Jiroušek, Kratochvíl and Shenoy
On the Relationship between Graphical and Compositional Models for the Dempster-Shafer Belief Function Theory
This paper studies the relationship between graphical and compositional models representing joint belief functions. In probability theory, the class of Bayesian networks (directed graphical models) is equivalent to compositional models. Such an equivalence does not hold for the Dempster-Shafer belief function theory. We show that each directed graphical belief function model can be represented as a compositional model, but the converse does not hold. As there are two composition operators for belief functions, there are two types of compositional models. In studying their relation to graphical models, they are closely connected. Namely, one is more specific than the other. A precise relationship between these two composition operators is described.