Bayesian tolerance regions with an application to linear mixed models

TL;DR

This paper reviews Bayesian and frequentist tolerance regions, establishes conditions for Bayesian regions to have frequentist validity, and applies Bayesian tolerance intervals to linear mixed models in quality control.

Contribution

It introduces a computational strategy for Bayesian tolerance intervals in linear mixed models and compares Bayesian and frequentist approaches.

Findings

Bayesian regions can have frequentist validity under certain conditions

A new computational method for Bayesian tolerance intervals is proposed

Application to pharmaceutical quality control demonstrates practical utility

Abstract

We review and contrast frequentist and Bayesian definitions of tolerance regions. We give conditions under which for large samples a Bayesian region also has frequentist validity, and study the latter for smaller samples in a simulation study. We discuss a computational strategy for computing a Bayesian two-sided tolerance interval for a Gaussian future variable, and apply this to the case of possibly unbalanced linear mixed models. We illustrate the method on a quality control experiment from the pharmaceutical industry.