This article investigates the computation of posterior upper expectations i
nduced by imprecise probabilities, with emphasis on the effects of irreleva
nce and independence judgements. Algorithms that handle imprecise priors an
d imprecise likelihoods are reviewed, and a new result on the limiting dive
rgence of posterior upper probabilities is presented. Algorithms that handl
e irrelevance and independence relations in multivariate models are analyze
d through graphical representations, inspired by the popular Bayesian netwo
rk model. (C) 2000 Elsevier Science Inc. All rights reserved.