Stationary Process Approximation for the Analysis of Large Spatial Datasets

In a spatial data analysis problem, usually we build a hierarchical model with spatial structure described though random effects using a Gaussian process. If the sample size is very large, exact likelihood based inference becomes unstable and, eventually, infeasible since it involves computing quadratic forms and determinants associate with a large covariance matrix. If we wish to fit a Bayesian model, implementing a suitable MCMC algorithm, the large matrix will make repeated calculations impractical. A number of strategies for handling large spatial data sets have been discussed. We propose a finite sum process approximation model which is conceptually simple and routine to implement. Simulated and real data examples are given to illustrate the method.