Bernoulli

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

Markov properties for mixed graphs

Kayvan Sadeghi and Steffen Lauritzen

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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.

Article information

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

Dates
First available in Project Euclid: 28 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1393594002

Digital Object Identifier
doi:10.3150/12-BEJ502

Mathematical Reviews number (MathSciNet)
MR3178514

Zentralblatt MATH identifier
1303.60064

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

Citation

Sadeghi, Kayvan; Lauritzen, Steffen. Markov properties for mixed graphs. Bernoulli 20 (2014), no. 2, 676--696. doi:10.3150/12-BEJ502. https://projecteuclid.org/euclid.bj/1393594002


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