R. R. Bouckaert and M. Studeny: Chain graphs: semantics and expressiveness. In Symbolic and Quantitative Approaches to Reasoning and Uncertainty (Ch. Froidevaux, J. Kohlas eds.), Lecture Notes in Artificial Intelligence 946 (subseries of Lecture Notes in Computer Science), Springer-Verlag, Berlin - Heidelberg 1995, pp. 69-76.

The paper describes some results published later in the journal paper:
M. Studeny and R. R. Bouckaert: On chain graph models for description of conditional independence structures. To appear in The Annals of Statistics.

Two equivalent criteria for reading independency statements from a chain graph are formulated, namely the moralization criterion and the separation criterion. It is proved that these criteria give exactly the graphoid closure of the input list for the chain graph. Moreover, a construction of a chain graph from a graphoid (through an input list), which produces a minimal I-map of that graphoid, is given.

AMS classification 68T30, 62H05

chain graph
moralization criterion
separation criterion
input list
minimal I-map

A pdf copy (converted postscript version) (174kB) is available.

The paper builds on the following works: