"Research Note" BAYESIAN PREDICTION IN GEOSTATISTICAL MODELS WITH MATERN

This paper deals with Bayesian geostatistical prediction under the Matern correlation function which involves a smoothness parameter in addition to the range parameter. In fact, we consider the reference prior for the range parameter and an inverse gamma prior for the smoothness parameter. We then propose an attractive and straightforward Monte Carlo method to sample the posterior distribution of the model parameters and achieve Bayesian prediction. In a sensitivity analysis, the importance of the prior choice is assessed. Since the posterior results greatly depend on the prior hyperparameters, the Monte Carlo EM algorithm is applied to determine their maximum likelihood estimates. Finally, we utilize this procedure in the geostatistical prediction of carbon monoxide concentrations in Tehran.