DESCRIPTION OF STRUCTURES OF STOCHASTIC CONDITIONAL INDEPENDENCE BY MEANS OF FACES AND IMSETS 1st part: introduction and basic concepts1
Milan Studený · International Journal of General Systems · 1995
Global Abstract (for all three parts) The work presents a new approach to the mathematical description of stochastic conditional independence structures of a finite number of random variables. The new approach is related to the classical approaches, that is to the use of directed acyclic graphs (Bayesian networks), undirected graphs (Markov networks) and dependency models (semigraphoids). The approach provides a deductive mechanism to infer probabilistically valid consequences of positive information about conditional independence structure. This mechanism is much more powerful than the use of semigraphoids as it includes, from the classical point of view, an infinite number of inference rules. Nevertheless, from the theoretical point of view, it is finitely implementable The developed theory is illustrated by examples showing how it is applicable.