  In the environmental modeling field, the exploratory analysis of responses
often exhibits spatial correlation as well as some non-Gaussian attributes such
as skewness and/or heavy-tailedness. Consequently, we propose a general spatial
model based on scale-shape mixtures of the multivariate skew-normal
distribution. Intuitively, it incorporates distinct random effects to account
for the spatial dependencies not explained by a simple Gaussian random field
model. Importantly, the proposed model is capable of generating a wide range of
skewness and kurtosis levels. Meanwhile, we demonstrate that the skewness
mixing can induce asymmetric tail dependence at sub-asymptotic and/or
asymptotic levels.
