This paper investigates the computation of posterior upper expectations induced by imprecise probabilities, with emphasis on the consequences of Walley's concepts of irrelevance and independence. Algorithms that simultaneously handle imprecise priors and imprecise likelihoods are derived through linear fractional programming; sequences of independent measurements are then analyzed, and a result on the limiting divergence of posterior upper probabilities is presented. Algorithms that handle irrelevance and independence relations in multivariate models are analyzed through graphical representations, inspired by the popular Bayesian network model.
Keywords. Convex sets of probability measures,linear and linear fractional programming,graphical models and directed acyclic graphs.
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