Chapter 1 gives a brief background to Exercise Testing and its importance as well as a literature review of relevant topics including reproducibility, comparability, components of variance and the estimation of common correlation; the latter two are essential building blocks for the estimation of Comparability. Chapter 2 deals with the estimation of measurement reproducibility of data from mixed effects models involving two variance components. Two approaches, one based on sums of squares and the other on Profile Likelihood are used for the separate cases of balanced and unbalanced data. This is carried out in two distinct contexts, one for simple replication and the other assuming an order effect to the replications. Applicability of the approaches to Exercise Testing data shows that while point estimates from both approaches are often identical, interval estimates from the Profile Likelihood approach tend to be narrower. Chapter 3 involves a simulation study to investigate and assess the performances of the two approaches. Data are simulated from a variety of underlying configurations and the performances then compared according to three statistical criteria. The results of this study again favour the Profile Likelihood approach. The estimation of Comparability between two variables is the other aspect of the thesis put forward in chapter 4 where, first of all, the estimation of a common correlation coefficient from a population of correlation coefficients is considered. Five different methods for point and interval estimation of a common correlation coefficient are introduced. An illustrative example using data from an Exercise Testing procedure is used to compare the performances of the methods. Further investigation on the performances of the five methods was carried out by means of a simulation study across a variety of underlying configurations. The overall results suggest the 'Fisher method' as the best method of point and interval estimate of common correlation. Finally, chapter 6 outlines the conclusions from the previous chapters and suggests some ideas for further work.

Environmental statistics are known to be important factors shaping our perceptual system. The visual and auditory systems have evolved to be effcient for processing natural images or speech. The com- mon characteristics between natural images and speech are that they are both highly structured, therefore having much redundancy. Our perceptual system may use redundancy reduction and sparse coding strategies to deal with complex stimuli every day. Both redundancy reduction and sparse coding theory emphasise the importance of high order statistics signals. This thesis includes psycho-acoustical experiments designed to inves- tigate how higher order statistics affect our speech perception. Sparse- ness can be defined by the fourth order statistics, kurtosis, and it is hypothesised that greater kurtosis should be reflected by better speech recognition performance in noise. Based on a corpus of speech mate- rial, kurtosis was found to be significantly correlated to the glimps- ing area of noisy speech, an established measure that predicts speech recognition. Kurtosis was also found to be a good predictor of speech recognition and an algorithm based on increasing kurtosis was also found to improve speech recognition score in noise. The listening experiment for the first time showed that higher order statistics are important for speech perception in noise. It is known the hearing impaired listeners have diffculty understand- ing speech in noise. Increasing kurtosis of noisy speech may be par- ticularly helpful for them to achieve better performance. Currently, neither hearing aids nor cochlear implants help hearing impaired users greatly in adverse listening enviroments, partly due to having a re- duced dynamic range of hearing. Thus there is an information bot- tleneck, whereby these devices must transform acoustical sounds with a large dynamic range into the smaller range of hearing impaired lis- teners. The limited dynamic range problem can be thought of as a communication channel with limited capacity. Information could be more effciently encoded for such a communication channel if redun- dant information could be reduced. For cochlear implant users, un- wanted channel interaction could also contribute lower speech recog- nition scores in noisy conditions. This thesis proposes a solution to these problems for cochlear im- plant users by reducing signal redundancy and making signals more sparse. A novel speech processing algorithm, SPARSE, was devel- oped and implemented. This algorithm aims to reduce redundant information and transform signals input into more sparse stimulation sequences. It is hypothesised that sparse firing patterns of neurons will be achieved, which should be more biological efficient based on sparse coding theory. Listening experiments were conducted with ten cochlear implant users who listened to speech signals in modulated and speech babble noises, either using the conventional coding strat- egy or the new SPARSE algorithm. Results showed that the SPARSE algorithm can help them to improve speech understanding in noise, particularly for those with low baseline performance. It is concluded that signal processing algorithms for cochlear implants, and possibly also for hearing aids, that increase signal sparseness may deliver ben- efits for speech recognition in noise. A patent based on the algorithm has been applied for.