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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. 4268. ISSN 00043702
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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 networkequivalent in the symmetric caseor 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:  00043702  
Official Date:  January 2008  
Dates: 


Volume:  Vol.172  
Number:  No.1  
Number of Pages:  27  
Page Range:  pp. 4268  
Identifier:  10.1016/j.artint.2007.05.004  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Open Access  
References:  [1] P.E. Anderson, J.Q. Smith, A graphical framework for representing the semantics of asymmetric models, Technical Report 0512, CRiSM 

URI:  http://wrap.warwick.ac.uk/id/eprint/30802 
Data sourced from Thomson Reuters' Web of Knowledge
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