A set of recurrences is developed for computing the probability content of any prior or posterior confidence bands for a distribution function assuming the parameter of the prior Dirichlet process known. When the prior parameter is unknown and is estimated from the sample, nonparametric estimates of the probability content of the posterior bands are obtained.
"Bayesian Confidence Bands for a Distribution Function." Ann. Statist. 6 (3) 649 - 657, May, 1978. https://doi.org/10.1214/aos/1176344209