Expressing imprecision in probabilistic knowledge

Summary The representation of imprecise knowledge in probabilistic expert systems is investigated. It is argued that Bayesian statistics offers a multitude of models and methods that may be employed to express probabilistic knowledge by first and second order probability distributions. Distributions offer a much richer repertoire to express uncertainty that point probabilities. Special attention is payed to Dirichletian weights of evidence in discrete systems and to predictons and inverse predictions in linear regression. Approximate methods for non-conjugate distributions and for incomplete data are discussed. An important property of imprecision in complex systems is that it explodes rapidly when the conclusions are derived from long chains of premises. Thus, imprecision is a pruning criterion is a pruning criterion in complex knowledge systems. This research was supported by the Fonds zur F?rderung der wissenschftlichen Forschung, Vienna.