The Classification Limit of Detection: Estimating Sample-Level Classification Uncertainty in Spectroscopy Using Monte Carlo Error Propagation of Spectral Noise

Abstract

This study presents a novel Monte Carlo–based methodology for estimating classification uncertainty in chemometric models by propagating spectral measurement noise. Unlike traditional approaches that treat classification as deterministic, this method simulates realistic noise structures, both independent and correlated, captured from multiple spectrum measurements to quantify sample-specific uncertainty. The technique is applicable to both linear and non-linear models, including partial least squares discriminant analysis (PLS-DA) and various support vector machine (SVM) kernels. The methodology was validated using three datasets: synthetic 2D simulations for controlled model geometry, X-ray fluorescence (XRF) spectra from colored glass rods, and laser-induced breakdown spectroscopy (LIBS) data from Dalbergia wood species. Results revealed that uncertainty increases with spectral similarity and perpendicular alignment between noise structures and decision boundaries. In real-world applications, classification metrics alone proved insufficient to assess model reliability. The inclusion of uncertainty intervals enabled identification of ambiguous predictions even in cases of perfect classification accuracy. This work advances chemometric analysis by linking measurement uncertainty to classification outcomes, offering a robust framework for decision-making in high-stakes analytical contexts.