Frequentist validity of posterior quantiles in the presence of a nuisance parameter: Higher order asymptotics

Abstract

SUMMARY Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ 1 , θ 2 ), we are concerned with frequentist validity, up to o ( n −1 ), of posterior quantiles of θ 1 , treating θ 2 as a nuisance parameter. We propose to make the best choice of the prior on θ by matching, as far as practicable, the posterior and frequentist coverage probabilities up to o ( n −1 ).