On the Markov Equivalence of Chain Graphs, Undirected Graphs, and Acyclic Digraphs

@article{citeulike:116409, abstract = {Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or for general chain graphs (which include both UDGs and ADGs as special cases). This paper addresses three questions regarding the equivalence of graphical Markov models: when is a given chain graph Markov equivalent (1) to some UDG? (2) to some (at least one) ADG? (3) to some decomposable UDG? The answers are obtained by means of an extension of Frydenberg's (1990) elegant graph-theoretic characterization of the Markov equivalence of chain graphs.}, author = {Andersson, S. A. and Madigan, D. and Perlman, M. D. }, citeulike-article-id = {116409}, comment = {Gives a criterion for a chain graph to be equivalent to some undirected graph, or to some acyclic digraph}, issn = {0303-6898}, journal = {Scandinavian Journal of Statistics}, keywords = {models}, month = {March}, number = {1}, pages = {81--102}, posted-at = {2005-03-07 21:25:18}, priority = {2}, title = {On the Markov Equivalence of Chain Graphs, Undirected Graphs, and Acyclic Digraphs}, url = {http://www.ingentaconnect.com/content/bpl/sjos/1997/00000024/00000001/art00050}, volume = {24}, year = {1997} }

TY - JOUR ID - citeulike:116409 L3 - citeulike-article-id:116409 TI - On the Markov Equivalence of Chain Graphs, Undirected Graphs, and Acyclic Digraphs JF - Scandinavian Journal of Statistics VL - 24 IS - 1 SP - 81 EP - 102 SN - 0303-6898 N2 - Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or for general chain graphs (which include both UDGs and ADGs as special cases). This paper addresses three questions regarding the equivalence of graphical Markov models: when is a given chain graph Markov equivalent (1) to some UDG? (2) to some (at least one) ADG? (3) to some decomposable UDG? The answers are obtained by means of an extension of Frydenberg's (1990) elegant graph-theoretic characterization of the Markov equivalence of chain graphs. KW - models N1 - Gives a criterion for a chain graph to be equivalent to some undirected graph, or to some acyclic digraph AU - Andersson, SA AU - Madigan, D AU - Perlman, MD PY - 1997/03// UR - http://www.ingentaconnect.com/content/bpl/sjos/1997/00000024/00000001/art00050 ER -