Abstract

This papers deals with chain graph models under alternative AMP interpretation. A new representative of na 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.

Keywords

chain graph

AMP Markov equivalence

largest deflagged graph

strong equivalence

deflagging procedure

component merging procedure

A pdf version of the paper (308kB) is available.

The paper partially builds on the following papers:

• S. A. Andersson, D. Madigan, M. D. Perlman: Alternative Markov properties for chain graphs. Scandinavian Journal of Statistics 28 (2001), pp. 33-85.
• A. Roverato: A unified approach to the characterisation of equivalence classes of DAGs, chain graphs with no flags and chain graphs. Scandinavian Journal of Statistics 32 (2005), pp. 295-312.