Probabilistic Abduction Without Priors

Abstract

This paper considers the simple problem of abduction in the
framework of Bayes theorem, i.e. computing a posterior probability of an hypothesis when its prior probability is not available, either because there are no statistical data on which to rely on, or simply because a human
expert is reluctant to provide a subjective assessment of this
prior probability. The  problem remains an open issue since a
simple sensitivity analysis on the value of the unknown prior
yields empty results. This paper tries to survey and comment on
various solutions to this problem: the use of likelihood functions
(as in classical statistics), the use of information principles
like maximal entropy, Shapley value, maximum likelihood. We also
study the problem in the setting of de Finetti coherence approach,
which does not exclude conditioning on contingent events with zero
probability. We show that the ad hoc likelihood function method,
that can be reinterpreted in terms of possibility theory,  is
consistent with most other formal approaches. However, the maximal
entropy solution is significantly different.