A Skew-Gaussian‎ ‎Spatio-Temporal Process with Non-Stationary Correlation Structure

. This paper develops a new class of spatio-temporal process models that can simultaneously capture skewness and non-stationarity. The proposed approach which is based on using the closed skew-normal distribution in the low-rank representation of stochastic processes, has several favorable properties. In particular, it greatly reduces the dimension of the spatio-temporal latent variables and induces flexible correlation structures. Bayesian analysis of the model is implemented through a Gibbs MCMC algorithm which incorporates a version of the Kalman filtering algorithm. All fully conditional posterior distributions have closed forms which show another advanta-geous property of the proposed model. We demonstrate the e (cid:14) ciency of our model through an extensive simulation study and an application to a real data set comprised of precipitation measurements.