Title: Processing distortion models: A comparative study
Authors: Enrique Miranda - University of Oviedo (Spain) [presenting]
Ignacio Montes - University of Oviedo (Spain)
Sebastien Destercke - Universite de Technologie de Compiegne (France)
Abstract: When dealing with sets of probabilities, distortion or neighbourhood models are convenient, practical tools, as very few parameters determine them: an initial probability distribution $pr_0$, a distortion factor $\delta>0$ and a specific distortion procedure. The different choices have led to several different families of neighbourhood models, with applications in robust statistics or machine learning. We compare the performance of several distortion models under several processing procedures. First of all, we study their behaviour when merging different distortion models quantifying uncertainty on the same quantity using conjunction, disjunction or convex mixtures. Secondly, we investigate whether the marginal credal sets of a distortion model are also members of the same family, as well as the procedure for determining a global model from marginal ones using independence or natural extension. The analysis is made for six different families of distortion models: the pari-mutuel, epsilon-contamination, constant odds-ratio, total variation, Kolmogorov and $L_1$.