The Dempster-Shafer calculus for statisticians

The Dempster-Shafer (E)S) theory of probabilistic reasoning is presented in terms of a semantics whereby every meaningful formal assertion is associated with a triple (p, q, r) where p is the probability for the assertion, q is the probability against the assertion, and r is the probability of don't know. Arguments are presented for the necessity of don't know. Elements of the calculus are sketched, including the extension of a DS model from a margin to a full state space, and DS combination of independent DS uncertainty assessments on the full space. The methodology is applied to inference and prediction from Poisson counts, including an introduction to the use of join-tree model structure to simplify and shorten computation. The relation of DS theory to statistical significance testing is elaborated, introducing along the way the new concept of dull null hypothesis. (C) 2007 Elsevier Inc. All rights reserved.