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Conditional independence and chain event graphs

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Smith, J. Q. and Anderson, Paul E.. (2008) Conditional independence and chain event graphs. Artificial Intelligence, Vol.172 (No.1). pp. 42-68. ISSN 0004-3702

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Official URL: http://dx.doi.org/10.1016/j.artint.2007.05.004

Abstract

Graphs provide an excellent framework for interrogating symmetric models of measurement random. variables and discovering their implied conditional independence structure. However, it is not unusual for a model to be specified from a description of how a process unfolds (i.e. via its event tree), rather than through relationships between a given set of measurements. Here we introduce a new mixed graphical structure called the chain event graph that is a function of this event tree and a set of elicited equivalence relationships. This graph is more expressive and flexible than either the Bayesian network-equivalent in the symmetric case-or the probability decision graph. Various separation theorems are proved for the chain event graph. These enable implied conditional independencies to be read from the graph's topology. We also show how the topology can be exploited to tease out the interesting conditional independence structure of functions of random variables associated with the underlying event tree. (c) 2007 Elsevier B.V. All rights reserved.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Graph theory, Random variables, Probabilites, Bayesian statistical decision theory

Journal or Publication Title:

Artificial Intelligence

Publisher:

Elsevier BV

ISSN:

0004-3702

Official Date:

January 2008

Dates:

Date	Event
January 2008	Published

Volume:

Vol.172

Number:

No.1

Number of Pages:

Page Range:

pp. 42-68

Identifier:

10.1016/j.artint.2007.05.004

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Open Access

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