Probabilistic networks and expert systems: statistics for engineering and information science

Başlık:

Yazar:

Cowell, Robert G.

ISBN:

9780387987675

Yayım Bilgisi:

New York : Springer, c1999.

Fiziksel Tanım:

xii, 321 s. : şkl. ; 24 cm.

Series:

Statistics for engineering and information science

Series Title:

Statistics for engineering and information science

Contents:

Introduction -- Logic, uncertainty, and probability -- Building and using probabilistic networks -- Graph theory -- Markov properties on graphs -- Discrete networks -- Gaussian and mixed discrete-Gaussian networks -- Discrete multistage decision networks -- Learning about probabilities -- Checking models against data -- Structural learning.

Giriş - mantık, belirsizlik ve olasılık - Bina ve olasılıksal ağları - diyagram teorisi - grafiklerde Markov özellikleri - Ayrık ağları - Gaussian ve karışık ayrık Gauss ağları kullanarak - Kesikli çok aşamalı karar ağlar - öğrenme olasılıkları hakkında - Veri karşı kontrol modelleri - Yapısal öğrenme.

Konu Terimleri:

Uzman sistemler (Bilgisayar bilimi).

Expert systems (Computer science)

Olasılıklar.

Probabilities.

Added Author:

Cowell, Robert G.

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Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0017542	QA76.76.E95P755 1999	Searching... Unknown

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Özet

WINNER OF THE 2001 DEGROOT PRIZE!

Probabilistic expert systems are graphical networks that support the modelling of uncertainty and decisions in large complex domains, while retaining ease of calculation. Building on original research by the authors over a number of years, this book gives a thorough and rigorous mathematical treatment of the underlying ideas, structures, and algorithms, emphasizing those cases in which exact answers are obtainable. It covers both the updating of probabilistic uncertainty in the light of new evidence, and statistical inference, about unknown probabilities or unknown model structure, in the light of new data. The careful attention to detail will make this work an important reference source for all those involved in the theory and applications of probabilistic expert systems.

This book was awarded the first DeGroot Prize by the International Society for Bayesian Analysis for a book making an important, timely, thorough, and notably original contribution to the statistics literature.

Author Notes

Robert G. Cowell is Research Fellow and Computer Manager in the Department of Actuarial Science and Statistics of City University, London.
A. Philip Dawid is Professor of Statistics at University College London.
Steffen L. Lauritzen is Professor of Mathematics and Statistics at the University of Aalborg.
David J. Spiegelhalter is a Senior Scientist at the MRC Biostatistics Unit in the Cambridge University Institute of Public Health.

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

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