Generalized sinh-Gaussian random fields

The aim of this contribution is to propose new flexible spatial models based on a class of generalized sinh transformations. Our proposal greatly extends the Gaussian random field mainly in terms of asymmetry, heavy tail behavior, and bimodality. We demonstrate that we obtain a valid random field. We ensure that it is mean square continuous. We derive explicit expressions for the moments, the covariance function, the skewness, and the kurtosis of the random fields. In comparison with the available skew-Gaussian models, the proposed models could capture a greater amount of skewness and also accommodate clustered spatial outliers. The proposed models are computationally very tractable within the Bayesian framework here adopted. They are compared with the Gaussian and skew-Gaussian spatial models through simulation studies and an application to the spatial prediction of weekly rainfall near Darwin, Australia. The result suggests that the predictive performance in terms of different criteria under our method tends to be smaller than those obtained from the competing ones.