  In this work, we propose a two-stage algorithm based on Bayesian modeling and
computation aiming at quantifying analyte concentrations or quantities in
complex mixtures with Raman spectroscopy. A hierarchical Bayesian model is
built for spectral signal analysis, and reversible-jump Markov chain Monte
Carlo (RJMCMC) computation is carried out for model selection and spectral
variable estimation. Processing is done in two stages. In the first stage, the
peak representations for a target analyte spectrum are learned. In the second,
the peak variables learned from the first stage are used to estimate the
concentration or quantity of the target analyte in a mixture. Numerical
experiments validated its quantification performance over a wide range of
simulation conditions and established its advantages for analyte quantification
tasks under the small training sample size regime over conventional
multivariate regression algorithms. We also used our algorithm to analyze
experimental spontaneous Raman spectroscopy data collected for glucose
concentration estimation in biopharmaceutical process monitoring applications.
Our work shows that this algorithm can be a promising complementary tool
alongside conventional multivariate regression algorithms in Raman
spectroscopy-based mixture quantification studies, especially when collecting a
large training dataset with high quality is challenging or resource-intensive.
