  Graphical Markov models use graphs, either undirected, directed, or mixed, to
represent possible dependences among statistical variables. Applications of
undirected graphs (UDGs) include models for spatial dependence and image
analysis, while acyclic directed graphs (ADGs), which are especially convenient
for statistical analysis, arise in such fields as genetics and psychometrics
and as models for expert systems and Bayesian belief networks. Lauritzen,
Wermuth and Frydenberg (LWF) introduced a Markov property for chain graphs,
which are mixed graphs that can be used to represent simultaneously both causal
and associative dependencies and which include both UDGs and ADGs as special
cases. In this paper an alternative Markov property (AMP) for chain graphs is
introduced, which in some ways is a more direct extension of the ADG Markov
property than is the LWF property for chain graph.
