Nonstationary Spatial Gaussian Markov Random Fields

Thin-plate splines have been widely used as spatial smoothers. In this article, we present a Bayesian adaptive thin-plate spline (BATS) suitable for modeling nonstationary spatial data. Fully Bayesian inference can be carried out through efficient Markov chain Monte Carlo simulation. Performance is demonstrated with simulation studies and by an application to a rainfall dataset. A FORTRAN program implementing the method, a proof of the theorem, and the dataset in this article are available online.