The Consistency of Dempster-Shafer Updating

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The Dempster-Shafer theory of evidential reasoning has been proposed as a generalization of Bayesian probabilistic analysis suitable for classification and identification problems. Discriminatory information is given by basic probability assignments, a set-based representation of evidential support. The generation of support from multiple pieces of evidence uses Dempster's rule, an intuitively appealing combining function that employs set-theoretic compatibility checking augmented with a numeric calculus to quantify the support assigned to each consistent subset. When evidence may be represented as both a basic probability assignment and probabilistic support, Dempster-Shafer updating is consistent with the Bayesian analysis if, and only if, prior probabilities are uniform and the evidence is conditionally independent given the frame of discernment. These conditions are extended to define the consistency of Dempster-Shafer updating with probabilistic analysis for arbitrary basic probability assignments. The generation of support is examined in five families of basic probability assignments. It is shown that, even with suitable independence assumptions, support generation using Dempster's rule of combination produces results that are not consistent with a probabilistic analysis of the evidence.