The Annals of Statistics

Marginalization and conditioning for LWF chain graphs

Kayvan Sadeghi

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Abstract

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.

Article information

Source
Ann. Statist., Volume 44, Number 4 (2016), 1792-1816.

Dates
Received: May 2014
Revised: January 2016
First available in Project Euclid: 7 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.aos/1467894716

Digital Object Identifier
doi:10.1214/16-AOS1451

Mathematical Reviews number (MathSciNet)
MR3519941

Zentralblatt MATH identifier
1359.62284

Subjects
Primary: 62H99: None of the above, but in this section
Secondary: 62A99: None of the above, but in this section

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

Citation

Sadeghi, Kayvan. Marginalization and conditioning for LWF chain graphs. Ann. Statist. 44 (2016), no. 4, 1792--1816. doi:10.1214/16-AOS1451. https://projecteuclid.org/euclid.aos/1467894716


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