THE SENSITIVITY OF BELIEF NETWORKS TO IMPRECISE PROBABILITIES - AN EXPERIMENTAL INVESTIGATION

Bayesian belief networks are being increasingly used as a knowledge re presentation for reasoning under uncertainty. Some researchers have qu estioned the practicality of obtaining the numerical probabilities wit h sufficient precision to create belief networks for large-scale appli cations. In this work, we investigate how precise the probabilities ne ed to be by measuring how imprecision in the probabilities affects dia gnostic performance. We conducted a series of experiments on a set of real-world belief networks for medical diagnosis in liver and bile dis ease. We examined the effects on diagnostic performance of (1) varying the mappings from qualitative frequency weights into numerical probab ilities, (2) adding random noise to the numerical probabilities, (3) s implifying from quaternary domains for diseases and findings-absent, m ild, moderate, and severe-to binary domains-absent and present, and (4 ) using test cases that contain diseases outside the network. We found that even extreme differences in the probability mappings and large a mounts of noise lead to only modest reductions in diagnostic performan ce. We found no significant effect of the simplification from quaterna ry to binary representation. We also found that outside diseases degra ded performance modestly. Overall, these findings indicate that even h ighly imprecise input probabilities may not impair diagnostic performa nce significantly, and that simple binary representations may often be adequate. These findings of robustness suggest that belief networks a re a practical representation without requiring undue precision.