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arXiv · 2209.08496

Bayesian tolerance regions with an application to linear mixed models

X. Gregory Chen·Aad van der Vaart
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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.

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X. Gregory Chen, Aad van der Vaart. 2022-09-18. Bayesian tolerance regions with an application to linear mixed models. https://arxiv.org/abs/2209.08496

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