Likelihood-based belief function: justification and some extensions to low-quality data

Given a parametric statistical model, evidential methods of statistical in-ference aim at constructing a belief function on the parameter space from observations. The two main approaches are Dempster’s method, which re-gards the observed variable as a function of the parameter and an auxiliary variable with known probability distribution, and the likelihood-based ap-proach, which considers the relative likelihood as the contour function of a consonant belief function. In this paper, we revisit the latter approach and prove that it can be derived from three basic principles: the likelihood principle, compatibility with Bayes ’ rule and the minimal commitment prin-ciple. We then show how this method can be extended to handle low-quality data. Two cases are considered: observations that are only partially rele-vant to the population of interest, and data acquired through an imperfect observation process