Preface |
|
v | |
|
|
1 | (4) |
|
1.1 What is this book about? |
|
|
1 | (1) |
|
1.2 What is in this book? |
|
|
2 | (1) |
|
1.3 What is not in this book? |
|
|
3 | (1) |
|
1.4 How should this be book be used? |
|
|
4 | (1) |
|
2 Logic, Uncertainty, and Probability |
|
|
5 | (20) |
|
2.1 What is an expert system? |
|
|
5 | (1) |
|
2.2 Diagnostic decision trees |
|
|
6 | (1) |
|
|
7 | (1) |
|
2.4 Coping with uncertainty |
|
|
8 | (2) |
|
2.5 The naive probabilistic approach |
|
|
10 | (1) |
|
2.6 Interpretations of probability |
|
|
11 | (2) |
|
|
13 | (1) |
|
|
14 | (3) |
|
2.9 Bayesian reasoning in expert systems |
|
|
17 | (4) |
|
2.10 A broader context for probabilistic expert systems |
|
|
21 | (4) |
|
3 Building and Using Probabilistic Networks |
|
|
25 | (18) |
|
3.1 Graphical modelling of the domain |
|
|
26 | (5) |
|
3.1.1 Qualitative modelling |
|
|
27 | (1) |
|
3.1.2 Probabilistic modelling |
|
|
28 | (1) |
|
3.1.3 Quantitative modelling |
|
|
29 | (1) |
|
3.1.4 Further background to the elicitation process |
|
|
29 | (2) |
|
3.2 From specification to inference engine |
|
|
31 | (3) |
|
|
31 | (2) |
|
3.2.2 From moral graph to junction tree |
|
|
33 | (1) |
|
3.3 The inference process |
|
|
34 | (3) |
|
3.3.1 The clique-marginal representation |
|
|
36 | (1) |
|
3.3.2 Incorporation of evidence |
|
|
36 | (1) |
|
3.4 Bayesian networks as expert systems |
|
|
37 | (3) |
|
3.5 Background references and further reading |
|
|
40 | (3) |
|
3.5.1 Structuring the graph |
|
|
40 | (1) |
|
3.5.2 Specifying the probability distribution |
|
|
40 | (3) |
|
|
43 | (20) |
|
|
43 | (6) |
|
4.2 Chordal and decomposable graphs |
|
|
49 | (3) |
|
|
52 | (3) |
|
4.4 From chain graph to junction tree |
|
|
55 | (6) |
|
|
57 | (2) |
|
|
59 | (2) |
|
4.5 Background references and further reading |
|
|
61 | (2) |
|
5 Markov Properties on Graphs |
|
|
63 | (20) |
|
5.1 Conditional independence |
|
|
63 | (3) |
|
5.2 Markov fields over undirected graphs |
|
|
66 | (4) |
|
5.3 Markov properties on directed acyclic graphs |
|
|
70 | (5) |
|
5.4 Markov properties on chain graphs |
|
|
75 | (4) |
|
5.5 Current research directions |
|
|
79 | (1) |
|
|
79 | (1) |
|
5.5.2 Other graphical representations |
|
|
80 | (1) |
|
5.6 Background references and further reading |
|
|
80 | (3) |
|
|
83 | (42) |
|
6.1 An illustration of local computation |
|
|
84 | (1) |
|
|
85 | (2) |
|
|
86 | (1) |
|
6.3 Local computation on the junction tree |
|
|
87 | (8) |
|
6.3.1 Graphical specification |
|
|
87 | (1) |
|
6.3.2 Numerical specification and initialization |
|
|
87 | (1) |
|
|
88 | (1) |
|
6.3.4 Flow of information between adjacent cliques |
|
|
88 | (1) |
|
|
89 | (1) |
|
6.3.6 Reaching equilibrium |
|
|
90 | (2) |
|
6.3.7 Scheduling of flows |
|
|
92 | (1) |
|
6.3.8 Two-phase propagation |
|
|
92 | (1) |
|
6.3.9 Entering and propagating evidence |
|
|
93 | (2) |
|
6.3.10 A propagation example |
|
|
95 | (1) |
|
6.4 Generalized marginalization operations |
