Bayesian linear regression and variable selection for spectroscopic calibration.

Area of Science:

• Chemometrics
• Statistical Modeling
• Spectroscopy

Background:

• Spectroscopic calibration models are crucial for quantitative analysis.
• Existing methods like partial least squares have limitations in predictive performance.
• Bayesian approaches offer a probabilistic framework for model development.

Purpose of the Study:

• To develop and evaluate a Bayesian approach for spectroscopic calibration.
• To incorporate variable selection within the Bayesian framework to improve predictions.
• To compare the performance of the proposed Bayesian models against established methods.

Main Methods:

• Formulation of a Bayesian linear regression model.
• Utilizing Bayesian evidence approximation for hyper-parameter estimation.
• Implementation of a variable selection strategy within the Bayesian framework.

Main Results:

• The proposed Bayesian calibration models demonstrated improved prediction results.
• The Bayesian approach showed superior performance compared to partial least squares.
• Variable selection within the Bayesian framework enhanced predictive performance.

Conclusions:

• Bayesian methods provide a robust framework for developing advanced spectroscopic calibration models.
• The integration of variable selection offers a significant advantage in predictive accuracy.
• This approach holds potential for multivariate response variable calibration.