Comparison of Bayesian and Dempster’s Rules in Evidence Combination

Suppose we have a hypothesis H and two evidential variables A and B. Suppose the conditional probabilities P(H|A) and P(H|B) are known to lie in specified intervals. We compare the intervals for the combination P(H|A,B) given by the Bayesian method and the Dempster’s method. We show that the width of the interval given by the Dempster rule is narrower than that of Bayes. We discuss the onesided cases, i. e., when we are given bounds on P(H|A) and P(H|B), H being the negation of H. Finally, we mention the sensitivity of the combination rules to small deviations of the members, especially when these values are near zero.