  Although the usefulness of belief networks for reasoning under uncertainty is
widely accepted, obtaining numerical probabilities that they require is still
perceived a major obstacle. Often not enough statistical data is available to
allow for reliable probability estimation. Available information may not be
directly amenable for encoding in the network. Finally, domain experts may be
reluctant to provide numerical probabilities. In this paper, we propose a
method for elicitation of probabilities from a domain expert that is
non-invasive and accommodates whatever probabilistic information the expert is
willing to state. We express all available information, whether qualitative or
quantitative in nature, in a canonical form consisting of (in) equalities
expressing constraints on the hyperspace of possible joint probability
distributions. We then use this canonical form to derive second-order
probability distributions over the desired probabilities.
