Bayesian wavelength selection in multicomponent analysis

Multicomponent analysis attempts to simultaneously predict the ingredients of a mixture. If near-infrared spectroscopy provides the predictor variables, then modern scanning instruments may offer absorbances at a very large number of wavelengths. Although it is perfectly possible to use whole spectrum methods (e.g. PLS, ridge and principal component regression), for a number of reasons it is often desirable to select a small number of wavelengths from which to construct the prediction equation relating absorbances to composition. This paper considers wavelength selection with a view to using the chosen wavelengths to simultaneously predict the compositional ingredients and is therefore an example of multivariate variable selection. It adopts a binary exclusion/inclusion latent variable formulation of selection and uses a Bayesian approach. Problems of search of the vast number of possible selected models are overcome by a Markov chain Monte Carlo sampling technique.