Bayesian nonparametric confidence bounds for a distribution function

Consider the problem of estimating a distribution function F based on a random sample. A Bayesian nonparametric approach would proceed by placing a prior probability on the class of all distribution functions. The difficulty lies in conceptualizing the information that the prior, and later the posterior, is providing about the true distribution function. Specifically, when a Dirichlet process or a mixture of Dirichlet processes is used as a prior, the problem of finding a closed form expression for Bayesian confidence bounds pertaining to the entire distribution function remains unsolved. In this paper, we adopt the idea of simulating distribution functions as realizations of a random process to develop an approach for computing Bayesian confidence bounds.