Evaluating Maximum Likelihood Estimation Methods to Determine the Hurst Coefficient

A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5\u3cHS-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 210. A modified method is proposed to correct for this bias. It gives reliable estimates of H for both fd and fGn processes of length greater than or equal to 211

A physiologically based mathematical model of arterial pressure recordings

This thesis is concerned with the development of a mathematical model to concisely capture the direct effect of baroreceptor reflex response on arterial pressure. The development is motivated by the need to identify and quantify physiologically informative characteristics of arterial pressure recordings obtained from hypertensive and normotensive rat populations. Such a quantification can provide insight into and information about the particular functioning or malfunctioning behavior of the baroreceptor reflex which may result in hypertension. The mathematical model is a non-linear stochastic difference equation which incorporates the response of the baroreceptor reflex measured experimentally. The deterministic component of a simplified model and a related stochastic model are analyzed theoretically. The dynamics of the deterministic system are completely characterized. Furthermore, regions of the parameter space resulting in period two doubling bifurcations are identified. A comparison of these results with results obtained from an analysis of the stochastic model gives rise to theoretical connections between deterministic stability and stationarity. As an application, we use the model to obtain a physiologically based quantification of arterial pressure recordings. In particular, the quantification of baroreceptor reflex response derived from the physiologically based mathematical model is shown to distinguish between hypertensive and normotensive populations and is used in a gene mapping study. Significant correlations between marker genotypes and the model derived phenotypes are demonstrated; and, thus, the model is shown to provide a connection between gene location and function of the baroreceptor reflex response