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Chain event graphs

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A chain event graph (CEG) is an important generalization of the Bayesian Network (BN). BNs have been extremely useful for modeling discrete processes. However, they are not appropriate for all applications. Over the past six years or so, teams of researchers led by Jim Smith have established a strong theoretical underpinning for CEGs. This book systematically and transparently presents the scope and promise of this  Read more...

Abstract: A chain event graph (CEG) is an important generalization of the Bayesian Network (BN). BNs have been extremely useful for modeling discrete processes. However, they are not appropriate for all applications. Over the past six years or so, teams of researchers led by Jim Smith have established a strong theoretical underpinning for CEGs. This book systematically and transparently presents the scope and promise of this emerging class of models, together with its underpinning methodology, to a wide audience

Author(s): Collazo, Rodrigo; Görgen, Christiane; Smith, J. Q
Series: Series in computer science and data analysis
Publisher: CRC Press is an imprint of Taylor & Francis Group
Year: 2018

Language: English
Pages: 233
Tags: Bayesian statistical decision theory.;Mathematical statistics -- Graphic methods.;Trees (Graph theory)

Content: 1. Introduction --
1.1. Some motivation --
1.2. Why event trees? --
1.3. Using event trees to describe populations --
1.4. How we have arranged the material in this book --
1.5. Exercises --
2. Bayesian inference using graphs --
2.1. Inference on discrete statistical models --
2.1.1. Two common sampling mass functions --
2.1.2. Two prior-to-posterior analyses --
2.1.3. Poisson-Gamma and Multinomial --
Dirichlet --
2.1.4. MAP model selection using Bayes Factors --
2.2. Statistical models and structural hypotheses --
2.2.1. An example of competing models --
2.2.2. The parametric statistical model --
2.3. Discrete Bayesian networks --
2.3.1. Factorisations of probability mass functions --
2.3.2. The d-separation theorem --
2.3.3. DAGs coding the same distributional assumptions --
2.3.4. Estimating probabilities in a BN --
2.3.5. Propagating probabilities in a BN --
2.4. Concluding remarks --
2.5. Exercises --
3. The Chain Event Graph --
3.1. Models represented by tree graphs --
3.1.1. Probability trees --
3.1.2. Staged trees --
3.2. The semantics of the Chain Event Graph --
3.3. Comparison of stratified CEGs with BNs --
3.4. Examples of CEG semantics --
3.4.1. The saturated CEG --
3.4.2. The simple CEG --
3.4.3. The square-free CEG --
3.5. Some related structures --
3.6. Exercises --
4. Reasoning with a CEG --
4.1. Encoding qualitative belief structures with CEGs --
4.1.1. Vertex- and edge-centred events --
4.1.2. Intrinsic events --
4.1.3. Conditioning in CEGs --
4.1.4. Vertex-random variables, cuts and independence --
4.2. CEG statistical models --
4.2.1. Parametrised subsets of the probability simplex --
4.2.2. The swap operator --
4.2.3. The resize operator --
4.2.4. The class of all statistically equivalent staged trees --
4.3. Exercises --
5. Estimation and propagation on a given CEG --
5.1. Estimating a given CEG --
5.1.1. A conjugate analysis --
5.1.2. How to specify a prior for a given CEG --
5.1.3. Example: Learning liver and kidney disorders --
5.1.4. When sampling is not random --
5.2. Propagating information on trees and CEGs --
5.2.1. Propagation when probabilities are known --
5.2.2. Example: Propagation for liver and kidney disorders --
5.2.3. Propagation when probabilities are estimated --
5.2.4. Some final comments --
5.3. Exercises --
6. Model selection for CEGs --
6.1. Calibrated priors over classes of CEGs --
6.2. Log-posterior Bayes Factor scores --
6.3. CEG greedy and dynamic programming search --
6.3.1. Greedy SCEG search using AHC --
6.3.2. SCEG exhaustive search using DP --
6.4. Technical advances for SCEG model selection --
6.4.1. DP and AHC using a block ordering --
6.4.2. A pairwise moment non-local prior --
6.5. Exercises --
7. How to model with a CEG: A real-world application --
7.1. Previous studies and domain knowledge --
7.2. Searching the CHDS dataset with a variable order --
7.3. Searching the CHDS dataset with a block ordering --
7.4. Searching the CHDS dataset without a variable ordering --
7.5. Issues associated with model selection --
7.5.1. Exhaustive CEG model search --
7.5.2. Searching the CHDS dataset using NLPs --
7.5.3. Setting a prior probability distribution --
7.6. Exercises --
8. Causal inference using CEGs --
8.1. Bayesian networks and causation --
8.1.1. Extending a BN to a causal BN --
8.1.2. Problems of describing causal hypotheses using a BN --
8.2. Defining a do-operation for CEGs --
8.2.1. Composite manipulations --
8.2.2. Example: student housing situation --
8.2.3. Some special manipulations of CEGs --
8.3. Causal CEGs --
8.3.1. When a CEG can legitimately be called causal --
8.3.2. Example: Manipulations of the CHDS --
8.3.3. Backdoor theorems --
8.4. Causal discovery algorithms for CEGs --
8.5. Exercises.