, Volume 123, Issue 3, pp 347-364

First online:

Connecting Dempster–Shafer Belief Functions with Likelihood-based Inference

  • Mikel AickinAffiliated withCenter for Health Research

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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.