  Skewness is often present in a wide range of spatial prediction problems, and
modeling it in the spatial context remains a challenging problem. In this study
a skew-Gaussian random field is considered. The skew-Gaussian random field is
constructed by using the multivariate closed skew-normal distribution, which is
a generalization of the traditional normal distribution. We present a
Metropolis-Hastings algorithm for simulating realizations efficiently from the
random field, and an algorithm for estimating parameters by maximum likelihood
with a Monte Carlo approximation of the likelihood. We demonstrate and evaluate
the algorithms on synthetic cases. The skewness in the skew-Gaussian random
field is found to be strongly influenced by the spatial correlation in the
field, and the parameter estimators appear as consistent with increasing size
of the random field. Moreover, we use the closed skew-normal distribution in a
multivariate random field predictive setting on real seismic data from the
Sleipner field in the North Sea.
