Probability matching priors for two-sided tolerance intervals in balanced one-way and two-way nested random effects models

Abstract

We consider two-sided Bayesian tolerance intervals, with approximate frequentist validity, for a future observation in balanced one-way and two-way nested random effects models. Probability matching conditions, specific to this problem, are derived in either case via a technique that involves inversion of approximate posterior characteristic functions. In addition to yielding probability matching priors for the present problem, these conditions are useful in evaluating certain other priors that have received attention in the literature.

Keywords:

• frequentist validity
• posterior characteristic function
• shrinkage argument

Acknowledgements

We thank the referees for very constructive suggestions. This work was supported by a grant from the Indian Institute of Management Calcutta.