Lower previsions induced by filter maps

Abstract

Coherent lower previsions are amongst the most prominent uncertainty models within imprecise probability theory. We show how they can model information about the joint behaviour of two variables, when these are related by means of a filter map: a model for the imprecise observation of a random variable by means of a class of filters. Our construction preserves a number of interesting properties, such as n-monotonicity, and it generalises a number of existing results for multi-valued mappings. © 2012 Springer-Verlag Berlin Heidelberg.