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.