Abstract

The theory of belief functions is a generalization of the Bayesian theory of subjective probability judgement. The author's 1976 book, A Mathematical Theory of Evidence, is still a standard reference for this theory, but it is concerned primarily with mathematical foundations. Since 1976, considerable work has been done on interpretation and implementation of the theory. This article reviews this work, as well as newer work on mathematical foundations. It also considers the place of belief functions within the broader topic of probability and the place of probability within the larger set of formalisms used by artificial intelligence.

Keywords: Bayesian theory; belief functions; Dempster-Shafer theory; independence; inner measures; interactive systems; join trees; lower probabilities; multivalued mappings; probability propagation; random sets; statistical inference