Dempster-Shafer theory, Bayesian theory, and measure theory

Abstract

We use measure theoretic methods to describe the relationship between the Dempster Shafer (DS) theory and Bayesian (i.e. probability) theory. Within this framework, we demonstrated the relationships among Shafer's belief and plausibility, Dempster's lower and upper probabilities and inner and outer measures. Dempster's multivalued mapping is an example of a random set, a generalization of the concept of the random variable. Dempster's rule of combination is the product measure on the Cartesian product of measure spaces. The independence assumption of Dempster's rule arises from the nature of the problem in which one has knowledge of the marginal distributions but wants to calculate the joint distribution. We present an engineering example to clarify the concepts.