Bayesian spatial modeling and interpolation using copulas

Copulas have attracted much attention in spatial statistics over the past few years. They are used as a flexible alternative to traditional methods for nonGaussian spatial modeling and interpolation. We adopt this methodology and show how it can be incorporated in a Bayesian framework by assigning priors to all model parameters. In the absence of simple analytical expressions for the joint posterior distribution an MCMC algorithm is used to obtain posterior samples. The posterior predictive density is approximated by averaging the plug-in predictive densities. In the case of the Gaussian copula we specify the priors for the correlation structure of the multivariate copula in an objective Bayesian way by using a conditional Jeffreys’ prior for the nugget and the range. Finally, we illustrate our methodology by means of the so-called Gomel data set, which includes Caesium-137 values in the region near Chernobyl, Belarus.

• Type: Journal
• Year: 2011
• Where: GANDC
• Authors: Hannes Kazianka, Jürgen Pilz
• Keywords: Correlation Structure, GANDC 2011, Gaussian Copula, Model Parameters