Bayesian inference with uncertain data of imprecise observations

Bayesian inference is a technique of statistical inference which uses the Bayes’ theorem to update the probability distribution as new observed data are available. Uncertain variables are a tool of modeling imprecisely observed quantities associated with experiential information. By integrating Bayesian inference and uncertain variables, this paper proposes an approach of uncertain Bayesian inference to deal with Bayesian inference problems involving imprecise observations. The posterior distribution is derived which gives the probability distribution of an unknown parameter conditional on uncertain observations. And based on the posterior distribution, some inference problems including the point estimation, the interval estimation and the Bayesian prediction, are investigated.