Nonstationary Spatial Process Models with Spatially Varying Covariance Kernels

Building spatial process models that capture nonstationary behavior while delivering computationally efficient inference is challenging. Nonstationary spatially varying kernels (see, e.g., Paciorek, 2003) offer flexibility and richness, but computation is impeded by high-dimensional parameter spaces resulting from spatially varying process parameters. Matters are exacerbated if the number of locations recording measurements is massive. With limited theoretical tractability, obviating computational bottlenecks requires synergy between model construction and algorithm development. We build a class of scalable nonstationary spatial process models using spatially varying covariance kernels. We implement a Bayesian modeling framework using Hybrid Monte Carlo with nested interweaving. We conduct experiments on synthetic data sets to explore model selection and parameter identifiability, and assess inferential improvements accrued from nonstationary modeling. We illustrate strengths and pitfalls with a data set on remote sensed normalized difference vegetation index.