Revision of possibility distributions: A Bayesian inference pattern

In probability theory, the Bayes' rule of inference plays a central role as corroborated by the ever-increasing number of applications in various fiel ds. The rule allows to revise a prior probability distribution when new inf ormation becomes available; the posterior probability distribution takes th e form of a conditional distribution. Although several similarities between the possibilistic and probabilistic frameworks have already been reported, very few studies in possibility theory have dealt with Bayesian inference. The objective of this work is to thoroughly study this type of inference a nd to develop the counterpart of the Bayes' rule in the possibilistic frame work with the use of conditional possibility distributions. Application of possibility theory wherever Bayes' theory has already been applied can now be envisaged as a new perspective to uncertainty modeling and processing. I n the last part of this paper, the suitability of the proposed framework fo r the problem of forecast processing is discussed, and an example illustrat es the application of Various rules of inference corresponding to different aggregation operators. (C) 2000 Elsevier Science B.V. All rights reserved.