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.