Markov properties for mixed graphs

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Markov properties for mixed graphs. / Sadeghi, Kayvan Sadeghi; Lauritzen, Steffen L.

In: Bernoulli, Vol. 30, No. 2, 2014, p. 676-696.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Sadeghi, KS & Lauritzen, SL 2014, 'Markov properties for mixed graphs', Bernoulli, vol. 30, no. 2, pp. 676-696. https://doi.org/10.3150/12-BEJ502

APA

Sadeghi, K. S., & Lauritzen, S. L. (2014). Markov properties for mixed graphs. Bernoulli, 30(2), 676-696. https://doi.org/10.3150/12-BEJ502

Vancouver

Sadeghi KS, Lauritzen SL. Markov properties for mixed graphs. Bernoulli. 2014;30(2):676-696. https://doi.org/10.3150/12-BEJ502

Author

Sadeghi, Kayvan Sadeghi ; Lauritzen, Steffen L. / Markov properties for mixed graphs. In: Bernoulli. 2014 ; Vol. 30, No. 2. pp. 676-696.

Bibtex

@article{dd81d6f153ad4fb488c08c87e635240e,
title = "Markov properties for mixed graphs",
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.",
author = "Sadeghi, {Kayvan Sadeghi} and Lauritzen, {Steffen L.}",
year = "2014",
doi = "10.3150/12-BEJ502",
language = "English",
volume = "30",
pages = "676--696",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "2",

}

RIS

TY - JOUR

T1 - Markov properties for mixed graphs

AU - Sadeghi, Kayvan Sadeghi

AU - Lauritzen, Steffen L.

PY - 2014

Y1 - 2014

N2 - 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.

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.

U2 - 10.3150/12-BEJ502

DO - 10.3150/12-BEJ502

M3 - Journal article

VL - 30

SP - 676

EP - 696

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 2

ER -

ID: 128107826