Spatial smoothing in statistical regression models

: (Alternative Format Thesis)

Abstract

Spatial regression models are commonly used in applied statistics to model data collected at different spatial locations. Such models use spatial random effects to account for residual spatial correlation in the response variable and result in fitted values that are, to some degree, smoothed across the spatial domain of the data. The main focus of this thesis is a problem known as spatial confounding, which causes covariate effect estimates in spatial models to be unreliable. By investigating the estimation theory in a commonly used spatial model formulation based on thin plate splines, we gain a deeper understanding of the problem and the existing methodology. Using this, we develop a novel and easily implementable method for avoiding spatial confounding in practice. Moreover, we include some initial analysis on spatial confounding in models with non-linear covariate effects; an area that has not yet been explored in the literature. The thesis also contains another project within the field of spatial statistics. Here, spatial modelling techniques are used to develop a method for detecting spatially coherent trends in environmental time series data. Specifically, we model river flow data from gauging stations across Great Britain. Using our methodology, we are able to verify, for the first time, a significant upward trend in flood risk over time and identify the regions with the largest trends.

Date of Award	16 Jun 2021
Original language	English
Awarding Institution	University of Bath
Supervisor	Nicole Augustin (Supervisor), Simon Wood (Supervisor), Matthew Nunes (Supervisor) & Ilaria Prosdocimi (Supervisor)