Unifying Markov properties for graphical models
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Unifying Markov properties for graphical models. / Lauritzen, Steffen L.; Sadeghi, Kayvan Sadeghi.
In: Annals of Statistics, Vol. 46, No. 5, 2018, p. 2251-2278.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Unifying Markov properties for graphical models
AU - Lauritzen, Steffen L.
AU - Sadeghi, Kayvan Sadeghi
PY - 2018
Y1 - 2018
N2 - Several types of graphs with different conditional independence interpretations—also known as Markov properties—have been proposed and used in graphical models. In this paper, we unify these Markov properties by introducing a class of graphs with four types of edges—lines, arrows, arcs and dotted lines—and a single separation criterion. We show that independence structures defined by this class specialize to each of the previously defined cases, when suitable subclasses of graphs are considered. In addition, we define a pairwise Markov property for the subclass of chain mixed graphs, which includes chain graphs with the LWF interpretation, as well as summary graphs (and consequently ancestral graphs). We prove the equivalence of this pairwise Markov property to the global Markov property for compositional graphoid independence models.
AB - Several types of graphs with different conditional independence interpretations—also known as Markov properties—have been proposed and used in graphical models. In this paper, we unify these Markov properties by introducing a class of graphs with four types of edges—lines, arrows, arcs and dotted lines—and a single separation criterion. We show that independence structures defined by this class specialize to each of the previously defined cases, when suitable subclasses of graphs are considered. In addition, we define a pairwise Markov property for the subclass of chain mixed graphs, which includes chain graphs with the LWF interpretation, as well as summary graphs (and consequently ancestral graphs). We prove the equivalence of this pairwise Markov property to the global Markov property for compositional graphoid independence models.
U2 - 10.1214/17-AOS1618
DO - 10.1214/17-AOS1618
M3 - Journal article
VL - 46
SP - 2251
EP - 2278
JO - Annals of Statistics
JF - Annals of Statistics
SN - 0090-5364
IS - 5
ER -
ID: 201166112