Bayesian inference: the role of coherence to deal with a prior belief function

<Para ID="Par1">Starting from a likelihood function and a prior information represented by a belief function, a closed form expression is provided for the lower envelope of the set of all the possible “posterior probabilities” in finite spaces. The same problem, removing the hypothesis of finiteness for the domain of the prior, is then studied in the finitely additive probability framework by considering either the whole set of coherent extensions or the subset of disintegrable extensions. Copyright Springer-Verlag Berlin Heidelberg 2014