Marginalization and Conditioning for LWF Chain Graphs

TL;DR

This paper introduces chain mixed graphs (CMGs) and anterial graphs, providing methods and criteria for marginalization and conditioning in chain graphs with the LWF property, ensuring stability of these classes.

Contribution

It defines CMGs and anterial graphs, establishing their stability under marginalization and conditioning, and offers methods to generate these graphs from LWF chain graphs.

Findings

CMGs are stable under marginalization and conditioning.

Anterial graphs are simpler and also stable under these operations.

Methods for generating CMGs and anterial graphs from LWF CGs are provided.

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.