Dynamic Bayesian Nonlinear Calibration

Abstract: Statistical calibration where the curve is nonlinear is important in many areas, such as analytical chemistry and radiometry. Especially in radiometry, instrument characteristics change over time, thus calibration is a process that must be conducted as long as the instrument is in use. We propose a dynamic Bayesian method to perform calibration in the presence of a curvilinear relationship between the reference measurements and the response variable. The dynamic calibration approach adequately derives time dependent calibration distributions in the presence of drifting regression parameters. The method is applied to microwave radiometer data and simulated spectroscopy data based on work by Lundberg and de Mar\'{e} (1980).