In this thesis we develop several kinds of latent variable models in order to address three types of bio-statistical problem. The three problems are the treatment effect of carcinogens on tumour development, spatial interactions between plant species and motor unit number estimation (MUNE). The three types of data looked at are: highly heterogeneous longitudinal count data, quadrat counts of species on a rectangular lattice and lastly, electrophysiological data consisting of measurements of compound muscle action potential (CMAP) area and amplitude. Chapter 1 sets out the structure and the development of ideas presented in this thesis from the point of view of: model structure, model selection, and efficiency of estimation. Chapter 2 is an introduction to the relevant literature that has in influenced the development of this thesis. In Chapter 3 we use the EM algorithm for an application of an autoregressive hidden Markov model to describe longitudinal counts. The data is collected from experiments to test the effect of carcinogens on tumour growth in mice. Here we develop forward and backward recursions for calculating the likelihood and for estimation. Chapter 4 is the analysis of a similar kind of data using a more sophisticated model, incorporating random effects, but estimation this time is conducted from the Bayesian perspective. Bayesian model selection is also explored. In Chapter 5 we move to the two dimensional lattice and construct a model for describing the spatial interaction of tree types. We also compare the merits of directed and undirected graphical models for describing the hidden lattice. Chapter 6 is the application of a Bayesian hierarchical model (MUNE), where the latent variable this time is multivariate Gaussian and dependent on a covariate, the stimulus. Model selection is carried out using the Bayes Information Criterion (BIC). In Chapter 7 we approach the same problem by using the reversible jump methodology (Green, 1995) where this time we use a dual Gaussian-Binary representation of the latent data. We conclude in Chapter 8 with suggestions for the direction of new work. In this thesis, all of the estimation carried out on real data has only been performed once we have been satisfied that estimation is able to retrieve the parameters from simulated data. Keywords: Amyotrophic lateral sclerosis (ALS), carcinogens, hidden Markov models (HMM), latent variable models, longitudinal data analysis, motor unit disease (MND), partially ordered Markov models (POMMs), the pseudo auto- logistic model, reversible jump, spatial interactions.

Many neurodegenerative diseases are characterized by the accumulation of misfolded proteins that often share common morphological and biochemical features, and can similarly co-localize with several other proteins, including various chaperone proteins. Chaperone proteins, like heat shock protein 27 (HSP27), heme oxygenase 1 (HO-1) and clusterin, have been implicated as potent modulators of misfolded proteins, thus may play important roles in the pathogenesis of neurodegenerative diseases. The present study aims to investigate their roles in the pathogenesis of Frontotemporal lobar degeneration (FTLD), Alzheimer's disease (AD), Parkinson's disease (PD), and Motor neuron disease (MND) by determining their distribution and amount via immunohistochemical staining and western blotting in diseased and control subjects.There were distinct patterns of HSP27 and clusterin immunostaining in different brain regions. For HSP27, patients with AD and FTLD were in general more severely affected than were patients with MND and control subjects. For clusterin, patients with AD and FTLD were more severely affected than control subjects where neurons and glial cells were concerned, while patients with AD and control subjects were more severely affected than those with FTLD where diffuse and cored plaques were concerned. However, there were no obvious differences in the pattern of HO-1 immunostaining in various brain regions in patients with AD or FTLD relative to control subjects. Moreover, there was no association between HSP27, HO-1 and clusterin with disease or histological type, and the ‘classic’ neuropathological changes in FTLD, AD and MND were not immunoreactive to any of these proteins. There were significant correlations between the degrees of HO-1 and clusterin immunostaining in many brain areas for both AD and FTLD cases, and for all cases overall, but none between HSP27 and clusterin or HSP27 and HO-1. Present results suggest an involvement with ongoing cellular stress, misfolded or unfolded protein accumulation or the deficits/failure of other relevant protein quality control systems, in the pathogenesis of these neurodegenerative diseases. Present work may therefore have implications for the further development of ideas concerning the cause or treatment of neurodegenerative diseases where there is aberrant accumulation of misfolded, aggregated protein, and perhaps for conformational diseases in general. However, there are still many issues remain to be elucidated. Further research aimed at understanding the function and mechanisms of the chaperone system, and other protein quality control mechanisms, in the pathogenesis of neurodegenerative diseases is still needed.