Inverse, Classical, Empirical and Non-Parametric Calibrations in a Bayesian Framework

Abstract

The calibration paradigm for near infrared (NIR) spectroscopy is explored in a Bayesian framework in which a model for the dependence of the NIR spectrum on the composition of the sample is combined with a prior distribution representing beliefs about the composition of the sample to be predicted. With appropriate choices for this prior distribution, it is possible to reproduce standard regression results, remove the shrinkage to the mean that is sometimes seen as a problem in inverse regression, or improve predictions by taking account of non-standard distributions of composition in the population of interest. These options are illustrated by applying them to the prediction of wheat and sunflower content using a database of 7532 commercial animal feed samples which has been studied extensively in the past. Various options for the modelling of the relationship between spectra and composition are investigated, including linear and non-linear regressions and a non-parametric approach based on kernels. This Bayesian kernel approach, which has features in common with local calibration methods, gave results better than anything previously achieved with the animal feed database.