From Likelihood to Plausibility

TL;DR

This paper introduces a new general measure of evidence, based on Dempster-Shafer plausibility, that extends the likelihood ratio to evaluate both simple and composite hypotheses in statistical analysis.

Contribution

It proposes a novel weight of evidence grounded in plausibility, generalizing the likelihood ratio for broader hypothesis testing scenarios.

Findings

The new measure applies to simple and composite hypotheses.

Illustrated with urn and medical case studies.

Shows advantages over traditional likelihood ratio methods.

Abstract

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.