ASkew–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 eciency of our model through an extensive simulation study and an application to a real data set comprised of precipitation measurements.