  Recent research has found that diagnostic performance with Bayesian belief
networks is often surprisingly insensitive to imprecision in the numerical
probabilities. For example, the authors have recently completed an extensive
study in which they applied random noise to the numerical probabilities in a
set of belief networks for medical diagnosis, subsets of the CPCS network, a
subset of the QMR (Quick Medical Reference) focused on liver and bile diseases.
The diagnostic performance in terms of the average probabilities assigned to
the actual diseases showed small sensitivity even to large amounts of noise. In
this paper, we summarize the findings of this study and discuss possible
explanations of this low sensitivity. One reason is that the criterion for
performance is average probability of the true hypotheses, rather than average
error in probability, which is insensitive to symmetric noise distributions.
But, we show that even asymmetric, logodds-normal noise has modest effects. A
second reason is that the gold-standard posterior probabilities are often near
zero or one, and are little disturbed by noise.
