Preface | p. v |
Introduction | p. 1 |
What is this book about? | p. 1 |
What is in this book? | p. 2 |
What is not in this book? | p. 3 |
How should this be book be used? | p. 4 |
Logic, Uncertainty, and Probability | p. 5 |
What is an expert system? | p. 5 |
Diagnostic decision trees | p. 6 |
Production systems | p. 7 |
Coping with uncertainty | p. 8 |
The naive probabilistic approach | p. 10 |
Interpretations of probability | p. 11 |
Axioms | p. 13 |
Bayes' theorem | p. 14 |
Bayesian reasoning in expert systems | p. 17 |
A broader context for probabilistic expert systems | p. 21 |
Building and Using Probabilistic Networks | p. 25 |
Graphical modelling of the domain | p. 26 |
Qualitative modelling | p. 27 |
Probabilistic modelling | p. 28 |
Quantitative modelling | p. 29 |
Further background to the elicitation process | p. 29 |
From specification to inference engine | p. 31 |
Moralization | p. 31 |
From moral graph to junction tree | p. 33 |
The inference process | p. 34 |
The clique-marginal representation | p. 36 |
Incorporation of evidence | p. 36 |
Bayesian networks as expert systems | p. 37 |
Background references and further reading | p. 40 |
Structuring the graph | p. 40 |
Specifying the probability distribution | p. 40 |
Graph Theory | p. 43 |
Basic concepts | p. 43 |
Chordal and decomposable graphs | p. 49 |
Junction trees | p. 52 |
From chain graph to junction tree | p. 55 |
Triangulation | p. 57 |
Elimination tree | p. 59 |
Background references and further reading | p. 61 |
Markov Properties on Graphs | p. 63 |
Conditional independence | p. 63 |
Markov fields over undirected graphs | p. 66 |
Markov properties on directed acyclic graphs | p. 70 |
Markov properties on chain graphs | p. 75 |
Current research directions | p. 79 |
Markov equivalence | p. 79 |
Other graphical representations | p. 80 |
Background references and further reading | p. 80 |
Discrete Networks | p. 83 |
An illustration of local computation | p. 84 |
Definitions | p. 85 |
Basic operations | p. 86 |
Local computation on the junction tree | p. 87 |
Graphical specification | p. 87 |
Numerical specification and initialization | p. 87 |
Charges | p. 88 |
Flow of information between adjacent cliques | p. 88 |
Active flows | p. 89 |
Reaching equilibrium | p. 90 |
Scheduling of flows | p. 92 |
Two-phase propagation | p. 92 |
Entering and propagating evidence | p. 93 |
A propagation example | p. 95 |
Generalized marginalization operations | p. 95 |
Maximization | p. 97 |
Degeneracy of the most probable configuration | p. 99 |
Simulation | p. 99 |
Finding the M most probable configurations | p. 101 |
Sampling without replacement | p. 103 |
Fast retraction | p. 104 |
Moments of functions | p. 106 |
Example: Ch-Asia | p. 109 |
Description | p. 109 |
Graphical specification | p. 109 |
Numerical specification | p. 109 |
Initialization | p. 112 |
Propagation without evidence | p. 114 |
Propagation with evidence | p. 114 |
Max-propagation | p. 119 |
Dealing with large cliques | p. 120 |
Truncating small numbers | p. 121 |
Splitting cliques | p. 122 |
Current research directions and further reading | p. 123 |
Gaussian and Mixed Discrete-Gaussian Networks | p. 125 |
CG distributions | p. 126 |
Basic operations on CG potentials | p. 127 |
Marked graphs and their junction trees | p. 131 |
Decomposition of marked graphs | p. 131 |
Junction trees with strong roots | p. 133 |
Model specification | p. 135 |
Operating in the junction tree | p. 137 |
Initializing the junction tree | p. 138 |
Charges | p. 138 |
Entering evidence | p. 139 |
Flow of information between adjacent cliques | p. 139 |
Two-phase propagation | p. 141 |
A simple Gaussian example | p. 143 |
Example: Waste | p. 144 |
Structural specification | p. 145 |
Numerical specification | p. 146 |
