The combination of belief: When and how fast?

Nic Wilson

Abstract: The cornerstone of Dempster-Shafer therory is Dempster's rule and to use the theory it is essential to know when the rule is justified. This paper discusses, and attempts to clarify, this issue. It is also argued that Bayesian belief functions do not fit well into the theory. It is suggested that belief functions in Dempster-Shafer theory can be usefully viewed in terms of families of additive probability functions. A Monte-Carlo algorithm is described which can be used to greatly improve the complexity of the calculation of combined belief.