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).
Autorentext
Rodrigo A. Collazo, Christiane Goergen, Jim Q. Smith
Inhalt
1.Introduction Some motivation Why event trees? Using event trees to describe populations How we have arranged the material in this book Exercises
2.Bayesian inference using graphs Inference on discrete statistical models Two common sampling mass functions Two prior-to-posterior analyses Poisson-Gamma and Multinomial-Dirichlet MAP model selection using Bayes Factors Statistical models and structural hypotheses An example of competing models The parametric statistical model Discrete Bayesian networks Factorisations of probability mass functions The d-separation theorem assumptions Estimating probabilities in a BN Propagating probabilities in a BN Concluding remarks Exercises
3.The Chain Event Graph Models represented by tree graphs Probability trees Staged trees The semantics of the Chain Event Graph Comparison of stratified CEGs with Examples of CEG semantics The saturated CEG The simple CEG The square-free CEG Some related structures Exercises
4.Reasoning with a CEG Encoding qualitative belief structures with CEGs Vertex- and edge-centred events Intrinsic events Conditioning in CEGs Vertex-random variables, cuts and independence CEG statistical models Parametrised subsets of the probability simplex The swap operator The resize operator The class of all statistically equivalent staged trees Exercises
5.Estimation and propagation on a given CEG Estimating a given CEG A conjugate analysis How to specify a prior for a given CEG Example: learning liver and kidney disorders When sampling is not random Propagating information on trees and CEGs Propagation when probabilities are known Example: propagation for liver and kidney disorders Propagation when probabilities are estimated Some final comments Exercises
6.Model selection for CEGs Calibrated priors over classes of CEGs Log-posterior Bayes Factor (lpBF) scores CEG greedy and dynamic programming Greedy SCEG search using AHC SCEG exhaustive search using Technical advances for SCEG model selection DP and AHC using a block ordering A pairwise moment non-local prior (pm-NLP) Exercises 7.How to model with a CEG: a real-world application Previous studies and domain knowledge Searching the CHDS dataset with a variable order Searching the CHDS dataset with a block ordering Searching the CHDS dataset without a variable ordering Issues associated with model selection Exhaustive CEG model search Searching the CHDS dataset using NLPs Setting a prior probability distribution 8.Causal inference using CEGs Bayesian networks and causation Extending a BN to a causal BN Problems of describing causal hypotheses using a BN Defining a do-operation for CEGs Composite manipulations Example: student housing situation Some special manipulations of CEGs Causal CEGs When a CEG can legitimately be called 'causal Example: manipulations of the CHDS Backdoor theorems Causal discovery algorithms for CEGs Exercises
Bibliography