[Paper Review] Bayesian Modeling and Computation for Analyte Quantification in Complex Mixtures Using Raman Spectroscopy

Ningren Han, Rajeev J. Ram|arXiv (Cornell University)|May 20, 2018

Spectroscopy and Chemometric AnalysesChemistry35 references4 citations

TL;DR

This paper proposes a two-stage Bayesian framework for quantifying analyte concentrations in complex mixtures using Raman spectroscopy, leveraging hierarchical modeling and reversible-jump Markov chain Monte Carlo (RJMCMC) for joint peak detection and concentration estimation. It demonstrates superior performance over conventional multivariate regression under small training sample regimes, particularly in baseline correction and peak identification, with validated results on glucose quantification in biopharmaceutical process monitoring data.

ABSTRACT

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.

Motivation & Objective

• To address the challenge of analyte quantification in complex mixtures when large, high-quality training datasets are unavailable.
• To develop a unified framework that jointly estimates spectral peaks and baseline signals, reducing bias from sequential processing.
• To improve quantification accuracy in Raman spectroscopy under small sample sizes and noisy, autofluorescent backgrounds.
• To provide a complementary alternative to conventional multivariate regression methods like PLSR and PCR in biopharmaceutical process monitoring.

Proposed method

• Employs a hierarchical Bayesian model to represent spectral signals with mixture components for peaks and baseline.
• Uses reversible-jump Markov chain Monte Carlo (RJMCMC) for trans-dimensional model selection and joint estimation of peak locations, intensities, and baseline parameters.
• Processes data in two stages: first, learns analyte-specific peak representations from reference spectra; second, applies these to estimate concentrations in mixtures.
• Incorporates g-prior distributions for variable selection and regularization in the regression component.
• Models baseline as a non-linear, smooth function using splines or polynomial terms within the Bayesian framework.
• Performs model inference via MCMC sampling with reversible jumps to explore varying numbers of spectral components.

Experimental results

Research questions

• RQ1 Can a Bayesian framework jointly estimate spectral peaks and baseline in Raman spectra more accurately than sequential methods?
• RQ2 How does the proposed method compare to conventional multivariate regression (e.g., PLSR) in terms of quantification accuracy under limited training data?
• RQ3 To what extent can the two-stage Bayesian approach reduce bias from baseline correction in autofluorescent biological samples?
• RQ4 Can the method reliably estimate analyte concentrations in mixtures without requiring extensive calibration datasets?

Key findings

• The proposed Bayesian method outperforms conventional multivariate regression algorithms in analyte quantification under small training sample sizes, particularly in noisy or complex spectral environments.
• The RJMCMC-based model selection effectively identifies the correct number of spectral peaks and baseline components, reducing overfitting and estimation bias.
• In experimental Raman data from biopharmaceutical processes, the method achieved accurate glucose concentration estimation with minimal calibration data.
• The two-stage approach enables robust peak representation learning from limited reference spectra, improving generalization to mixture samples.
• The method demonstrated improved stability and lower prediction error compared to PLSR when training data were scarce or noisy.
• Baseline correction was implicitly handled within the Bayesian framework, avoiding errors introduced by separate baseline subtraction steps.