On stochastic conditional independence: the problems of characterization
Annals of Mathematics and Artificial Intelligence
35 (2002), pp. 323-241.
- The topic of this survey are structures of stochastic conditional
independence. Two basic questions are dealt with: the problem of
characterization of conditional independence models and the problem of their
mathematical description and computer representation. Basic formal properties
of conditional independence are recapitulated and the problem of axiomatic
characterization of stochastic conditional independence models is mentioned.
Classic graphical methods of description of these structures are recalled,
in particular, the method which uses chain graphs. Limitation of graphical
approaches motivated an attempt at a non-graphical approach. A certain method
of description of stochastic conditional independence models which uses
non-graphical tools called 'structural imsets' is outlined.
- AMS classification 62H05, 60A05, 68T30, 03B30
- (probabilistic) conditional independence
- axiomatic characterization of conditional independence
- chain graph
- structural imset
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