Credible and con'dence sets for restricted parameter spaces

Recent experiments in high-energy physics have sparked interest in problems where a parameter is restricted to a portion of its natural range—for example, a positive normal mean or a Poisson mean that is known to exceed some background level. A recent article has shown that the Bayesian credible intervals that arise when the parameter is given a uniform distribution over the restricted range have good frequentist coverage probabilities. Here, the latter result is examined for robustness when nuisance parameters are included in the model. It is shown that the frequentist coverage probabilities are still high, but there is a mild surprise in the nature of the intervals. c © 2002 Elsevier Science B.V. All rights reserved.