An Experimental Comparison of Numerical and Qualitative Probabilistic
  Reasoning
  Qualitative and infinitesimal probability schemes are consistent with the
axioms of probability theory, but avoid the need for precise numerical
probabilities. Using qualitative probabilities could substantially reduce the
effort for knowledge engineering and improve the robustness of results. We
examine experimentally how well infinitesimal probabilities (the kappa-calculus
of Goldszmidt and Pearl) perform a diagnostic task - troubleshooting a car that
will not start by comparison with a conventional numerical belief network. We
found the infinitesimal scheme to be as good as the numerical scheme in
identifying the true fault. The performance of the infinitesimal scheme worsens
significantly for prior fault probabilities greater than 0.03. These results
suggest that infinitesimal probability methods may be of substantial practical
value for machine diagnosis with small prior fault probabilities.
