On Walley's Combination Rule for Statistical Evidence

Abstract

Dempster’s rule of combination is the commonly used rule for combining independent belief functions. In 1987, Peter Walley proposed an alternative rule for combining belief function representations of independent statistical evidence that result in partially consonant belief functions. In this paper, we examine in detail Walley’s combination rule and compare it with Dempster’s rule. We illustrate the commonalities and differences between the two rules using a simple coin tossing example. Also, we characterize the class of partially consonant belief functions. Finally we show that if we reduce a belief function to a probability distribution using the plausibility transformation, the two combination rules result in the same probability distribution function.