M. Studeny:
On stochastic conditional independence: the problems of characterization
and description.
Annals of Mathematics and Artificial Intelligence
35 (2002), pp. 323241.
 Abstract
 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 nongraphical approach. A certain method
of description of stochastic conditional independence models which uses
nongraphical tools called 'structural imsets' is outlined.
 AMS classification 62H05, 60A05, 68T30, 03B30
 Keywords
 (probabilistic) conditional independence
 semigraphoid
 axiomatic characterization of conditional independence
 chain graph
 structural imset

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