deform: An R Package for Nonstationary Spatial Gaussian Process Models by Deformations and Dimension Expansion

Abstract: Gaussian processes (GP) are a popular and powerful tool for spatial modelling of data, especially data that quantify environmental processes. However, in stationary form, whether covariance is isotropic or anisotropic, GPs may lack the flexibility to capture dependence across a continuous spatial process, especially across a large domains. The deform package aims to provide users with user-friendly R functions for the fitting and visualization of nonstationary spatial Gaussian processes. Users can choose to capture nonstationarity with either the spatial deformation approach of Sampson and Guttorp (1992) or the dimension expansion approach of Bornn, Shaddick, and Zidek (2012). Thin plate regression splines are used for both approaches to bring transformations of locations to give a new set of locations that bring isotropic covariance. Fitted models in deform can be used to predict these new locations and to simulate nonstationary Gaussian processes for an arbitrary set of locations.