Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis (eBook)

Preface 7
Contents 12
Fundamentals 17
1 Introduction 18
1.1 Expert Systems 18
1.2 Rule-Based Systems 20
1.3 Bayesian Networks 23
1.4 Bayesian Decision Problems 28
1.5 When to Use Probabilistic Nets 29
1.6 Concluding Remarks 30
2 Networks 31
2.1 Graphs 32
2.2 Graphical Models 34
2.3 Evidence 37
2.4 Causality 38
2.5 Flow of Information in Causal Networks 39
2.6 Two Equivalent Irrelevance Criteria 45
2.7 Summary 49
Exercises 50
3 Probabilities 51
3.1 Basics 52
3.2 Probability Distributions for Variables 54
3.3 Probability Potentials 58
3.4 Fundamental Rule and Bayes’ Rule 64
3.5 Bayes’ Factor 67
3.6 Independence 68
3.7 Chain Rule 72
3.8 Summary 74
Exercises 75
4 Probabilistic Networks 77
4.1 Reasoning Under Uncertainty 78
4.2 Decision Making Under Uncertainty 88
4.3 Object-Oriented Probabilistic Networks 105
4.4 Dynamic Models 112
4.5 Summary 116
Exercises 117
5 Solving Probabilistic Networks 121
5.1 Probabilistic Inference 122
5.2 Solving Decision Models 138
5.3 Solving OOPNs 150
5.4 Summary 151
Exercises 151
Model Construction 154
6 Eliciting the Model 155
6.1 When to Use Probabilistic Networks 156
6.2 Identifying the Variables of a Model 159
6.3 Eliciting the Structure 164
6.4 Model Verification 171
6.5 Eliciting the Numbers 175
6.6 Concluding Remarks 182
6.7 Summary 184
Exercises 187
7 Modeling Techniques 189
7.1 Structure Related Techniques 189
7.2 Probability Distribution Related Techniques 208
7.3 Decision Related Techniques 224
7.4 Summary 237
Exercises 237
8 Data-Driven Modeling 239
8.1 The Task and Basic Assumptions 240
8.2 Structure Learning From Data 241
8.3 Batch Parameter Learning From Data 258
8.4 Sequential Parameter Learning 264
8.5 Summary 266
Exercises 267
Model Analysis 270
9 Conflict Analysis 271
9.1 Evidence Driven Conflict Analysis 272
9.2 Hypothesis Driven Conflict Analysis 277
9.3 Summary 279
Exercises 279
10 Sensitivity Analysis 282
10.1 Evidence Sensitivity Analysis 283
10.2 Parameter Sensitivity Analysis 290
10.3 Summary 296
Exercises 297
11 Value of Information Analysis 300
11.1 VOI Analysis in Bayesian Networks 301
11.2 VOI Analysis in Influence Diagrams 306
11.3 Summary 309
Exercises 310
References 313
List of Symbols 318
Index 320