Sensitivity analysis and model selection for a generalized convolution model for spatial processes

Abstract

We examine a flexible class of nonstationary stochastic models for multivariate spatial data proposed by Majumdar et al. (2010). This covariance model is based on convolutions of spatially varying covariance kernels with centers corresponding to the centers of "local stationarity". A Bayesian method for estimation of the parameters in the model based on a Gibbs sampler is applied to simulated data to check for model sensitivity. The effect of a perturbation of the model in terms of kernel centers is also examined. Finally, the method is applied to a bivariate soil chemistry data from the the Central Arizona Phoenix Long Term Ecological Project (CAP LTER). Prediction bias, prediction standard deviation and predictive coverage are examined for different candidate models. In addition, a comparison with the bivariate stationary coregionalization model introduced by Wackernagel (2003) is carried out. A variant of the model proposed in Majumdar et al. (2010), with random kernel centers, is also examined. The latter model is seen to work much better than the stationary coregionalization model, and to perform comparably with the model with random kernel centers. Simulations indicate that the model is sensitive to under- or over-specification of kernel centers. On the other hand, application to real data seems to indicate that centroids of the regions that are homogeneous can be used as means of the random kernel centers. Cross validation can be used as a way of finding the best model with an appropriate number of kernels.