arXiv subjects

Steen A. Andersson

Publications and source records attributed to Steen A. Andersson.

2 recordsLinked to original sources

arXiv2019

On the structure of essential graphs for AMP chain graph models

Chain graphs (CG) use undirected and directed edges to represent both structural and associative dependences. Like acyclic directed graphs (ADGs), the CG associated with a statistical Markov model may not be unique, so CGs fall into Markov equivalence classes, which may be superexponentially large, leading to unidentifiability and computational inefficiency in model search and selection.Under the Andersson--Madigan--Perlman (AMP) interpretation of a CG, each Markov-equivalence class can be uniquely represented by a single CG, the AMP essential graph, that can be used for efficient inference and model search and selection. Here the graphical structure of an AMP essential graph is studied in detail. This structural information will be useful for algorithmic construction of the essential graph.

math.ST↗

arXiv2013

An Alternative Markov Property for Chain Graphs

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.

cs.AI↗