From Likelihood to Plausibility
  Several authors have explained that the likelihood ratio measures the
strength of the evidence represented by observations in statistical problems.
This idea works fine when the goal is to evaluate the strength of the available
evidence for a simple hypothesis versus another simple hypothesis. However, the
applicability of this idea is limited to simple hypotheses because the
likelihood function is primarily defined on points (simple hypotheses) of the
parameter space. In this paper we define a general weight of evidence that is
applicable to both simple and composite hypotheses. It is based on the
Dempster-Shafer concept of plausibility and is shown to be a generalization of
the likelihood ratio. Functional models are of a fundamental importance for the
general weight of evidence proposed in this paper. The relevant concepts and
ideas are explained by means of a familiar urn problem and the general analysis
of a real-world medical problem is presented.
