessible to a student who has completed introductory courses in probability and mathematical statistics.

Author Biography

Jim Q. Smith is a Professor of Statistics at the University of Warwick.

Table of Contents

Preface	p. viii
Foundations of Decision Modelling
Introduction	p. 3
Getting started	p. 9
A simple framework for decision making	p. 9
Bayes rule in court	p. 20
Models with contingent decisions	p. 24
Summary	p. 26
Exercises	p. 26
Explanations of processes and trees	p. 28
Introduction	p. 28
Using trees to explain how situations might develop	p. 29
Decision trees	p. 34
Some practical issues*	p. 41
Rollback decision trees	p. 46
Normal form trees	p. 54
Temporal coherence and episodic trees*	p. 58
Summary	p. 59
Exercises	p. 60
Utilities and rewards	p. 62
Introduction	p. 62
Utility and the value of a consequence	p. 64
Properties and illustrations of rational choice	p. 77
Eliciting a utility function with a dimensional attribute	p. 82
The expected value of perfect information	p. 84
Bayes decisions when reward distributions are continuous	p. 86
Calculating expected losses	p. 87
Bayes decisions under conflict*	p. 91
Summary	p. 98
Exercises	p. 99
Subjective probability and its elicitation	p. 103
Defining subjective probabilities	p. 103
On formal definitions of subjective probabilities	p. 108
Improving the assessment of prior information	p. 112
Calibration and successful probability predictions	p. 118
Scoring forecasters	p. 123
Summary	p. 127
Exercises	p. 128
Bayesian inference for decision analysis	p. 131
Introduction	p. 131
The basics of Bayesian inference	p. 133
Prior to posterior analyses	p. 136
Distributions which are closed under sampling	p. 139
Posterior densities for absolutely continuous parameters	p. 140
Some standard inferences using conjugate families	p. 145
Non-conjugate inference*	p. 151
Discrete mixtures and model selection	p. 154
How a decision analysis can use Bayesian inferences	p. 158
Summary	p. 162
Exercises	p. 162
Multidimensional Decision Modelling
Multiattribute utility theory	p. 169
Introduction	p. 169
Utility independence	p. 171
Some general characterisation results	p. 177
Eliciting a utility function	p. 178
Value independent attributes	p. 180
Decision conferencing and utility elicitation	p. 187
Real-time support within decision processes	p. 193
Summary	p. 196
Exercises	p. 196
Bayesian networks	p. 199
Introduction	p. 199
Relevance, informativeness and independence	p. 200
Bayesian networks and DAGs	p. 204
Eliciting a Bayesian network: a protocol	p. 217
Efficient storage on Bayesian networks	p. 224
Junction trees and probability propagation	p. 229
Bayesian networks and other graphs	p. 239
Summary	p. 243
Exercises	p. 243
Graphs, decisions and causality	p. 248
Influence diagrams	p. 248
Controlled causation	p. 261
DAGs and causality	p. 265
Time series models*	p. 276
Summary	p. 279
Exercises	p. 280
Multidimensional learning	p. 282
Introduction	p. 282
Separation, orthogonality and independence	p. 286
Estimating probabilities on trees	p. 292
Estimating probabilities in Bayesian networks	p. 298
Technical issues about structured learning*	p. 302
Robustness of inference given copious data*	p. 306
Summary	p. 313
Exercises	p. 313
Conclusions	p. 318
A summary of what has been demonstrated above	p. 318
Other types of decision analyses	p. 318
References	p. 322
Index	p. 335
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