Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process

In this paper, we introduce a unified skew Gaussian-log Gaussian model and propose a general class of spatial sampling models that can account for both heavy tails and skewness. This class includes some models proposed previously in the literature. The likelihood function involves analytically intractable integrals and direct maximization of the marginal likelihood is numerically difficult. We obtain maximum likelihood estimates of the model parameters, using a stochastic approximation of the EM algorithm (SAEM). The predictive distribution at unsampled sites is approximated based on Markov chain Monte Carlo samples. The identifiability of the parameters and the performance of the proposed model is investigated by a simulation study. The usefulness of our methodology is demonstrated by analyzing a Pb data set in a region of north Iran.