Spatial interpolation with Gaussian processes and spatially varying regression coefficients

Abstract

Linear regression is undoubtedly one of the most widely used statistical techniques, however because it assumes independent observations it can miss important features of a dataset when observations are spatially dependent. This report presents the spatially varying coefficients model, which augments a linear regression with a multivariate Gaussian spatial process to allow regression coefficients to vary over the spatial domain of interest. We develop the mathematics of Gaussian processes and illustrate their use, and demonstrate the spatially varying coefficients model on simulated data. We show that it achieves lower prediction error and a better fit to data than a standard linear regression.