Statistical Modelling in Chemistry - Applications to Nuclear Magnetic Resonance and Polymerase Chain Reaction

Halfdan Grage

Centre for Mathematical Sciences
Mathematical Statistics
Lund University,
2002

ISBN 91-628-5459-3
LUNFMS--1013-2002

Abstract:

This thesis consists of two parts with the common theme of statistical modelling in chemistry. The first part is concerned with applications in nuclear magnetic resonance (NMR) spectroscopy, while the second part deals with applications in polymerase chain reaction (PCR).

The problems considered in the first part all have their origin in protein NMR spectroscopy, although they are treated mainly

from a statistical perspective in the thesis. The interpretation of complex and crowded protein NMR spectra contaminated by noise is a challenging task where the method of maximum likelihood based on the Gaussian distribution has been used with good results. In Paper A it is investigated under what conditions on the processing of the NMR signal the distributional assumptions usually made concerning the noise in the sampled signal may be appropriate. In Paper B some properties of the inverse Fisher information matrix pertaining to the model for a one-dimensional NMR signal are studied with respect to the influence of correlated noise and the problem of parameter resolution. In Paper C the combined effects of filtering and sampling are investigated in terms of their influence on the Cramér-Rao bounds for the estimated parameters of a one-dimensional NMR signal model. Finally, in Paper D a new algorithm, M-RELAX, for estimation of the parameters of several consecutive time series with amplitude decay is proposed. Such problems arise for instance in certain screening experiments in  medical drug discovery.

In the second part of the thesis some problems encountered in connection with diagnostic PCR analysis and detection of pathogenic bacteria in the food-chain are considered. The focus is on design of pre-PCR strategies for future routine analysis to get a reliable and robust detection of pathogenic Yersinia enterocolitica and Salmonella in complex samples from the food-chain. In Paper A a logistic regression model for the reliability of PCR detection of Yersinia enterocolitica is presented, whereby it is possible to define a practical operating range, determined by the model and a pre-specified detection probability. The development, through a statistical approach using screening, factorial design experiments and confirmatory tests, of a new medium specifically optimised for PCR is described in Paper B. A combined linear and logistic regression model for real-time PCR amplification and detection is presented in Paper C.

Key words:

NMR spectroscopy, Gaussian noise, maximum likelihood estimation, Cramér-Rao bounds, sampling.

Diagnostic PCR, region of operability, detection probability, logistic regression, experimental design.