Open Access
May 2014 Markov properties for mixed graphs
Kayvan Sadeghi, Steffen Lauritzen
Bernoulli 20(2): 676-696 (May 2014). DOI: 10.3150/12-BEJ502


In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such graphs are compositional graphoids. We focus in particular on the subclass of ribbonless graphs which as special cases include undirected graphs, bidirected graphs, and directed acyclic graphs, as well as ancestral graphs and summary graphs. We define maximality of such graphs as well as a pairwise and a global Markov property. We prove that the global and pairwise Markov properties of a maximal ribbonless graph are equivalent for any independence model that is a compositional graphoid.


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Kayvan Sadeghi. Steffen Lauritzen. "Markov properties for mixed graphs." Bernoulli 20 (2) 676 - 696, May 2014.


Published: May 2014
First available in Project Euclid: 28 February 2014

zbMATH: 1303.60064
MathSciNet: MR3178514
Digital Object Identifier: 10.3150/12-BEJ502

Keywords: $m$-separation , composition property , global Markov property , graphoid , independence model , maximality , pairwise Markov property

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

Vol.20 • No. 2 • May 2014
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