Connecting Dempster-Shafer belief functions with likelihood-based inference

The Dempster-Shafer approach to expressing belief about a parameter in a st atistical model is not consistent with the likelihood principle. This incon sistency has been recognized for some time, and manifests itself as a non-c ommutativity, in which the order of operations (combining belief, combining likelihood) makes a difference. It is proposed here that requiring the exp ression of belief to be committed to the model (and to certain of its submo dels) makes likelihood inference very nearly a special case of the Dempster -Shafer theory.