Multivariate calibration uncertainty

The uncertainty in multivariate calibration is characterized with respect to the evaluation functions at Eqs. (6.75) and (6.79). The prediction of a row vector x of dimension n from a row vector y of dimension m results from... 

A. C. Olivieri, N. M. Faber, J. Ferre, R. Boque, J. H. Kalivas and H. Mark, Uncertainty estimation and figures of merit for multivariate calibration (lUPAC Technical Report), Pure Appl. Chem., 78, 2006, 633-661. 

Olivieri, A.C., A simple approach to uncertainty propagation in preprocessed multivariate calibration, J. Chemom., 16, 207-217, 2002. 

International Union of Pure and Applied Chemistry, Guidelines for Calibration in Analytical Chemistry. Uncertainty Estimation and Figures of Merit for Multivariate Calibration, 2006. 

Ohvieri A, Faber NM, Ferre J, Bouque R, Kalivas JH, Mark H. Guidelines for calibration in analytical chemistry. Part 3. Uncertainty estimation of figures of merit for multivariate calibration. Pure Appl Chem 2006 78 633-61. 

Discriminant Analysis (DA) is a multivariate statistical method that generates a set of classification functions that can be used to predict into which of two or more categories an observation is most likely to fall, based on a certain combination of input variables. DA may be more effective than regression for relating groundwater age to major ion hydrochemistry and well construction because it can account for complex, non-continuous relationships between age and each individual variable used in the algorithm while inherently coping with uncertainty in the age values used for calibration, and there is no need to... 

Equation (4.20) was proposed by Hoskuldsson [65] many years ago and has been adopted by the American Society for Testing and Materials (ASTM) [59]. It generalises the univariate expression to the multivariate context and concisely describes the error propagated from three uncertainty sources to the standard error of the predicted concentration calibration concentration errors, errors in calibration instrumental signals and errors in test sample signals. Equations (4.19) and (4.20) assume that calibrations standards are representative of the test or future samples. However, if the test or future (real) sample presents uncalibrated components or spectral artefacts, the residuals will be abnormally large. In this case, the sample should be classified as an outlier and the analyte concentration cannot be predicted by the current model. This constitutes the basis of the excellent outlier detection capabilities of first-order multivariate methodologies. 

Einbu et al. (4) also assessed the use of a combination of FTIR spectroscopy and a multivariate model for composition predictions, but applied to a CO2 absorption process using aqueous MEA. They constructed a model based on a very extensive calibration set of 86 samples, covering MEA concentration of 10 to 80 wt% and CO2 eoneentration of 0.0 to 0.5 mol CO2 per mol amine. Based on these calibration samples, the model was calculated to have a relative predictive uncertainty of 1.4% for MEA and 3.0% for CO2. It has also successfully been use for continuous in-line monitoring of an operating pilot plant, but no quantitative results for the prediction accuracy ate given. 

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