The focus of interest in a statistical calibration problem is the estimation of an unknown regressor valuex0 corresponding to an observed responsey0. A calibration experiment is typically carried out in two stages. At a first stage of data collection, responses are observed corresponding toknown regressor values; from these observations information is obtained about the regression relationship. At a second stage of data collection, one or more responses are observed which correspond to anunknown value of the regressor; estimation of this unknown regressor value is of primary importance. In this paper, we consider the calibration problem for polynomial regression models. In particular, a reference prior and corresponding posterior inferences are derived. The results are illustrated with an example, and comparisons are made between the polynomial reference prior analysis and alternative analyses.
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