Collazo / Görgen / Goergen Chain Event Graphs

1. Auflage 2018
ISBN: 978-1-4987-2961-1
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 254 Seiten

Reihe: Chapman & Hall/CRC Computer Science & Data Analysis

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).

Autoren/Hrsg.

Collazo, Rodrigo A.

Görgen, Christiane

Goergen, Christiane

Smith, Jim Q.

Fachgebiete

• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
• Mathematik | Informatik Mathematik Stochastik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftsstatistik, Demographie

Inhaltsverzeichnis

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