Constructing guaranteed and mean coverage Bayesian tolerance intervals in an unbalanced one-way random effects model with heterogeneous error variances

This study introduces a Bayesian framework for constructing the two-sided mean coverage tolerance interval, alongside the one-sided and two-sided guaranteed coverage tolerance intervals for an unbalanced one-way random effects model with heterogeneous error variances. The Bayesian simulation technique originally proposed by Wolfinger was utilized to develop the two-sided Bayesian guaranteed coverage tolerance interval. Inference of the posterior distribution of the variance components was conducted utilizing the generalized No U-Turn Sampler (NUTS). The performance of the intervals under different forms of a general class of priors was substantiated by a comprehensive simulation study, validating the selection of an optimal non-informative prior, that would result in intervals that are robust against varying degrees of heteroskedasticity and unbalancedness. Finally, a real-data application demonstrates the execution and practicality of the procedure.