Sage Journals: Discover world-class research

Abstract

The calibration paradigm for near infrared (NIR) spectroscopy is explored in a Bayesian framework in which a model for the dependence of the NIR spectrum on the composition of the sample is combined with a prior distribution representing beliefs about the composition of the sample to be predicted. With appropriate choices for this prior distribution, it is possible to reproduce standard regression results, remove the shrinkage to the mean that is sometimes seen as a problem in inverse regression, or improve predictions by taking account of non-standard distributions of composition in the population of interest. These options are illustrated by applying them to the prediction of wheat and sunflower content using a database of 7532 commercial animal feed samples which has been studied extensively in the past. Various options for the modelling of the relationship between spectra and composition are investigated, including linear and non-linear regressions and a non-parametric approach based on kernels. This Bayesian kernel approach, which has features in common with local calibration methods, gave results better than anything previously achieved with the animal feed database.

Keywords

NIR spectroscopy calibration inverse classical empirical non-linear local Bayes kernel density estimation compound feedstuff

Get full access to this article

View all access options for this article.

References

Norris

K.H.

Barnes

R.F.

Moore

J.E.

and Shenk

J.S.

, “Predicting forage quality by infrared reflectance spectroscopy”, J. Anim. Sci. 43, 889 (1976).

Martens

and Næs

, Multivariate Calibration. John Wiley & Sons Ltd, Chichester, UK (1989).

Næs

Kvaal

Isaksson

and Miller

, “Artificial neural networks in multivariate calibration”, J. Near Infrared Spectrosc. 1, 1 (1993). doi: 10.1255/jnirs.1.

Cogdill

R.P.

and Dardenne

, “Least-squares support vector machines for chemometrics: An introduction and evaluation”, J. Near Infrared Spectrosc. 12, 93 (2004). doi: 10.1255/jnirs.412.

Davies

A.M.C.

and Fearn

, “Quantitative analysis via near infrared databases: Comparison analysis using restructured near infrared and constituent data-deux (CARNAC-D)”, J. Near Infrared Spectrosc. 14, 403 (2006). doi: 10.1255/jnirs.712.

Pérez-Marín

Garrido-Varo

and Guerrero

J.E.

, “Implementation of LOCAL algorithm with near-infrared spectroscopy for compliance assurance in compound feedingstuffs”, Appl. Spectrosc. 59, 69 (2005). doi: 10.1366/0003702052940585.

Pérez-Marín

Garrido-Varo

Guerrero

J.E.

and Gutiérrez-Estrada

J.C.

, “Use of artificial neural networks in near-infrared reflectance spectroscopy calibrations for predicting the inclusion percentages of wheat and sunflower meal in compound feedingstuffs”, Appl. Spectrosc. 60, 1062 (2006). doi: 10.1366/000370206778397506.

Pérez-Marín

Garrido-Varo

Guerrero

J.E.

Fearn

and Davies

A.M.C.

, “Advanced non-linear approaches for predicting the ingredient composition in compound feedingstuffs by near-infrared reflection spectroscopy”, Appl. Spectrosc. 62, 536 (2008). doi: 10.1366/000370208784344389.

Lee

P.M.

, Bayesian Statistics an Introduction, 3rd Edn. Arnold, London, UK (2004).

10.

Gelman

Carlin

J.B.

Stern

H.S.

and Rubin

D.B.

, Bayesian Data Analysis, 2nd Edn. Chapman and Hall/CRC, London, UK (2004).

11.

Brown

P.J.

, Measurement, Regression and Calibration. Clarendon Press, Oxford, UK (1993).

12.

Fearn

, “Flat or natural? A note on the choice of calibration samples”, in Near Infra-Red Spectroscopy: Bridging the Gap between Data Analysis and NIR Applications, Ed by Hildrum

K.I.

Isaksson

Næs

and Tandberg

Ellis Horwood, Chichester, UK, p. 61 (1992).

13.

Lwin

and Maritz

J.S.

, “A note on the problem of statistical calibration”, J. R. Statist. Soc., C 29, 135 (1980).

14.

Brown

P.J.

, “Multivariate calibration”, J. R. Statist. Soc., B 44, 287 (1982).

15.

de Boor

, A Practical Guide to Splines. Springer Verlag, New York, USA (1978).

16.

Wand

M.P.

and Jones

M.C.

, Kernel Smoothing. Chapman and Hall/CRC, London, UK (2004).

Inverse,Classical,Empirical and Non-Parametric Calibrations in a Bayesian Framework

Abstract

Keywords

Get full access to this article

References