Connecting dempster–shafer belief functions with likelihood-based inference

Mikel Aickin

pp. 347-364

in: Synthese 123 (3), 2000.

Abstract

The Dempster–Shafer approach to expressing beliefabout a parameter in a statistical model is notconsistent with the likelihood principle. Thisinconsistency has been recognized for some time, andmanifests itself as a non-commutativity, in which theorder of operations (combining belief, combininglikelihood) makes a difference. It is proposed herethat requiring the expression of belief to be committed to the model (and to certain of itssubmodels) makes likelihood inference very nearly aspecial case of the Dempster–Shafer theory.