A Graphical Representation of Equivalence Classes of AMP Chain Graphs

This paper deals with chain graph models under alternative AMP interpretation. A new representative of an AMP Markov equivalence class, called the largest deflagged graph, is proposed. The representative is based on revealed internal structure of the AMP Markov equivalence class. More specifically, the AMP Markov equivalence class decomposes into finer strong equivalence classes and there exists a distinguished strong equivalence class among those forming the AMP Markov equivalence class. The largest deflagged graph is the largest chain graph in that distinguished strong equivalence class. A composed graphical procedure to get the largest deflagged graph on the basis of any AMP Markov equivalent chain graph is presented. In general, the largest deflagged graph differs from the AMP essential graph, which is another representative of the AMP Markov equivalence class.