Characterizing the Uncertainty in Near-Infrared Spectroscopic Prediction of Mixed-Oxygenate Concentrations in Gasoline:  Sample-Specific Prediction Intervals

Abstract

Oxygenates are added to gasoline to reduce exhaust emission levels of carbon monoxide and to boost octane. The U.S. National Institute of Standards and Technology (NIST) provides 12 Standard Reference Materials (SRMs) for single oxygenates in reference gasoline. A previous study demonstrated the feasibility of nondestructively quantifying oxygenate concentration in SRM gasoline ampules using near-infrared (near-IR) spectroscopy combined with multivariate calibration techniques. A drawback of this approach has been that an average prediction uncertainty, rather than a sample-specific one, is obtained. Recent developments in multivariate calibration theory for prediction error variance cure this problem. This report characterizes the significant sources of uncertainties in multivariate calibration using principal component regression and partial least-squares, validating near-IR and other multivariate spectroscopic techniques for use in assigning certified values (expected value with specified uncertainty) to selected materials. This report interprets prediction results in terms of multivariate analytical figures of merit, enabling the visualization of complex multivariate models as univariate graphs.

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

“…A literature survey shows that deriving formulas using the method of error propagation has been a major research topic. When employing first-order multivariate data, most publications are concerned with standard (i.e., linear) PLSR [22,23,[82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101] 8 The limit of detection is the analyte level that with sufficiently high probability (1 -β) will lead to a correct positive detection decision. The detection decision amounts to comparing the prediction ĉ with the critical level (L c ).…”

Simultaneous quantitative analysis of mebendazole polymorphs A–C in powder mixtures by DRIFTS spectroscopy and ANN modeling

“…In Table 3 is listed the observed polymorphic contents (%) of forms A-C, together with the values predicted by the ANN and the PLS model, and in Table 4 is listed the corresponding RMSEP (%), and linear regression parameters (coefficients of determination, slopes and intercepts) of observed vs predicted concentrations on the test subset selected by the Kennard-Stone algorithm, together with the limit of detection (LOD) calculated by the product 3× RMSEP, which is considered by Faber et al [38] as a reasonable approximation of the LOD. From Table 3 it is seen that the ANN model performs considerably better than the PLS model in the low content range, which means that it is more suitable than the PLS model for the quantitation of impurities.…”

Validation and Error

“…Most publications are concerned with standard PLSR, 19,20,[67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85] including the derivation of parameter results, which leads directly to a formula for standard error of prediction. Most publications are concerned with standard PLSR, 19,20,[67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85] including the derivation of parameter results, which leads directly to a formula for standard error of prediction.…”