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
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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