The chain graph Markov property. (English) Zbl 0713.60013

Frydenberg, Morten

Scand. J. Stat. 17, No. 4, 333-353 (1990).

Summary: 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, 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.

MSC:

60C05	Combinatorial probability
05C80	Random graphs (graph-theoretic aspects)
60J99	Markov processes

Keywords:

Gibbs-factorization; graphical models; influence diagrams; modelling conditional independencies; Markov properties