Inner Approximations of Credal Sets by Non-additive Measures

Enrique Miranda, Ignacio Montes, Andrés Presa

Abstract: We consider the problem of transforming a coherent lower probability into another one that (i) belongs to some subclass with better mathematical properties, such as 2- or complete monotonicity; (ii) is at least as informative as the original model, while being as close as possible to it. We show that the problem can be approached in terms of linear programming and that it can be connected with the one of determining the incenter of a credal set. Finally, we compare the performance of the original and the transformed model in a decision problem.