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.
Preface
Part I Foundations of Decision Modelling
1 Introduction 3
1.1 Getting Started 9
1.2 A simple framework for decision making 9
1.3 Bayes rule in court 20
1.4 Models with contingent decisions 24
1.5 Summary 26
1.6 Exercises 26
2 Explanations of processes and trees 28
2.1 Introduction 28
2.2 Using trees to explain how situations might develop 29
2.3 Decision trees 34
2.4 Some practical issues 41
2.5 Rollback decision trees 46
2.6 Normal form trees 54
2.7 Temporal coherence and episodic trees 58
2.8 Summary 59
2.9 Exercises 60
3 Utilities and rewards 62
3.1 Introduction 62
3.2 Utility and the value of a consequence 64
3.3 Properties and illustrations of rational choice 77
3.4 Eliciting a utility function with a dimensional attribute 82
3.5 The expected value of perfect information 84
3.6 Bayes decisions when reward distributions are continuous 86
3.7 Calculating expected losses 87
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