Hierarchical Bayesian Calibration of Untested Devices

Abstract

We consider calibration of mass-produced measuring devices and extend inferences from tested devices to untested ones. When the reference instrument is subject to measurement error, and particularly when point and interval predictions from an untested device are desired, Landes et al. (2006) appear to be the first to introduce a suitable method. Landes et al. employed a Bayes hierarchical model for this problem, but omited a full description of the method and its statistical properties. This work provides the details of the method, an abbreviated illustration of a real calibration experiment, and the method's statistical properties.

Keywords:

• Covariate measurement error
• Inverse prediction
• Markov chain Monte Carlo

Mathematics Subject Classification:

• 62-XX
• 62-07
• 62F15
• 62Hxx
• 62Jxx

Acknowledgments

The author thanks Stephen B. Vardeman for his direction of this work when the author was writing his dissertation.