Empirical Bayes spatial prediction using a Monte Carlo EM algorithm

This paper deals with an empirical Bayes approach for spatial prediction of a Gaussian random field. In fact, we estimate the hyperparameters of the prior distribution by using the maximum likelihood method. In order to maximize the marginal distribution of the data, the EM algorithm is used. Since this algorithm requires the evaluation of analytically intractable and high dimensionally integrals, a Monte Carlo method based on discretizing parameter space, is proposed to estimate the relevant integrals. Then, the approach is illustrated by its application to a spatial data set. Finally, we compare the predictive performance of this approach with the reference prior method.