ANALYTICAL METHOD OF ESTIMATING CHEMOMETRIC PREDICTION ERROR

We present an analytical formula that estimates the uncertainty in con centrations predicted by linear multivariate calibration, particularly partial least-squares (PLS). We emphasize the analysis of spectroscop ic data. The derivation addresses the important limit in which calibra tion error is negligible in comparison to noise in the prediction spec tra. The formula is expressed in terms of standard PUS calibration par ameters and the amplitude of spectral noise; it is therefore straightf orward to evaluate. To test the formula, we performed PLS analysis upo n simulated spectra and upon experimental Raman spectra of dissolved b iological analytes in water. In each instance, the root-mean-squared e rror of prediction was compared to the estimate from the formula. Accu rate uncertainty estimates were obtained in cases where calibration no ise was lower than prediction noise, and surprisingly good estimates w ere obtained even when the noise levels were equal. By comparing measu red and estimated uncertainties, we assessed the robustness of each PL S calibration model. The scaling of prediction uncertainty with the sp ectral signal-to-noise ratio is also discussed.