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This paper develops a novel spatial process using generalized skew-normal/independent distributions when the usual Gaussian process assumptions are questionable and transformation to a Gaussian random field is not appropriate. The proposed model provides flexibility in capturing the effects of skewness and heavy tail behavior of the data while maintaining spatial dependence using a conditional autoregressive structure. We use Bayesian hierarchical methods to fit such models and show the validity of our approach. Furthermore, we use Bayesian model selection criteria to choose appropriate models for a real data set on the dengue fever infection in the state of Rio de Janeiro. [ABSTRACT FROM AUTHOR]