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Chain Event Graphs: Chapman & Hall/CRC Computer Science and Data Analysis Series [Kietas viršelis]

(University of Warwick, United Kingdom), (University of Warwick, United Kingdom), (University of Warwick, United Kingdom)
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Chain Event Graphs: Chapman & Hall/CRC Computer Science and Data Analysis SeriesDidesnis paveikslėlis
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Raktažodžiai:
Written by some major contributors to the development of this class of graphical models, Chain Event Graphs introduces a viable and straightforward new tool for statistical inference, model selection and learning techniques. The book extends established technologies used in the study of discrete Bayesian Networks so that they apply in a much more general setting As the first book on Chain Event Graphs, this monograph is expected to become a landmark work on the use of event trees and coloured probability trees in statistics, and to lead to the increased use of such tree models to describe hypotheses about how events might unfold.

Features:











introduces a new and exciting discrete graphical model based on an event tree





focusses on illustrating inferential techniques, making its methodology accessible to a very broad audience and, most importantly, to practitioners





illustrated by a wide range of examples, encompassing important present and future applications





includes exercises to test comprehension and can easily be used as a course book





introduces relevant software packages

Rodrigo A. Collazo is a methodological and computational statistician based at the Naval Systems Analysis Centre (CASNAV) in Rio de Janeiro, Brazil. Christiane Görgen is a mathematical statistician at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany. Jim Q. Smith is a professor of statistics at the University of Warwick, UK. He has published widely in the field of statistics, AI, and decision analysis and has written two other books, most recently Bayesian Decision Analysis: Principles and Practice (Cambridge University Press 2010).

Recenzijos

"Statisticians Collazo, Görgen, and Smith provide a thorough introduction to the methodology of chain event graphs. The authors present background on discrete statistical modeling and the use of Bayesian inference. The chain event graph method is shown to be less restrictive than that of Bayesian networks, though it represents something of a generalization of that method. Beginning with an event tree, the chain event graph is a graphical representation that can represent a process of developing events. The authors present an array of examples to illustrate the concepts, and exercises are scattered throughout the text. Included with the book's purchase is access to software to create these models. Readers interested in this subject may also wish to consult the works of Judea Pearl, who developed Bayesian Networks and promoted the use of a probabilistic approach to the field of artificial intelligence (see, for example, Causality: Models, Reasoning, and Inference, CH, Mar'10, 47-3771)." ~CHOICE, R. L. Pour, emeritus, Emory and Henry College Summing Up: Recommended. Upper-division undergraduates through faculty and professionals. "Statisticians Collazo, Görgen, and Smith provide a thorough introduction to the methodology of chain event graphs. The authors present background on discrete statistical modeling and the use of Bayesian inference. The chain event graph method is shown to be less restrictive than that of Bayesian networks, though it represents something of a generalization of that method. Beginning with an event tree, the chain event graph is a graphical representation that can represent a process of developing events. The authors present an array of examples to illustrate the concepts, and exercises are scattered throughout the text. Included with the book's purchase is access to software to create these models. Readers interested in this subject may also wish to consult the works of Judea Pearl, who developed Bayesian Networks and promoted the use of a probabilistic approach to the field of artificial intelligence (see, for example, Causality: Models, Reasoning, and Inference, CH, Mar'10, 47-3771)." ~CHOICE, R. L. Pour, emeritus, Emory and Henry College Summing Up: Recommended. Upper-division undergraduates through faculty and professionals.

