Graphical Models (Google eBook)

Front Cover
Oxford University Press, May 2, 1996 - 308 pages
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The idea of modelling systems using graph theory has its origin in several scientific areas: in statistical physics (the study of large particle systems), in genetics (studying inheritable properties of natural species), and in interactions in contingency tables. The use of graphical models in statistics has increased considerably over recent years and the theory has been greatly developed and extended. This book provides the first comprehensive and authoritative account of the theory of graphical models and is written by a leading expert in the field. It contains the fundamental graph theory required and a thorough study of Markov properties associated with various type of graphs. The statistical theory of log-linear and graphical models for contingency tables, covariance selection models, and graphical models with mixed discrete-continous variables in developed detail. Special topics, such as the application of graphical models to probabilistic expert systems, are described briefly, and appendices give details of the multivarate normal distribution and of the theory of regular exponential families. The author has recently been awarded the RSS Guy Medal in Silver 1996 for his innovative contributions to statistical theory and practice, and especially for his work on graphical models.
  

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Contents

Introduction
1
12 Outline of book
2
Graphs and hypergraphs
4
212 Decompositions of marked graphs
7
213 Simplicial subsets and perfect sequences
13
214 Subgraphs of decomposable graphs
19
22 Hypergraphs
21
222 Graphs and hypergraphs
22
62 Graphical interaction models
173
622 Maximum likelihood estimation
175
63 Decomposable models
187
632 Maximum likelihood estimation
188
633 Exact tests in decomposable models
191
64 Hierarchical interaction models
199
642 Generators and canonical statistics
201
643 Maximum likelihood estimation
205

223 Junction trees and forests
24
23 Notes
26
Conditional independence and Markov properties
28
32 Markov properties
32
322 Markov properties on directed acyclic graphs
46
323 Markov properties on chain graphs
53
33 Notes
60
Contingency tables
62
422 Saturated models
70
423 Logaffine and loglinear models
71
43 Hierarchical models
81
431 Estimation in hierarchical logafrine models
82
432 Test in hierarchical models
85
433 Interaction graphs and graphical models
88
44 Decomposable models
90
442 Maximum likelihood estimation
91
443 Exact tests in decomposable models
98
444 Asymptotic tests in decomposable models
105
45 Recursive models
106
451 Recursive graphical models
107
452 Recursive hierarchical models
112
46 Blockrecursive models
113
461 Chain graph models
114
462 Blockrecursive hierarchical models
118
463 Decomposable blockrecursive models
119
Multivariate normal models
123
512 The saturated model
124
513 Conditional independence
129
514 Interaction
131
521 Maximum likelihood estimation
132
522 Deviance tests
142
53 Decomposable models
144
532 Maximum likelihood estimation
145
533 Exact tests in decomposable models
149
54 Notes
153
542 Lattice models
156
Models for mixed data
158
612 The saturated models
168
644 Mixed hierarchical model subspaces
213
65 Chain graph models
216
651 CG regressions
217
652 Estimation in chain graph models
218
66 Notes
219
662 Bibliographical notes
220
Further topics
221
711 Specification of the joint distribution
223
712 Local computation algorithm
226
713 Extensions
228
72 Model selection
229
73 Modelling complexity
230
731 Markov chain Monte Carlo methods
231
732 Applications
232
74 Missingdata problems
233
742 Hierarchical loglinear models
234
743 Recursive models
235
Various prerequisites
237
A2 KullbackLeibler divergence
238
A3 Mobius inversion
239
A 5 Sufficiency
241
Linear algebra and random vectors
243
B2 Factor subspaces and interactions
246
B3 Random vectors
250
The multivariate normal distribution
254
C2 The Wishart distribution
258
C3 Other derived distributions
262
C32 Wilkss distribution
263
C33 Test for identical covariances
264
Exponential models
266
D12 Analytic properties
267
D13 Maximum likelihood estimation
268
D15 Iterative computational methods
269
D2 Curved exponential models
272
D22 The singular case
276
Bibliography
278
Index
295
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