Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis Book

Fundamentals
Introduction     3
Expert Systems     3
Representation of Uncertainty     4
Normative Expert Systems     5
Rule-Based Systems     5
Causality     6
Uncertainty in Rule-Based Systems     7
Explaining Away     7
Bayesian Networks     8
Inference in Bayesian Networks     9
Construction of Bayesian Networks     10
An Example     10
Bayesian Decision Problems     13
When to Use Probabilistic Nets     14
Concluding Remarks     15
Networks     17
Graphs     18
Graphical Models     20
Variables     20
Vertices vs. Variables     21
Taxonomy of Vertices/Variables     22
Vertex Symbols     23
Summary of Notation     23
Evidence     23
Causality     24
Flow of Information in Causal Networks     25
Serial Connections     26
Diverging Connections     28
Converging Connections     29
The Importance of Correct Modeling of Causality     30
Two Equivalent IrrelevanceCriteria     31
d-Separation Criterion     32
Directed Global Markov Criterion     33
Summary     35
Probabilities     37
Basics     38
Events     38
Conditional Probability     38
Axioms     39
Probability Distributions for Variables     40
Rule of Total Probability     41
Graphical Representation     43
Probability Potentials     44
Normalization     44
Evidence Potentials     45
Potential Calculus     46
Barren Variables     49
Fundamental Rule and Bayes' Rule     50
Interpretation of Bayes' Rule     51
Bayes' Factor     53
Independence     54
Independence and DAGs     56
Chain Rule     58
Summary     60
Probabilistic Networks     63
Reasoning Under Uncertainty     64
Discrete Bayesian Networks     65
Conditional Linear Gaussian Bayesian Networks     70
Decision Making Under Uncertainty     74
Discrete Influence Diagrams     75
Conditional LQG Influence Diagrams      85
Limited Memory Influence Diagrams     89
Object-Oriented Probabilistic Networks     91
Chain Rule     96
Unfolded OOPNs     96
Instance Trees     97
Inheritance     98
Dynamic Models     98
Summary     102
Solving Probabilistic Networks     107
Probabilistic Inference     108
Inference in Discrete Bayesian Networks     108
Inference in CLG Bayesian Networks     121
Solving Decision Models     124
Solving Discrete Influence Diagrams     124
Solving CLQG Influence Diagrams     129
Relevance Reasoning     130
Solving LIMIDs     133
Solving OOPNs     136
Summary     137
Model Construction
Eliciting the Model     143
When to Use Probabilistic Networks     144
Characteristics of Probabilistic Networks     145
Some Criteria for Using Probabilistic Networks     145
Identifying the Variables of a Model     147
Well-Defined Variables     147
Types of Variables     150
Eliciting the Structure     152
A Basic Approach      152
Idioms     154
Model Verification     159
Eliciting the Numbers     163
Eliciting Subjective Conditional Probabilities     163
Eliciting Subjective Utilities     166
Specifying CPTs and UTs Through Expressions     166
Concluding Remarks     170
Summary     172
Modeling Techniques     177
Structure Related Techniques     177
Parent Divorcing     178
Temporal Transformation     182
Structural and Functional Uncertainty     184
Undirected Dependence Relations     188
Bidirectional Relations     191
Naive Bayes Model     193
Probability Distribution Related Techniques     196
Measurement Uncertainty     196
Expert Opinions     199
Node Absorption     201
Set Value by Intervention     202
Independence of Causal Influence     205
Mixture of Gaussian Distributions     210
Decision Related Techniques     212
Test Decisions     212
Missing Informational Links     216
Missing Observations     218
Hypothesis of Highest Probability      220
Constraints on Decisions     223
Summary     225
Data-Driven Modeling     227
The Task and Basic Assumptions     228
Structure Learning From Data     229
Basic Assumptions     230
Equivalent Models     231
Statistical Hypothesis Tests     232
Structure Constraints     235
PC Algorithm     235
PC* Algorithm     241
NPC Algorithm     241
Batch Parameter Learning From Data     246
Expectation-Maximization Algorithm     247
Penalized EM Algorithm     249
Sequential Parameter Learning     252
Summary     254
Model Analysis
Conflict Analysis     261
Evidence Driven Conflict Analysis     262
Conflict Measure     262
Tracing Conflicts     264
Conflict Resolution     265
Hypothesis Driven Conflict Analysis     267
Cost-of-Omission Measure     267
Evidence with Conflict Impact     267
Summary     269
Sensitivity Analysis     273
Evidence Sensitivity Analysis     274
Distance and Cost-of-Omission Measures      275
Identify Minimum and Maximum Beliefs     276
Impact of Evidence Subsets     277
Discrimination of Competing Hypotheses     278
What-If Analysis     279
Impact of Findings     280
Parameter Sensitivity Analysis     281
Sensitivity Function     282
Sensitivity Value     285
Admissible Deviation     286
Summary     287
Value of Information Analysis     291
VOI Analysis in Bayesian Networks     292
Entropy and Mutual Information     292
Hypothesis Driven Value of Information Analysis     293
VOI Analysis in Influence Diagrams     297
Summary     300
References     305
List of Symbols     311
Index     313