Bayesian Prediction in Spatial Data Analysis

When spatial data are realizations of a Gaussian model with parametric mean and covariance functions, then the function of observations that minimizes mean square prediction error depends on some unknown parameters. Usually, this parameters are replaced by their estimates to obtain the plug-in predictor. But, this method has some problems in estimation of the parameters and the optimality and min square error of the spatial predictor. In this paper, the problems related to plug-in method are discussed and to avid them, the Bayesian approach for spatial prediction is proposed. Then the Bayesian spatial prediction for Gaussian and trans Gaussian models according to observations, that may contain noise, are derived. Next, in a simulation study, the adequacy of Bayesian prediction is compared with plug-in prediction. Finally, a numerical example illustrates the Bayesian spatial prediction of rainfall in a region at the north of Iran.