Some Bounds for Conditional Lower Previsions

In this paper we consider some bounds for lower previsions that are either coherent or centered convex. As for coherent conditional previsions, we adopt a structure-free version of Williams’ coherence, which we compare with Williams’ original version and with other coherence concepts. We then focus on bounds concerning the classical product and Bayes’ rules. After discussing some implications of product rule bounds, we generalise a well-known lower bound, which is a (weak) version for coherent lower probabilities of Bayes’ theorem, to the case of (centered) convex previsions. We obtain a family of bounds and show that one of them is undominated in all cases.