  We propose a new model for regression and dependence analysis when addressing
spatial data with possibly heavy tails and an asymmetric marginal distribution.
We first propose a stationary process with $t$ marginals obtained through scale
mixing of a Gaussian process with an inverse square root process with Gamma
marginals. We then generalize this construction by considering a skew-Gaussian
process, thus obtaining a process with skew-t marginal distributions. For the
proposed (skew) $t$ process we study the second-order and geometrical
properties and in the $t$ case, we provide analytic expressions for the
bivariate distribution. In an extensive simulation study, we investigate the
use of the weighted pairwise likelihood as a method of estimation for the $t$
process. Moreover we compare the performance of the optimal linear predictor of
the $t$ process versus the optimal Gaussian predictor. Finally, the
effectiveness of our methodology is illustrated by analyzing a georeferenced
dataset on maximum temperatures in Australia
