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
pdf copy (converted postscript version) (174kB) is available.
The paper builds on the following works:
- M. Frydenberg: The chain graph Markov property.
Scandinavian Journal of Statistics
17 (1990), n. 3, pp. 333-353.
- T. Verma and J. Pearl: Causal networks:
semantics and expressiveness. In Uncertainty in Artificial
Intelligence 4 (R.D. Schachter, T.S. Lewitt, L.N. Kanal, J.F.
Lemmer eds.) North-Holland 1990, pp. 60-76.