Open Access
August 2016 Marginalization and conditioning for LWF chain graphs
Kayvan Sadeghi
Ann. Statist. 44(4): 1792-1816 (August 2016). DOI: 10.1214/16-AOS1451


In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs after marginalization and conditioning for a given CMG or a given LWF CG. We then define and study the class of anterial graphs, which is also stable under marginalization and conditioning and contains LWF CGs, but has a simpler structure than CMGs.


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Kayvan Sadeghi. "Marginalization and conditioning for LWF chain graphs." Ann. Statist. 44 (4) 1792 - 1816, August 2016.


Received: 1 May 2014; Revised: 1 January 2016; Published: August 2016
First available in Project Euclid: 7 July 2016

zbMATH: 1359.62284
MathSciNet: MR3519941
Digital Object Identifier: 10.1214/16-AOS1451

Primary: 62H99
Secondary: 62A99

Keywords: $c$-separation criterion , $m$-separation , chain graph , independence model , LWF Markov property , marginalization and conditioning , mixed graph

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 4 • August 2016
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