• Bernoulli
  • Volume 20, Number 2 (2014), 676-696.

Markov properties for mixed graphs

Kayvan Sadeghi and Steffen Lauritzen

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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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Bernoulli, Volume 20, Number 2 (2014), 676-696.

First available in Project Euclid: 28 February 2014

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


Sadeghi, Kayvan; Lauritzen, Steffen. Markov properties for mixed graphs. Bernoulli 20 (2014), no. 2, 676--696. doi:10.3150/12-BEJ502.

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