Estimation and prediction of a class of convolution-based spatial nonstationary models for large spatial data

In this paper we address two issues common to the analysis of large spatial datasets. One is the modeling of non-stationarity, and the other is the computational challenges in doing likelihood based estimation and kriging prediction. We model the spatial process as a convolution of independent Gaussian processes, with the spatially varying kernel function given by the modified Bessel functions. This is a generalization of the process-convolution approach in Higdon et al. (1999), which used Gaussian kernel to obtain a closed-form non-stationary covariance function. Our model can produce processes with richer local behavior similar to the processes with the Matérn class of covariance functions. Since the covariance function of our model does not have a closed-form expression, direct estimation and spatial prediction using kriging is infeasible for large datasets. Efficient algorithms are proposed and implemented for parameter estimation and spatial prediction. We compare our method with method based on stationary model and moving window kriging. Simulation results and application to a rainfall data show that our method has better prediction performance.