The Annals of Statistics
- Ann. Statist.
- Volume 44, Number 4 (2016), 1792-1816.
Marginalization and conditioning for LWF chain graphs
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.
Ann. Statist., Volume 44, Number 4 (2016), 1792-1816.
Received: May 2014
Revised: January 2016
First available in Project Euclid: 7 July 2016
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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
- Proofs. We provide proofs of non-trivial lemmas, propositions and theorems in the paper as well as some more technical and yet less informative lemmas that are used in the proofs.