Preface ...................................................... viii
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
3.8 Bayes decisions under conflict ......................... 91
3.9 Summary ................................................ 98
3.10 Exercises .............................................. 99
4 Subjective probability and its elicitation ................. 103
4.1 Defining subjective probabilities ..................... 103
4.2 On formal definitions of subjective probabilities ..... 108
4.3 Improving the assessment of prior information ......... 112
4.4 Calibration and successful probability predictions .... 118
4.5 Scoring forecasters ................................... 123
4.6 Summary ............................................... 127
4.7 Exercises ............................................. 128
5 Вayesian inference for decision analysis ................... 131
5.1 Introduction .......................................... 131
5.2 The basics of Bayesian inference ...................... 133
5.3 Prior to posterior analyses ........................... 136
5.4 Distributions which are closed under sampling ......... 139
5.5 Posterior densities for absolutely continuous
parameters ............................................ 140
5.6 Some standard inferences using conjugate families ..... 145
5.7 Non-conjugate inference ............................... 151
5.8 Discrete mixtures and model selection ................. 154
5.9 How a decision analysis can use Bayesian inferences ... 158
5.10 Summary ............................................... 162
5.11 Exercises ............................................. 162
Part II Multidimensional Decision Modelling
6 Multiattribute utility theory .............................. 169
6.1 Introduction .......................................... 169
6.2 Utility independence .................................. 171
6.3 Some general characterisation results ................. 177
6.4 Eliciting a utility function .......................... 178
6.5 Value independent attributes .......................... 180
6.6 Decision conferencing and utility elicitation ......... 187
6.7 Real-time support within decision processes ........... 193
6.8 Summary ............................................... 196
6.9 Exercises ............................................. 196
7 Bayesian networks .......................................... 199
7.1 Introduction .......................................... 199
7.2 Relevance, informativeness and independence ........... 200
7.3 Bayesian networks and DAGs ............................ 204
7.4 Eliciting a Bayesian network: a protocol .............. 217
7.5 Efficient storage on Bayesian networks ................ 224
7.6 Junction trees and probability propagation ............ 229
7.7 Bayesian networks and other graphs .................... 239
7.8 Summary ............................................... 243
7.9 Exercises ............................................. 243
8 Graphs, decisions and causality ............................ 248
8.1 Influence diagrams .................................... 248
8.2 Controlled causation .................................. 261
8.3 DAGs and causality .................................... 265
8.4 Time series models .................................... 276
8.5 Summary ............................................... 279
8.6 Exercises ............................................. 280
9 Multidimensional learning .................................. 282
9.1 Introduction .......................................... 282
9.2 Separation, orthogonality and independence ............ 286
9.3 Estimating probabilities on trees ..................... 292
9.4 Estimating probabilities in Bayesian networks ......... 298
9.5 Technical issues about structured learning ............ 302
9.6 Robustness of inference given copious data ............ 306
9.7 Summary ............................................... 313
9.8 Exercises ............................................. 313
10 Conclusions ................................................ 318
10.1 A summary of what has been demonstrated above ......... 318
10.2 Other types of decision analyses ...................... 319
References ................................................. 322
Index ......................................................... 335
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