An Alternative Markov Property for Chain Graphs

TL;DR

This paper introduces an alternative Markov property for chain graphs, providing a more direct extension of the directed acyclic graph Markov property, enhancing the representation of causal and associative dependencies.

Contribution

The paper proposes a new Markov property (AMP) for chain graphs that improves upon the existing LWF property by offering a more direct extension of ADG Markov properties.

Findings

AMP simplifies the representation of dependencies in chain graphs.

AMP aligns more closely with the Markov properties of directed acyclic graphs.

The new property broadens the applicability of chain graphs in statistical modeling.

Abstract

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.