Strong triangulation | p. 147 |
Forming the junction tree | p. 148 |
Initializing the junction tree | p. 148 |
Entering evidence | p. 149 |
Complexity considerations | p. 150 |
Numerical instability problems | p. 151 |
Exact marginal densities | p. 152 |
Current research directions | p. 152 |
Background references and further reading | p. 153 |
Discrete Multistage Decision Networks | p. 155 |
The nature of multistage decision problems | p. 156 |
Solving the decision problem | p. 157 |
Decision potentials | p. 159 |
Network specification and solution | p. 163 |
Structural and numerical specification | p. 163 |
Causal consistency lemma | p. 165 |
Making the elimination tree | p. 166 |
Initializing the elimination tree | p. 167 |
Message passing in the elimination tree | p. 168 |
Proof of elimination tree solution | p. 169 |
Example: Oil Wildcatter | p. 172 |
Specification | p. 172 |
Making the elimination tree | p. 175 |
Initializing the elimination tree | p. 176 |
Collecting evidence | p. 177 |
Example: Dec-Asia | p. 177 |
Triangulation issues | p. 183 |
Asymmetric problems | p. 184 |
Background references and further reading | p. 187 |
Learning About Probabilities | p. 189 |
Statistical modelling and parameter learning | p. 189 |
Parametrizing a directed Markov model | p. 190 |
Maximum likelihood with complete data | p. 192 |
Bayesian updating with complete data | p. 193 |
Priors for DAG models | p. 193 |
Specifying priors: An example | p. 197 |
Updating priors with complete data: An example | p. 199 |
Incomplete data | p. 200 |
Sequential and batch methods | p. 201 |
Maximum likelihood with incomplete data | p. 202 |
The EM algorithm | p. 202 |
Penalized EM algorithm | p. 204 |
Bayesian updating with incomplete data | p. 204 |
Exact theory | p. 206 |
Retaining global independence | p. 207 |
Retaining local independence | p. 209 |
Reducing the mixtures | p. 211 |
Simulation results: full mixture reduction | p. 213 |
Simulation results: partial mixture reduction | p. 214 |
Using Gibbs sampling for learning | p. 216 |
Hyper Markov laws for undirected models | p. 221 |
Current research directions and further reading | p. 222 |
Checking Models Against Data | p. 225 |
Scoring rules | p. 226 |
Standardization | p. 227 |
Parent-child monitors | p. 229 |
Batch monitors | p. 232 |
Missing data | p. 233 |
Node monitors | p. 234 |
Global monitors | p. 235 |
Example: Child | p. 236 |
Simulation experiments | p. 238 |
Further reading | p. 241 |
Structural Learning | p. 243 |
Purposes of modelling | p. 244 |
Inference about models | p. 244 |
Criteria for comparing models | p. 245 |
Maximized likelihood | p. 246 |
Predictive assessment | p. 247 |
Marginal likelihood | p. 248 |
Model probabilities | p. 249 |
Model selection and model averaging | p. 250 |
Graphical models and conditional independence | p. 251 |
Classes of models | p. 253 |
Models containing only observed quantities | p. 253 |
Models with latent or hidden variables | p. 254 |
Missing data | p. 255 |
Handling multiple models | p. 256 |
Search strategies | p. 256 |
Probability specification | p. 258 |
Prior information on parameters | p. 260 |
Variable precision | p. 261 |
Epilogue | p. 265 |
Conjugate Analysis for Discrete Data | p. 267 |
Bernoulli process | p. 267 |
Multinomial process | p. 269 |
Gibbs Sampling | p. 271 |
Gibbs sampling | p. 271 |
Sampling from the moral graph | p. 273 |
General probability densities | p. 274 |
Further reading | p. 275 |
Information and Software on the World Wide Web | p. 277 |
Information about probabilistic networks | p. 277 |
Software for probabilistic networks | p. 279 |
Markov chain Monte Carlo methods | p. 280 |
Bibliography | p. 281 |
Author Index | p. 307 |
Subject Index | p. 313 |
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