Abstract

The paper presents a direct (explicit) graphical characterization of the largest chain graph which serves as a unique representative of the class of Markov equivalent chain graphs. The characterization is a basis for an algorithm constructing for a given chain graph the largest chain graph equivalent to it. The algorithm was used to generate a catalogue of the largest chain graphs with at most five vertices. Every entry of the catalogue contains the largest chain graph of a class of Markov equivalent chain graphs and an economical record of the induced independency model.

Note that the characterization theorem and the algorithm presented in this paper differ substantially form a former characterization theorem and algorithm described in the paper:

M. Studeny: A recovery algorithm for chain graphs. International Journal of Approximate Reasoning 17 (1997), n. 2-3, pp. 265-293.

AMS classification 68T30, 62H05

Keywords

graphical models

conditional independence

chain graphs

Markov equivalence

the largest chain graph

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A scanned pdf copy of the published paper (1188kB) is already open-access available.

The paper also builds on the following works:

• M. Frydenberg: The chain graph Markov property. Scandinavian Journal of Statistics 17 (1990), n. 3, pp. 333-353.