Bayesian Wavelet-based Curve Classification via Discriminant Analysis with Markov Random Tree Priors.

Discriminant analysis is an effective tool for the classification of experimental units into groups. When the number of variables is much larger than the number of observations it is necessary to include a dimension reduction procedure into the inferential process. Here we present a typical example from chemometrics that deals with the classification of different types of food into species via near infrared spectroscopy. We take a nonparametric approach by modeling the functional predictors via wavelet transforms and then apply discriminant analysis in the wavelet domain. We consider a Bayesian conjugate normal discriminant model, either linear or quadratic, that avoids independence assumptions among the wavelet coefficients. We introduce latent binary indicators for the selection of the discriminatory wavelet coefficients and propose prior formulations that use Markov random tree (MRT) priors to map scale-location connections among wavelets coefficients. We conduct posterior inference via MCMC methods, we show performances on our case study on food authenticity and compare results to several other procedures..