# An Alternative Markov Property for Chain Graphs

arXiv: https://arxiv.org/abs/1302.3553 · HTML: https://mlsanity.com/paper/1302.3553/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2013.

## Built on by (most cited first, 2 of 2)

- [Causal Homotopy](https://mlsanity.com/paper/2112.01847/) (2021)
- [Categoroids: Universal Conditional Independence](https://mlsanity.com/paper/2208.11077/) (2022)

## Abstract (arXiv)

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.