Analyzing belief function networks with conditional beliefs

The success of Bayesian networks is due to their capability to simply represent (in)dependence and to be a compact representation of a full joint distribution of the set of random variables involved in the studied system. Since belief function theory is known as a general framework to reason under uncertainty, it is expected that belief function networks with conditional beliefs are a generalization of Bayesian networks. This paper studies different forms of belief function networks. We discuss the ones defined with one conditional for all parents and the ones defined per single parent. In particular, we discuss the case when beliefs are Bayesian situations where a belief function network fails to collapse into a Bayesian network.