Bayesian updating: On the interpretation of exhaustive and mutually exclusive assumptions

摘要

Duda, Hart and Nilsson proposed the use of an odds-likelihood Bayesian scheme for inexact reasoning. Pednault, Zucker and Muresan proved that no updating takes place if the hypotheses in the network are mutually exclusive and exhaustive. Glymour refuted the claim with a special example and Johnson later proved that at most one updating could take place. The implications of these results are disturbing to builders of expert systems who are using this scheme directly (e.g. PROSPECTOR) or indirectly (e.g. MYCIN). In this note, we summarise their work and indicate how their results should be interpreted. In particular, we argue that the significance of their results is not in showing that the odds-likelihood Bayesian scheme is restrictive, but how a network using this scheme should be constructed. Builders of expert systems must know whether their scheme for inexact reasoning works according to what the (probability) theory tells them.