Exploiting Bayesian network sensitivity functions for inference in credal networks

Abstract

A Bayesian network is a concise representation of a joint probability distribution, which can be used to compute any probability of interest for the represented distribution. Credal networks were introduced to cope with the inevitable inaccuracies in the parametrisation of such a network. Where a Bayesian network is parametrised by defining unique local distributions, in a credal network sets of local distributions are given. From a credal network, lower and upper probabilities can be inferred. Such inference, however, is often problematic since it may require a number of Bayesian network computations exponential in the number of credal sets. In this paper we propose a preprocessing step that is able to reduce this complexity. We use sensitivity functions to show that for some classes of parameter in Bayesian networks the qualitative effect of a parameter change on an outcome probability of interest is independent of the exact numerical specification. We then argue that credal sets associated with such parameters can be replaced by a single distribution.