Likelihood-based belief function: Justification and some extensions to low-quality data |
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Institution: | Université de Technologie de Compiègne, CNRS, UMR 7253 Heudiasyc, France |
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Abstract: | 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. |
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Keywords: | Statistical inference Dempster–Shafer theory Evidence theory Likelihood principle Uncertain data Partially relevant data |
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