Coverage Properties of One-Sided Intervals in the Discrete Case and Application to Matching Priors.

We consider asymptotic coverage properties of one-sided posterior confidence intervals for discrete distributions, with a unidimensional parameter of interest and a nuisance parameter of arbitrary dimension. In this case, no higher order asymptotic expansion of the frequentist coverage for these intervals is established, lest some randomization is added. We study here the existence of such frequentist expansions and we propose simple continuity corrections based on a uniform random vector.