Statistical Modelling in Chemistry - Applications to Nuclear Magnetic Resonance
and Polymerase Chain Reaction
Centre for Mathematical Sciences
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
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.
NMR spectroscopy, Gaussian noise, maximum likelihood estimation, Cramér-Rao
Diagnostic PCR, region of operability, detection probability, logistic
regression, experimental design.