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November 2013 Stable mixed graphs
Kayvan Sadeghi
Bernoulli 19(5B): 2330-2358 (November 2013). DOI: 10.3150/12-BEJ454

Abstract

In this paper, we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables using the $m$-separation criterion. These include MC, summary, and ancestral graphs. As a modification of MC graphs, we define the class of ribbonless graphs (RGs) that permits the use of the $m$-separation criterion. RGs contain summary and ancestral graphs as subclasses, and each RG can be generated by a DAG after marginalisation and conditioning. We derive simple algorithms to generate RGs, from given DAGs or RGs, and also to generate summary and ancestral graphs in a simple way by further extension of the RG-generating algorithm. This enables us to develop a parallel theory on these three classes and to study the relationships between them as well as the use of each class.

Citation

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Kayvan Sadeghi. "Stable mixed graphs." Bernoulli 19 (5B) 2330 - 2358, November 2013. https://doi.org/10.3150/12-BEJ454

Information

Published: November 2013
First available in Project Euclid: 3 December 2013

zbMATH: 1317.05077
MathSciNet: MR3160556
Digital Object Identifier: 10.3150/12-BEJ454

Keywords: $m$-separation criterion , ancestral graph , Directed acyclic graph , independence model , marginalisation and conditioning , MC graph , summary graph

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

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Vol.19 • No. 5B • November 2013
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