Functional graphical model for spectrometric data analysis

Motivated by the analysis of spectrographic data, we introduce a functional graphical model for learning the conditional independence structure of spectra. Absorbance spectra are modeled as continuous functional data through a cubic B-spline basis expansion. A Gaussian graphical model is assumed for basis ex- pansion coefficients, where a sparse structure is induced for the precision matrix. Bayesian inference is carried out, providing an estimate of the precision matrix of the coefficients, which translates into an estimate of the conditional independence structure between frequency bands of the spectrum. The proposed model is applied to the analysis of the infrared absorbance spectra of strawberry purees