Hierarchical Bayesian Statistical Analysis for a Calibration Experiment

In this paper, hierarchical Bayes analyses of an experiment conducted to enable calibration of a set of mass-produced resistance temperature devices (RTDs) are considered. These were placed in batches into a liquid bath with a precise National Institute of Standards and Technology (NIST)-approved thermometer, and resistances and temperatures were recorded approximately every 30 s. Under the assumptions that the thermometer is accurate and each RTD responds linearly to temperature change, hierarchical Bayes methods to estimate the parameters of the linear calibration equations are used. Predictions of the parameters for an untested RTD of the same type and interval estimates of temperature based on a realized resistance reading are also available for both the tested RTDs and an untested one