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April 2006 Characterizing Markov equivalence classes for AMP chain graph models
Steen A. Andersson, Michael D. Perlman
Ann. Statist. 34(2): 939-972 (April 2006). DOI: 10.1214/009053606000000173


Chain graphs (CG) (= adicyclic graphs) use undirected and directed edges to represent both structural and associative dependences. Like acyclic directed graphs (ADGs), the CG associated with a statistical Markov model may not be unique, so CGs fall into Markov equivalence classes, which may be superexponentially large, leading to unidentifiability and computational inefficiency in model search and selection. It is shown here that, under the Andersson–Madigan–Perlman (AMP) interpretation of a CG, each Markov-equivalence class can be uniquely represented by a single distinguished CG, the AMP essential graph, that is itself simultaneously Markov equivalent to all CGs in the AMP Markov equivalence class. A complete characterization of AMP essential graphs is obtained. Like the essential graph previously introduced for ADGs, the AMP essential graph will play a fundamental role for inference and model search and selection for AMP CG models.


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Steen A. Andersson. Michael D. Perlman. "Characterizing Markov equivalence classes for AMP chain graph models." Ann. Statist. 34 (2) 939 - 972, April 2006.


Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1096.62097
MathSciNet: MR2283399
Digital Object Identifier: 10.1214/009053606000000173

Primary: 60K99 , 62M45
Secondary: 68R10 , 68T30

Keywords: chain graph , essential graph , Graphical model , Markov equivalence

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 2 • April 2006
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