Analytical method of estimating chemometric prediction error
Analytical method of estimating chemometric prediction error
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DOI：
10.1366/0003702971940882
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发表时间：
1997-05-01
影响因子：
3.5
通讯作者：
Feld, MS
中科院分区：
文献类型：
--
作者：
Berger, AJ;Feld, MS
我们提出了一个分析公式，估计线性多元校正，特别是偏最小二乘法（PLS）预测的浓度的不确定性。我们强调光谱数据的分析。推导解决了重要的限制，其中校准误差与预测光谱中的噪声相比可以忽略不计。该公式以标准PUS校准参数和频谱噪声幅度表示;因此可以直接进行评估。为了测试公式，我们进行了PLS分析模拟光谱和实验拉曼光谱的溶解在水中的生物分析物。在每种情况下，将预测的均方根误差与公式的估计值进行比较。在校准噪声低于预测噪声的情况下，获得了准确的不确定性估计，即使在噪声水平相等的情况下，也获得了令人惊讶的良好估计。通过比较测量和估计的不确定度，我们评估了每个偏最小二乘校准模型的稳健性。还讨论了预测不确定性与光谱信噪比的比例关系。
We present an analytical formula that estimates the uncertainty in concentrations predicted by linear multivariate calibration, particularly partial least-squares (PLS). We emphasize the analysis of spectroscopic data. The derivation addresses the important limit in which calibration error is negligible in comparison to noise in the prediction spectra. The formula is expressed in terms of standard PUS calibration parameters and the amplitude of spectral noise; it is therefore straightforward to evaluate. To test the formula, we performed PLS analysis upon simulated spectra and upon experimental Raman spectra of dissolved biological analytes in water. In each instance, the root-mean-squared error of prediction was compared to the estimate from the formula. Accurate uncertainty estimates were obtained in cases where calibration noise was lower than prediction noise, and surprisingly good estimates were obtained even when the noise levels were equal. By comparing measured and estimated uncertainties, we assessed the robustness of each PLS calibration model. The scaling of prediction uncertainty with the spectral signal-to-noise ratio is also discussed.