Markov properties for mixed graphs

Kayvan Sadeghi Sadeghi; Steffen L. Lauritzen

doi:10.3150/12-BEJ502

Markov properties for mixed graphs

Kayvan Sadeghi Sadeghi, Steffen L. Lauritzen

29 Citationer (Scopus)

Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Bernoulli
Vol/bind	30
Udgave nummer	2
Sider (fra-til)	676-696
ISSN	1350-7265
DOI	https://doi.org/10.3150/12-BEJ502
Status	Udgivet - maj 2014
Udgivet eksternt	Ja

Adgang til dokumentet

10.3150/12-BEJ502

Citationsformater

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AB - 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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