Separable and Transitive Graphoids

Abstract

We examine the notion of “unrelatedness” in a probabilistic framework. Three formulations are presented. In the first formulation, two variables a and b are totally independent with respect to a set of variables U if they are independent given any value of the variables in U . In the second formulation, two variables are totally uncoupled if U can be partitioned into two marginally independent sets containing a and b respectively. In the third formulation, two variables are totally disconnected if the corresponding nodes are disconnected in any belief network representation. We explore the relationship between these three definitions of “unrelatedness” and explain their relevance to the process of acquiring probabilistic knowledge from human experts.