An Alternative Markov Property for Chain Graphs
This work provides a theoretical refinement for researchers in statistics and machine learning, though it appears incremental as it builds on prior Markov properties for chain graphs.
The paper introduces an alternative Markov property (AMP) for chain graphs, which extends the ADG Markov property more directly than the existing LWF property, addressing the representation of causal and associative dependencies in graphical models.
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.