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Bayesian linear regression and variable selection for spectroscopic calibration

Lookup NU author(s): Professor Elaine Martin

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Abstract

This paper presents a Bayesian approach to the development of spectroscopic calibration models By. formulating the linear regression in a probabilistic framework, a Bayesian linear regression model is derived, and a specific optimization method, i.e. Bayesian evidence approximation, is utilized to estimate the model "hyper-parameters". The relation of the proposed approach to the calibration models in the literature is discussed, including ridge regression and Gaussian process model. The Bayesian model may be modified for the calibration of multivariate response variables. Furthermore. a variable selection strategy is implemented within the Bayesian framework, the motivation being that the predictive performance may be improved by selecting a subset of the most informative spectral variables. The Bayesian calibration models are applied to two spectroscopic data sets, and they demonstrate improved prediction results in comparison with the benchmark method of partial least squares. (C) 2008 Elsevier B,V. All rights reserved.

Publication metadata

Author(s): Chen T, Martin E

Publication type: Article

Publication status: Published

Journal: Analytica Chimica Acta

Year: 2009

Volume: 631

Issue: 1

Pages: 13-21

ISSN (print): 0003-2670

ISSN (electronic): 1873-4324

Publisher: Elsevier BV

URL: http://dx.doi.org/10.1016/j.aca.2008.10.014

DOI: 10.1016/j.aca.2008.10.014

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