Tailoring Gaussian processes and large-scale optimisation

This thesis is centred around Gaussian processes and large-scale optimisation, where the main contributions are presented in the included papers. Provided access to linear constraints (e.g. equilibrium conditions), we propose a constructive procedure to design the covariance function in a Gaussian process. The constraints are thereby explicitly incorporated with guaranteed fulfilment. One such construction is successfully applied to strain field reconstruction, where the goal is to describe the interior of a deformed object. Furthermore, we analyse the Gaussian process as a tool for X-ray computed tomography, a field of high importance primarily due to its central role in medical treatments. This provides insightful interpretations of traditional reconstruction algorithms. Large-scale optimisation is considered in two different contexts. First, we consider a stochastic environment, for which we suggest a new method inspired by the quasi-Newton framework. Promising results are demonstrated on real world benchmark problems. Secondly, we suggest an approach to solve an applied deterministic optimisation problem that arises within the design of electrical circuit boards. We reduce the memory requirements through a tailored algorithm, while also benefiting from other parts of the setting to ensure a high computational efficiency. The final paper scrutinises a publication from the early phase of the COVID-19 pandemic, in which the aim was to assess the effectiveness of different governmental interventions. We show that minor modifications in the input data have important impact on the results, and we argue that great caution is necessary when such models are used as a support for decision making.