Y. Pan et Gj. Klir, BAYESIAN-INFERENCE BASED ON INTERVAL-VALUED PRIOR DISTRIBUTIONS AND LIKELIHOODS, Journal of intelligent & fuzzy systems, 5(3), 1997, pp. 193-203
Although Bayesian inference has been successful in many applications,
its serious limitation is the requirement that exact prior probabiliti
es be available. It has increasingly been recognized that this require
ment is often not realistic. To overcome this limitation of classical
Bayesian inference, we investigate a generalized Bayesian inference, i
n which prior probabilities as well as likelihoods are interval-valued
. Employing the tools of interval analysis and the theory of imprecise
probabilities, we develop a method for exact calculation of interval-
valued posterior probabilities for gh,en interval-valued prior probabi
lities and precise or interval-valued likelihoods. This method is furt
her generalized for fuzzy likelihood and fuzzy probabilities later. Th
e classical Bayesian inference is a special case of our method.