Abstract
In applied spectroscopy, the purpose of multivariate calibration is almost exclusively to relate analyte concentrations and spectroscopic measurements. The multivariate calibration model provides estimates of analyte concentrations based on the spectroscopic measurements. Predictive performance is often evaluated based on a mean squared error. While this average measure can be used in model selection, it is not satisfactory for evaluating the uncertainty of individual predictions. For a calibration, the uncertainties are sample specific. This is especially true for multivariate calibration, where interfering compounds may be present. Consider in-line spectroscopic measurements during a chemical reaction, production, etc. Here, reference values are not necessarily available. Hence, one should know the uncertainty of a given prediction in order to use that prediction for telling the state of the chemical reaction, adjusting the process, etc. In this paper, we discuss the influence of variance and bias on sample-specific prediction errors in multivariate calibration. We compare theoretical formulae with results obtained on experimental data. The results point towards the fact that bias contribution cannot necessarily be neglected when assessing sample-specific prediction ability in practice.
Highlights
Prediction uncertainty estimation is important for instance when using spectroscopic measurements for telling the state of a chemical reaction or doing process control.[1]
We compare sample-specific prediction errors obtained from experimental data with the sample-specific errors derived from theoretical formulae
By investigating leverages and squared residuals, we found that the calibration data are representative for the prediction samples
Summary
Prediction uncertainty estimation is important for instance when using spectroscopic measurements for telling the state of a chemical reaction or doing process control.[1] In such cases, a calibration model is fitted using a set of spectroscopic measurements with corresponding reference values. When applying the calibration model, for example during production, reference values are (normally) not available. One must solely rely on predicted values when controlling the process. In such situation, good estimates of sample-specific prediction errors are necessary to judge the validity of the prediction. We compare sample-specific prediction errors obtained from experimental data with the sample-specific errors derived from theoretical formulae
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