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.

中文翻译：

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EXPRESS：光谱学中特定于样本的预测误差测量

在应用光谱学中，多变量校准的目的几乎完全是为了关联分析物浓度和光谱测量。多变量校准模型提供基于光谱测量的分析物浓度估计值。通常基于均方误差来评估预测性能。虽然这种平均度量可用于模型选择，但它不能令人满意地评估单个预测的不确定性。对于校准，不确定度是特定于样本的。对于可能存在干扰化合物的多变量校准尤其如此。考虑化学反应、生产等过程中的在线光谱测量。在这里，参考值不一定可用。因此，人们应该知道给定预测的不确定性，以便使用该预测来说明化学反应的状态，调整过程等。 在本文中，我们讨论了方差和偏差对多元样本特定预测误差的影响校准。我们将理论公式与在实验数据上获得的结果进行比较。结果表明，在实践中评估特定于样本的预测能力时，不能忽略偏差贡献。