Factorization of Dempster-Shafer Belief Functions Based on Data

Abstract: One important obstacle in applying Dempster-Shafer Theory (DST) is its relationship to frequencies. In particular, there exist serious difficulties in finding factorizations of belief functions from data. In probability theory factorizations are usually related to notion of (conditional) independence and their possibility tested accordingly. However, in DST conditional belief distributions prove to be non-proper belief functions (that is ones connected with negative "frequencies"). This makes statistical testing of potential conditional independencies practically impossible, as no coherent interpretation could be found so far for negative belief function values. In this paper a novel attempt is made to overcome this difficulty. In the proposal no conditional beliefs are calculated, but instead a new measure F is introduced within the framework of DST, closely related to conditional independence, allowing to apply conventional statistical tests for detection of dependence/independence.