|
|
95 | (14) |
|
|
97 | (2) |
|
6.4.2 Degeneracy of the most probable configuration |
|
|
99 | (1) |
|
|
99 | (2) |
|
6.4.4 Finding the M most probable configurations |
|
|
101 | (2) |
|
6.4.5 Sampling without replacement |
|
|
103 | (1) |
|
|
104 | (2) |
|
6.4.7 Moments of functions |
|
|
106 | (3) |
|
|
109 | (11) |
|
|
109 | (1) |
|
6.5.2 Graphical specification |
|
|
109 | (1) |
|
6.5.3 Numerical specification |
|
|
109 | (3) |
|
|
112 | (2) |
|
6.5.5 Propagation without evidence |
|
|
114 | (1) |
|
6.5.6 Propagation with evidence |
|
|
114 | (5) |
|
|
119 | (1) |
|
6.6 Dealing with large cliques |
|
|
120 | (3) |
|
6.6.1 Truncating small numbers |
|
|
121 | (1) |
|
|
122 | (1) |
|
6.7 Current research directions and further reading |
|
|
123 | (2) |
|
7 Gaussian and Mixed Discrete-Gaussian Networks |
|
|
125 | (30) |
|
|
126 | (1) |
|
7.2 Basic operations on CG potentials |
|
|
127 | (4) |
|
7.3 Marked graphs and their junction trees |
|
|
131 | (4) |
|
7.3.1 Decomposition of marked graphs |
|
|
131 | (2) |
|
7.3.2 Junction trees with strong roots |
|
|
133 | (2) |
|
|
135 | (2) |
|
7.5 Operating in the junction tree |
|
|
137 | (6) |
|
7.5.1 Initializing the junction tree |
|
|
138 | (1) |
|
|
138 | (1) |
|
|
139 | (1) |
|
7.5.4 Flow of information between adjacent cliques |
|
|
139 | (2) |
|
7.5.5 Two-phase propagation |
|
|
141 | (2) |
|
7.6 A simple Gaussian example |
|
|
143 | (1) |
|
|
144 | (6) |
|
7.7.1 Structural specification |
|
|
145 | (1) |
|
7.7.2 Numerical specification |
|
|
146 | (1) |
|
7.7.3 Strong triangulation |
|
|
147 | (1) |
|
7.7.4 Forming the junction tree |
|
|
148 | (1) |
|
7.7.5 Initializing the junction tree |
|
|
148 | (1) |
|
|
149 | (1) |
|
7.8 Complexity considerations |
|
|
150 | (1) |
|
7.9 Numerical instability problems |
|
|
151 | (1) |
|
7.9.1 Exact marginal densities |
|
|
152 | (1) |
|
7.10 Current research directions |
|
|
152 | (1) |
|
7.11 Background references and further reading |
|
|
153 | (2) |
|
8 Discrete Multistage Decision Networks |
|
|
155 | (34) |
|
8.1 The nature of multistage decision problems |
|
|
156 | (1) |
|
8.2 Solving the decision problem |
|
|
157 | (2) |
|
|
159 | (4) |
|
8.4 Network specification and solution |
|
|
163 | (9) |
|
8.4.1 Structural and numerical specification |
|
|
163 | (2) |
|
8.4.2 Causal consistency lemma |
|
|
165 | (1) |
|
8.4.3 Making the elimination tree |
|
|
166 | (1) |
|
8.4.4 Initializing the elimination tree |
|
|
167 | (1) |
|
8.4.5 Message passing in the elimination tree |
|
|
168 | (1) |
|
8.4.6 Proof of elimination tree solution |
|
|
169 | (3) |
|
8.5 Example: OIL WILDCATTER |
|
|
172 | (5) |
|
|
172 | (3) |
|
8.5.2 Making the elimination tree |
|
|
175 | (1) |
|
8.5.3 Initializing the elimination tree |
|
|
176 | (1) |
|
8.5.4 Collecting evidence |
|
|
177 | (1) |
|
|
177 | (6) |
|
|
183 | (1) |
|
|
184 | (3) |
|
8.9 Background references and further reading |
|
|
187 | (2) |
|
9 Learning About Probabilities |
|
|
