Bayesian rule in the framework of uncertainty theory

In Bayesian rule an unknown parameter is thought to be a quantity whose variation can be characterized by a prior distribution. Then some data are observed from a population whose distribution function is indexed by the unknown parameter and then the prior distribution is updated according to the observed data. The updated prior distribution is named as the posterior distribution. Based on uncertainty theory, this paper first makes a connection between posterior uncertainty distribution and likelihood function, and proposes a new method to obtain the posterior uncertainty distribution from the prior uncertainty distribution with given observed data. Some examples with special uncertainty distributions are employed to explain the calculation. Furthermore, an uncertain urn problem is provided to illustrate the application of the new method.