Marginalization and conditioning for LWF chain graphs
Annals of Statistics
Institute of Mathematical Statistics
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Sadeghi, K. (2016). Marginalization and conditioning for LWF chain graphs. Annals of Statistics, 44 (4), 1792-1816. https://doi.org/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.
c-separation criterion, chain graph, independence model, LWF Markov property, m-separation, marginalization and conditioning, mixed graph
Supported by Grant #FA9550-12-1-0392 from the U.S. Air Force Office of Scientific Research (AFOSR) and the Defense Advanced Research Projects Agency (DARPA).
External DOI: https://doi.org/10.1214/16-AOS1451
This record's URL: https://www.repository.cam.ac.uk/handle/1810/267222