Prediction range estimation from noisy Raman spectra with robust optimization.

Inferences need to be drawn in biological systems using experimental multivariate data. The number of samples collected in many such experiments is small, and the data are noisy. We present and study the performance of a robust optimization (RO) model for such situations. We adapt this model to generate a minimum and a maximum estimation of analyte concentration for a given sample, producing a prediction range. The calibration model was applied to sets of Raman spectra. In particular we used normal Raman measurements of pyridine/deuterated pyridine mixtures and spectra from a more complex glucose detection system based on surface-enhanced Raman spectroscopy. The results from the RO model were compared with prediction intervals estimated from partial least squares (PLS) method. We find that the RO prediction ranges included the actual concentration value of the sample more consistently than the 99% prediction intervals built with PLS methods.