Application of the transferable belief model to diagnostic problems

Uncertainty is classically represented by probability functions, and diagnostic in an environment poised by uncertainty is usually handled through the application of the Bayesian theorem that permits the computation of the posterior probability over the diagnostic categories given the observed data from the prior probability over the same categories. We show here that the whole problem admits a similar solution when uncertainty is quantified by belief functions as in the transferable belief model. The classical Bayesian theorem admits a generalization within the transferable belief model (TBM) that we called the Generalized Bayesian Theorem (Smets, 1978, 1981, 1993a).