Bayesian nonstationary Gaussian process modeling: the BayesNSGP package for R

In spite of the diverse literature on nonstationary Gaussian process modeling, the software for implementing convolution-based methods is extremely limited, particularly for fully Bayesian analysis. To address this gap, here we present the BayesNSGP software package for R that enables off-the-shelf functionality for fully Bayesian, nonstationary Gaussian process modeling. Our approach to nonstationary modeling involves a closed-form, convolution-based covariance function with spatially-varying parameters; these parameter processes can be specified either deterministically (using covariates or basis functions) or stochastically (using approximate Gaussian processes). Stationary Gaussian processes are a special case of our methodology, and we furthermore implement approximate Gaussian process inference to account for very large spatial data sets. Bayesian inference is carried out using Markov chain Monte Carlo methods via the nimble package, which enables sampling of the highly correlated parameter spaces common to Gaussian process models (e.g., using adaptive block Metropolis-Hastings sampling). Posterior prediction for the Gaussian process at unobserved locations is also implemented as a straightforward post-processing step. As a demonstration, we use the package to analyze three data sets: first, the relatively small precipitation data set from Colorado that is used as a test case for related nonstationary methodology; second, a larger precipitation data set from a set of in situ measurements over the contiguous United States (with N ~ 1500 weather stations); and finally, a very large data set of return values for Boreal winter mean temperature at the surface derived from a general circulation model (with N ~ 50,000 grid cells).