Compositional Belief Function Models

Analogously to Graphical Markov models, also Compositional models serve as an efficient tool for multidimensional models representation. The main idea of the latter models resembles a jig saw puzzle: Multidimensional models are assembled (composed) from a large number of small pieces, from a large number of low-dimensional models. Originally they were designed to represent multidimensional probability distributions. In this paper they will be used to represent multidimensional belief functions (or more precisely, multidimensional basic belief assignments) with the help of a system of low-dimensional ones. In addition to a number of basic properties of such models, in the paper it will be shown that these models can serve as a real enrichment of probabilistic models. They can relieve a drawback of probabilistic models that can be, in case that the initial building blocks of the model are inconsistent, undefined. As a side result of the paper we propose a new way how to define the concept of conditional independence for belief functions.