Relatore: prof. Enrique Miranda - Department of Statistics and Operations Research, University of Oviedo, Spain

Abstract

We consider the problem of transforming a set of probabilities into another one that (i) belongs to some subclass with better mathematical properties, such as 2- or complete monotonicity; (ii) is as close as possible to the original model. We consider two possibilities: outer approximations, that do not add any new information to the original model, and inner approximations, that are as least as precise as the original model. We show that the problem can be approached in terms of linear programming and study some particular cases of interest, showing that the problem can be connected with that of determining the incenter of a credal set. Finally, we compare the performance of the original and the transformed model in a decision problem.