Preface xi
List of Figures
xiii
List of Tables
xvii
Symbols and abbreviations xix
1 Introduction
1(16)
1.1 Some motivation
1(4)
1.2 Why event trees?
5(7)
1.3 Using event trees to describe populations
12(2)
1.4 How we have arranged the material in this book
14(2)
1.5 Exercises
16(1)
2 Bayesian inference using graphs
17(28)
2.1 Inference on discrete statistical models
17(11)
2.1.1 Two common sampling mass functions
20(1)
2.1.2 Two prior-to-posterior analyses
20(4)
2.1.3 Poisson-Gamma and Multinomial--Dirichlet
24(2)
2.1.4 MAP model selection using Bayes Factors
26(2)
2.2 Statistical models and structural hypotheses
28(5)
2.2.1 An example of competing models
29(2)
2.2.2 The parametric statistical model
31(2)
2.3 Discrete Bayesian networks
33(10)
2.3.1 Factorisations of probability mass functions
33(3)
2.3.2 The d-separation theorem
36(1)
2.3.3 DAGs coding the same distributional assumptions
37(1)
2.3.4 Estimating probabilities in a BN
38(2)
2.3.5 Propagating probabilities in a BN
40(3)
2.4 Concluding remarks
43(1)
2.5 Exercises
44(1)
3 The Chain Event Graph
45(28)
3.1 Models represented by tree graphs
45(9)
3.1.1 Probability trees
46(4)
3.1.2 Staged trees
50(4)
3.2 The semantics of the Chain Event Graph
54(5)
3.3 Comparison of stratified CEGs with BNs
59(7)
3.4 Examples of CEG semantics
66(3)
3.4.1 The saturated CEG
66(1)
3.4.2 The simple CEG
67(1)
3.4.3 The square-free CEG
68(1)
3.5 Some related structures
69(2)
3.6 Exercises
71(2)
4 Reasoning with a CEG
73(34)
4.1 Encoding qualitative belief structures with CEGs
73(15)
4.1.1 Vertex- and edge-centred events
74(3)
4.1.2 Intrinsic events
77(2)
4.1.3 Conditioning in CEGs
79(2)
4.1.4 Vertex-random variables, cuts and independence
81(7)
4.2 CEG statistical models
88(18)
4.2.1 Parametrised subsets of the probability simplex
90(4)
4.2.2 The swap operator
94(6)
4.2.3 The resize operator
100(2)
4.2.4 The class of all statistically equivalent staged trees
102(4)
4.3 Exercises
106(1)
5 Estimation and propagation on a given CEG
107(30)
5.1 Estimating a given CEG
107(15)
5.1.1 A conjugate analysis
108(2)
5.1.2 How to specify a prior for a given CEG
110(3)
5.1.3 Example: Learning liver and kidney disorders
113(5)
5.1.4 When sampling is not random
118(4)
5.2 Propagating information on trees and CEGs
122(12)
5.2.1 Propagation when probabilities are known
123(6)
5.2.2 Example: Propagation for liver and kidney disorders
129(2)
5.2.3 Propagation when probabilities are estimated
131(2)
5.2.4 Some final comments
133(1)
5.3 Exercises
134(3)
6 Model selection for CEGs
137(28)
6.1 Calibrated priors over classes of CEGs
139(2)
6.2 Log-posterior Bayes Factor scores
141(2)
6.3 CEG greedy and dynamic programming search
143(11)
6.3.1 Greedy SCEG search using AHC
144(4)
6.3.2 SCEG exhaustive search using DP
148(6)
6.4 Technical advances for SCEG model selection
154(9)
6.4.1 DP and AHC using a block ordering
154(3)
6.4.2 A pairwise moment non-local prior
157(6)
6.5 Exercises
163(2)
7 How to model with a CEG: A real-world application
165(28)
7.1 Previous studies and domain knowledge
167(5)
7.2 Searching the CHDS dataset with a variable order
172(5)
7.3 Searching the CHDS dataset with a block ordering
177(6)
7.4 Searching the CHDS dataset without a variable ordering
183(3)
7.5 Issues associated with model selection
186(6)
7.5.1 Exhaustive CEG model search
186(1)
7.5.2 Searching the CHDS dataset using NLPs
187(1)
7.5.3 Setting a prior probability distribution
188(4)
7.6 Exercises
192(1)
8 Causal inference using CEGs
193(28)
8.1 Bayesian networks and causation
194(7)
8.1.1 Extending a BN to a causal BN
195(2)
8.1.2 Problems of describing causal hypotheses using a BN
197(4)
8.2 Defining a do-operation for CEGs
201(7)
8.2.1 Composite manipulations
203(2)
8.2.2 Example: student housing situation
205(3)
8.2.3 Some special manipulations of CEGs
208(1)
8.3 Causal CEGs
208(7)
8.3.1 When a CEG can legitimately be called causal
209(1)
8.3.2 Example: Manipulations of the CHDS
209(5)
8.3.3 Backdoor theorems
214(1)
8.4 Causal discovery algorithms for CEGs
215(3)
8.5 Exercises
218(3)
References 221(10)
Index 231
Rodrigo A. Collazo, Christiane Goergen, Jim Q. Smith