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

Thierry Denoeux (1, 2)

1 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"
2 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: Dempster-Shafer Theory; Statistical Inference; Partially relevant data; Uncertain data; Partially relevant data.; Evidence Theory; Likelihood Principle

Domaines: Intelligence artificielle [cs.AI]

Thierry Denoeux. Likelihood-based belief function: justification and some extensions to low-quality data. International Journal of Approximate Reasoning, 2014, 55 (7), pp.1535-1547. ⟨10.1016/j.ijar.2013.06.007⟩. ⟨hal-00813021v2⟩