On Stochastic Conditional Independence: the Problems of Characterization and Description

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 non-graphical approach. A certain method of description of stochastic conditional independence models which uses non-graphical tools called ‘structural imsets’ is outlined.