Variance Reduction in Analytical Chemistry : New Numerical Methods in Chemometrics and Molecular Simulation
Abstract: This thesis is based on five papers addressing variance reduction in different ways. The papers have in common that they all present new numerical methods.Paper I investigates quantitative structure-retention relationships from an image processing perspective, using an artificial neural network to preprocess three-dimensional structural descriptions of the studied steroid molecules.Paper II presents a new method for computing free energies. Free energy is the quantity that determines chemical equilibria and partition coefficients. The proposed method may be used for estimating, e.g., chromatographic retention without performing experiments.Two papers (III and IV) deal with correcting deviations from bilinearity by so-called peak alignment. Bilinearity is a theoretical assumption about the distribution of instrumental data that is often violated by measured data. Deviations from bilinearity lead to increased variance, both in the data and in inferences from the data, unless invariance to the deviations is built into the model, e.g., by the use of the method proposed in paper III and extended in paper IV.Paper V addresses a generic problem in classification; namely, how to measure the goodness of different data representations, so that the best classifier may be constructed. Variance reduction is one of the pillars on which analytical chemistry rests. This thesis considers two aspects on variance reduction: before and after experiments are performed. Before experimenting, theoretical predictions of experimental outcomes may be used to direct which experiments to perform, and how to perform them (papers I and II). After experiments are performed, the variance of inferences from the measured data are affected by the method of data analysis (papers III-V).
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