Bayesian diagnosis in expert systems

摘要

A Bayesian method for the diagnostic classification of a single case into one of several classes based on qualitative data by an expert system is presented. Both the expert's knowledge about the base rates of the classes and about the conditional probabilities of the data within each class are expressed by beta probability distributions. The Bayesian point probability that a single case belongs to a given class is treated as a parameter. Its probability distribution is derived and called ‘credibility distribution’. Because the numerical handling of the distribution is difficult, an approximation by a beta distribution is proposed. The credibility distribution expresses the imprecision of a diagnostic probability. It processes the amount of knowledge entering the probabilistic inference. It is shown that the total imprecision of a diagnostic classification can be decomposed into the sum of the imprecision of its knowledge components. Imprecision—not expertise—is additive. In cascaded inference, the total degree of diagnostic expertise is also not additive, but recursively discounted at each level of inference. The method allows one to work with subsets of the full problem space and thus reduces the combinatorial explosion.