Belief Functions and Parametric Models

Summary The theory of belief functions assesses evidence by fitting it to a scale of canonical examples in which the meaning of a message depends on chance. In order to analyse parametric statistical problems within the framework of this theory, we must specify the evidence on which the parametric model is based. This article gives several examples to show how the nature of this evidence affects the analysis. These examples also illustrate how the theory of belief functions can deal with problems where the evidence is too weak to support a parametric model.