An Alternative Markov Property for Chain Graphs

Graphical Markov models use graphs ei ther undirected directed or mixed to rep resent possible dependences among statis tical variables Applications of undirected graphs UDGs include models for spatial de pendence and image analysis while acyclic directed graphs ADGs which are espe cially convenient for statistical analysis arise in such elds as genetics and psychomet rics and as models for expert systems and Bayesian belief networks Lauritzen Wer muth 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