We characterize priors which asymptotically match the posterior
coverage probability of a Bayesian prediction region with the corresponding
frequentist coverage probability. This is done considering both posterior
quantiles and highest predictive density regions with reference to a future
observation. The resulting priors are shown to be invariant under
reparameterization. The role of Jeffreys’ prior in this regard is also
investigated. It is further shown that, for any given prior, it may be possible
to choose an interval whose Bayesian predictive and frequentist coverage
probabilities are asymptotically matched.