This paper investigates the nature of model error in complex deterministic nonlinear systems such as weather forecasting models. Forecasting systems incorporate two components, a forecast model and a data assimilation method. The latter projects a collection of observations of reality into a...

Ensemble prediction systems aim to account for uncertainties of initial conditions and model error. Ensemble forecasting is sometimes viewed as a method of obtaining (objective) probabilistic forecasts. How is one to judge the quality of an ensemble at forecasting a system? The probability that...

Parameter estimation in nonlinear models is a common task, and one for which there is no general solution at present. In the case of linear models, the distribution of forecast errors provides a reliable guide to parameter estimation, but in nonlinear models the facts that predictability may...

This work is motivated by dose-finding studies, where the number of events per subject within a specified study period form the primary outcome. The aim of the considered studies is to identify the target dose for which the new drug can be shown to be as effective as a competitor medication....

This thesis discusses issues arising in the analysis of repeated measurement studies with missing data. The first part of the thesis is motivated by a study where continuous and bounded longitudinal data form the outcome of interest. The aim of this study is to investigate the change over time...

In longitudinal and multivariate settings incomplete data, due to missed visits, dropouts or non-return of questionnaires are quite common. A longitudinal trial in which potentially informative missingness occurs is the Collaborative Ankle Support Trial (CAST). The aim of this study is to...

There is evidence to suggest that the effects of behavioral interventions may be limited to specific types of individuals, but methods for evaluating such outcomes have not been fully developed. This study proposes the use of finite mixture models to evaluate whether interventions, and,...

Pharmacokinetic studies are commonly analyzed using a two-stage approach where the first stage involves estimation of pharmacokinetic parameters for each subject separately and the second stage uses the individual parameter estimates for statistical inference. This two-stage approach is not...

We consider the problem of semi-parametric regression modelling when the data consist of a collection of short time series for which measurements within series are correlated. The objective is to estimate a regression function of the form E[Y(t) | x] =x'ß+μ(t), where μ(.) is an arbitrary,...

Marginal models for multivariate binary data permit separate modelling of the relationship of the response with explanatory variables, and the association between pairs of responses. When the former is the scientific focus, a first-order generalized estimating equation method (Liang & Zeger,...