UCLA

The advent of large scale data, particularly from the biological sciences, has accelerated interest in developing computational methods for analysis and prediction.Implementing such methods often requires software to either automate computational tasks or to carry out calculations that elude analytic techniques. This work focuses on the latter while paying respect to useful and elegant abstractions from mathematical theory.

The diverse set of topics in this dissertation span applied probability, mathematical optimization, and epidemiological modelling. First, we investigate simulation techniques for stochastic processes. Second, we elaborate on the proximal distance technique of constrained optimization as a computational framework with examples in orthogonal projection, clustering, regression, and imaging. Third, we use deterministic equation modelling to evaluate school reopening strategies under pandemic conditions. Finally, we conclude with preliminary work on an application of the proximal distance method to hierarchical linear models.