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

Thierry Denoeux (1)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

Given a parametric statistical model, evidential methods of statistical inference aim at constructing a belief function on the parameter space from observations. The two main approaches are Dempster's method, which regards the observed variable as a function of the parameter and an auxiliary variable with known probability distribution, and the likelihood-based approach, 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 principle. We then show how this method can be extended to handle low-quality data. Two cases are considered: observations that are only partially relevant to the population of interest, and data acquired through an imperfect observation process.

Mots clés: Evidence Theory; Likelihood Principle; Uncertain data; Partially relevant data.; Partially relevant data; Statistical Inference; Dempster-Shafer Theory

Domaines: Intelligence artificielle [cs.AI]

Thierry Denoeux. Likelihood-based belief function: justification and some extensions to low-quality data. 2013. ⟨hal-00813021v1⟩