Spatial regression with non-parametric modeling of Fourier coefficients

Abstract

© 2021, Korean Statistical Society.We consider modeling of Fourier coefficients, known as a spectral density function to represent spatial dependence of a stationary spatial random field and use it for spatial regression under a Bayesian framework. Especially, we switch from the space domain to the frequency domain and introduce a Gaussian process prior to the log spectral density. As we do not impose any further assumption on log spectral density, resulting covariance function is not of a parametric form and/or isotropic assumption. Simulation study supports that our approach is robust over various parametric covariance models. Also, our approach gives comparable or better prediction results over conventional spatial prediction under most parametric covariance models that we considered. Even though we need to estimate spectral density at all Fourier frequencies during the Bayesian procedure, our approach does not lose much computational efficiency compared to estimating only a few parameters in the parametric covariance models. We also compare our approach with some other existing spatial prediction approaches using two datasets of Korean ozone concentration. Our approach performs reasonably good in terms of mean absolute error and root mean squared error.