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The Chain Graph Markov Property

Morten Frydenberg
Scandinavian Journal of Statistics
Vol. 17, No. 4 (1990), pp. 333-353
Stable URL: http://www.jstor.org/stable/4616181
Page Count: 21
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Abstract

A new class of graphs, chain graphs, suitable for modelling conditional independencies are introduced and their Markov properties investigated. This class of graphs, which includes the undirected and directed acyclic graphs, which includes the undirected and directed acyclic graphs, enables modelling recursive models with multivariate response variables. Results concerning the equivalence of different definitions of their Markov properties including a factorization of the density are shown. Finally we give a necessary and sufficient condition for two chain graphs to have the same Markov properties.

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