Abstract: We propose a flexible class of nonstationary stochastic models for multivariate spatial data. The method is based on convolutions of spatially varying covariance kernels and produces mathematically valid covariance structures. This method generalizes the convolution approach suggested by Majumdar and Gelfand (2007) to extend multivariate spatial covariance functions to the nonstationary case. A Bayesian method for estimation of the parameters in the covariance model based on a Gibbs sampler is proposed, then applied to simulated data. Model comparison is performed with the coregionalization model of Wackernagel (2003) that uses a stationary bivariate model. Based on posterior prediction results, the performance of our model appears to be considerably better.
Key words and phrases: Convolution, nonstationary process, posterior inference, predictive distribution, spatial statistics, spectral density.