| Spatial models assuming an isotropic correlation structure—that is, correlation that is a function of geographic locations only through their distance—are not appropriate for most spatio-temporal environmental applications. One of the first approaches to deal with this issue was proposed by Sampson and Guttorp in 1992. This approach models heterogeneity in the anisotropy of a spatial random field by expressing the correlation function as isotropic in a plane represented as a deformation of the usual geographic coordinate system.; We formulate the Sampson-Guttorp model in a Bayesian framework that allows for uncertainty about the (numerous) model parameters to be reflected in posterior and predictive distributions. The modelling uses a parametric thin-plate spline family of functions for the spatial deformation. This same spatial deformation is proposed to describe similar heterogeneous structure in a spatial random field model of the temporal variance of the process.; The highly multivariate posterior distribution does not have a closed analytical form. We therefore build a Metropolis-Hastings Markov chain Monte Carlo algorithm through which we obtain samples from the posterior. Estimation is based on these samples. We also develop formulas for point predictions and predictive variances.; Throughout the dissertation our method is illustrated by means of simulations. We conclude by an application to a real data set consisting of 10-day aggregate precipitation measurements, in which we demonstrate the efficiency of this model for predictions at unmonitored locations. |
