  In recent years the belief network has been used increasingly to model
systems in Al that must perform uncertain inference. The development of
efficient algorithms for probabilistic inference in belief networks has been a
focus of much research in AI. Efficient algorithms for certain classes of
belief networks have been developed, but the problem of reporting the
uncertainty in inferred probabilities has received little attention. A system
should not only be capable of reporting the values of inferred probabilities
and/or the favorable choices of a decision; it should report the range of
possible error in the inferred probabilities and/or choices. Two methods have
been developed and implemented for determining the variance in inferred
probabilities in belief networks. These methods, the Approximate Propagation
Method and the Monte Carlo Integration Method are discussed and compared in
this paper.
