Thompson, Marten2023-11-282023-11-282023-06https://hdl.handle.net/11299/258676University of Minnesota Ph.D. dissertation. June 2023. Major: Statistics. Advisor: Snigdhansu Chatterjee. 1 computer file (PDF); viii, 202 pages.Gaussian processes provide a flexible, non-parametric prior for function estimation. We investigate the applicability of Gaussian processes in semi-parametric models to relax otherwise restrictive assumptions. Our first application of this perspective is climate time series, where we see both the advantage of Gaussian processes in semi-parametric models as well as their computational restrictions. Next, we use Gaussian processes to relax the assumed error distribution of traditional small area models. Finally, we turn our attention to stripping away assumptions on Gaussian processes themselves: can data be used to inform their parameterization? We detail our work on each of these problems and provide software for future researchers.enBayesianGaussian processsemi-parametricsmall area statisticsThesis or Dissertation