Bayesian estimation of semi-parametric non-stationary spatial covariance structures

We use the Sampson and Guttorp approach to model the non-stationary correlation function r(x, x′) of a Gaussian spatial process through a bijective space deformation, f, so that in the deformed space the spatial correlation function can be considered isotropic, namely r(x, x′) = ρ(∣ f(x)−f(x′)∣), where ρ belongs to a known parametric family. Given the locations in the deformed space of a number of geographic sites at which data are available, we smoothly extrapolate the deformation to the whole region of interest. Using a Bayesian framework, we estimate jointly these locations, as well as the parameters of the correlation function and the variance parameters. The advantage of our Bayesian approach is that it allows us to obtain measures of uncertainty of all these parameters. As the parameter space is of a very high dimension, we implement an MCMC method for obtaining samples from the posterior distributions of interest. We demonstrate our method through a simulation study, and show an application to a real data set. Copyright © 2001 John Wiley & Sons, Ltd.