189 | (36) |
|
9.1 Statistical modelling and parameter learning |
|
|
189 | (1) |
|
9.2 Parametrizing a directed Markov model |
|
|
190 | (2) |
|
9.3 Maximum likelihood with complete data |
|
|
192 | (1) |
|
9.4 Bayesian updating with complete data |
|
|
193 | (7) |
|
9.4.1 Priors for DAG models |
|
|
193 | (4) |
|
9.4.2 Specifying priors: An example |
|
|
197 | (2) |
|
9.4.3 Updating priors with complete data: An example |
|
|
199 | (1) |
|
|
200 | (2) |
|
9.5.1 Sequential and batch methods |
|
|
201 | (1) |
|
9.6 Maximum likelihood with incomplete data |
|
|
202 | (2) |
|
|
202 | (2) |
|
9.6.2 Penalized EM algorithm |
|
|
204 | (1) |
|
9.7 Bayesian updating with incomplete data |
|
|
204 | (12) |
|
|
206 | (1) |
|
9.7.2 Retaining global independence |
|
|
207 | (2) |
|
9.7.3 Retaining local independence |
|
|
209 | (2) |
|
9.7.4 Reducing the mixtures |
|
|
211 | (2) |
|
9.7.5 Simulation results: full mixture reduction |
|
|
213 | (1) |
|
9.7.6 Simulation results: partial mixture reduction |
|
|
214 | (2) |
|
9.8 Using Gibbs sampling for learning |
|
|
216 | (5) |
|
9.9 Hyper Markov laws for undirected models |
|
|
221 | (1) |
|
9.10 Current research directions and further reading |
|
|
222 | (3) |
|
10 Checking Models Against Data |
|
|
225 | (18) |
|
|
226 | (3) |
|
|
227 | (2) |
|
10.2 Parent-child monitors |
|
|
229 | (5) |
|
|
232 | (1) |
|
|
233 | (1) |
|
|
234 | (1) |
|
|
235 | (3) |
|
|
236 | (2) |
|
10.5 Simulation experiments |
|
|
238 | (3) |
|
|
241 | (2) |
|
|
243 | (22) |
|
11.1 Purposes of modelling |
|
|
244 | (1) |
|
11.2 Inference about models |
|
|
244 | (1) |
|
11.3 Criteria for comparing models |
|
|
245 | (6) |
|
11.3.1 Maximized likelihood |
|
|
246 | (1) |
|
11.3.2 Predictive assessment |
|
|
247 | (1) |
|
11.3.3 Marginal likelihood |
|
|
248 | (1) |
|
11.3.4 Model probabilities |
|
|
249 | (1) |
|
11.3.5 Model selection and model averaging |
|
|
250 | (1) |
|
11.4 Graphical models and conditional independence |
|
|
251 | (2) |
|
|
253 | (3) |
|
11.5.1 Models containing only observed quantities |
|
|
253 | (1) |
|
11.5.2 Models with latent or hidden variables |
|
|
254 | (1) |
|
|
255 | (1) |
|
11.6 Handling multiple models |
|
|
256 | (9) |
|
|
256 | (2) |
|
11.6.2 Probability specification |
|
|
258 | (2) |
|
11.6.3 Prior information on parameters |
|
|
260 | (1) |
|
11.6.4 Variable precision |
|
|
261 | (4) |
|
|
265 | (2) |
|
A Conjugate Analysis for Discrete Data |
|
|
267 | (4) |
|
|
267 | (2) |
|
|
269 | (2) |
|
|
271 | (6) |
|
|
271 | (2) |
|
B.2 Sampling from the moral graph |
|
|
273 | (1) |
|
B.3 General probability densities |
|
|
274 | (1) |
|
|
275 | (2) |
|
C Information and Software on the World Wide Web |
|
|
277 | (4) |
|
C.1 Information about probabilistic networks |
|
|
277 | (2) |
|
C.2 Software for probabilistic networks |
|
|
279 | (1) |
|
C.3 Markov chain Monte Carlo methods |
|
|
280 | (1) |
Bibliography |
|
281 | (26) |
Author Index |
|
307 | (6) |
Subject Index |
|
313 | |