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Markov properties for mixed graphs

Sadeghi, K; Lauritzen, S; (2014) Markov properties for mixed graphs. Bernoulli , 20 (2) pp. 676-696. 10.3150/12-BEJ502. Green open access

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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.

Type: Article
Title: Markov properties for mixed graphs
Open access status: An open access version is available from UCL Discovery
DOI: 10.3150/12-BEJ502
Publisher version: https://doi.org/10.3150/12-BEJ502
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Physical Sciences, Statistics & Probability, Mathematics, composition property, global Markov property, graphoid, independence model, m-separation, maximality, pairwise Markov property, CHAIN GRAPHS, CONDITIONAL-INDEPENDENCE, CAUSAL-MODELS, SYSTEMS
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10068613
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