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 9162854593
LUNFMS10132002

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 onedimensional 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 CramérRao bounds for the
estimated parameters of a onedimensional NMR signal model. Finally, in Paper
D a new algorithm, MRELAX, 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
foodchain are considered. The focus is on design of prePCR strategies for
future routine analysis to get a reliable and robust detection of pathogenic
Yersinia enterocolitica and Salmonella in complex samples from
the foodchain. 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 prespecified 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 realtime PCR amplification
and detection is presented in Paper C.




Key words:

NMR spectroscopy, Gaussian noise, maximum likelihood estimation, CramérRao
bounds, sampling.

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