Updating uncertain information

Abstract

In this paper, it is considered the concept of conditioning for a family of possible probability distributions. First, the most used definitions are reviewed, in particular, Dempster conditioning, and upper-lower probabilities conditioning. It is shown that the former has a tendency to be too informative, and the last, by the contrary, too uninformative. Another definitions are also considered, as weak and strong conditioning. After, a new concept of conditional information is introduced. It is based on lower-upper probabilities definition, but introduces an estimation of the true probability distribution, by a method analogous to statistical maximum likelihood.

Finally, it is deduced a Bayes formula in which there is no ’a prior’ information. This formula is used to combine informations from different sources and its behavior is compared with Dempster formula of combining informations. It is shown that our approach is compatible with operations with fuzzy sets.

This research was supported by the European Economic Community under Project DRUMS (ESPRIT B.R.A. 3085)