Pearl ’s well-known $d$-separation criterion for an acyclic
directed graph (ADG) is a pathwise separation criterion that can be used to
efficiently identify all valid conditional independence relations in the Markov
model determined by the graph. This paper introduces $p$-separation, a
pathwise separation criterion that efficiently identifies all valid conditional
independences under the Andersson–Madigan–Perlman (AMP)
alternative Markov property for chain graphs ( = adicyclic
graphs), which include both ADGs and undirected graphs as special cases.
The equivalence of p-separation to the augmentation criterion occurring
in the AMP global Markov property is established, and $p$-separation is
applied to prove completeness of the global Markov propertyfor AMP chain graph
models. Strong completeness of the AMP Markov property is established, that is,
the existence of Markov perfect distributions that satisfy those and
only those conditional independences implied by the AMP property (equivalently,
by $p$-separation). A linear-time algorithm for determining
$p$-separation is presented.
@article{1015345961,
author = {Levitz, Michael and Perlman, Michael D. and Madigan, David},
title = {Separation and Completeness Properties for Amp Chain Graph
Markov Models},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 1751-1784},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345961}
}
Levitz, Michael; Perlman, Michael D.; Madigan, David. Separation and Completeness Properties for Amp Chain Graph
Markov Models. Ann. Statist., Tome 29 (2001) no. 2, pp. 1751-1784. http://gdmltest.u-ga.fr/item/1015345961/