Bayesian Spatial Prediction for Discrete Closed Skew Gaussian Random Field

Most approaches in statistical spatial prediction assume that the spatial data are realizations of a Gaussian random field. However, this assumption is hard to justify for most applications. When the distribution of data is skewed but otherwise has similar properties to the normal distribution, a closed skew normal distribution can be used for modeling their skewness. Closed skew normal distribution is an extension of the multivariate skew normal distribution and has the advantage of being closed under marginalization and conditioning. In this paper, we generalize Bayesian prediction methods using closed skew normal distributions. A simulation study is performed to check the validity of the model and performance of the Bayesian spatial predictor. Finally, our prediction method is applied to Bayesian spatial prediction on the strain data near Semnan, Iran. The mean-square error of cross-validation is improved by the closed skew Gaussian model on the strain data.