Reference: Geiger, D. & Heckerman, D. Separable and Transitive Graphoids. 1990.
Abstract: An important step in organizing a large body of knowledge is the grouping of related pieces of information into more or less independent chunks. In constructing large Bayesian networks from expert's judgments, this amounts to identifying the connected components of the network. Asking the expert directly whether variables x and y are connected may be a hard question to answer, since the expert may not have a clear global view of the network topology. However, the query: "does the value of x ever tell you anything about the value of y?" should evoke a more reliable judgment. This paper identifies the class of distributions, called separable, for which the answer to this question can safely be interpreted as an assertion about the connectivity of x and y, and argues that it is reasonable to assume these distributions in the construction of Bayesian networks. Normal and strictly- positive binary distributions are examples of separable distributions.