Bayesian statistical models with uncertainty variables

Bayesian statistical inference is an important method of mathematical statistics in which both sample information and prior information are employed. Traditionally, it is often assumed that the sample observations from the population are observed precisely and characterized by crisp values. However, in many cases, the sample observations are collected in an imprecise way and characterized by uncertain values. In this paper, based on uncertain theory, we propose three kinds of uncertain Bayesian statistical inference including Bayesian point estimation, Bayesian interval estimation and Bayesian hypothesis test. Some numerical examples of uncertain Bayesian inference are presented to illustrate the proposed methods.