Bayesian inference for big spatial data using non-stationary spectral simulation

Abstract

It is increasingly understood that the assumption of stationarity is unrealistic for many spatial processes. In this article, we combine dimension expansion with a spectral method to model big non-stationary spatial fields in a computationally efficient manner. Specifically, we use Mejía and Rodríguez-Iturbe’s (1974) spectral simulation approach to simulate a spatial process with a covariogram at locations that have an expanded dimension. We introduce Bayesian hierarchical modeling to dimension expansion, which originally has only been modeled using a method of moments approach. We consider a novel scheme to re-weight levels in a Bayesian spatial hierarchical model that allows one to use non-stationary spectral simulation within a collapsed Gibbs sampler. Our method is both full rank and non-stationary, and can be applied to big spatial data because it does not involve storing and inverting large covariance matrices. We demonstrate the wide applicability of our approach through simulation studies, and an application using ozone data obtained from the National Aeronautics and Space Administration (NASA).