Bayesian Intervals with Good Frequentist Behaviour in the Presence of Nuisance Parameters

Abstract

SUMMARY Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ1 . . ., θp), we are concerned with the problem of setting confidence intervals for a particular component of it, say θ1, treating the remaining components as a nuisance parameter. Adopting an objective Bayesian approach, we show that the Bayes intervals with a certain conditional prior density on the parameter of interest, θ1, are confidence intervals as well, having nearly the correct frequency of coverage. The frequentist performance of the proposed intervals is tested in a simulation study for gamma mean and shape parameters.