Scalable modeling of nonstationary covariance functions with non-folding B-spline deformation

We propose a method for nonstationary covariance function modeling, based on the spatial deformation method of Sampson and Guttorp [1992], but using a low-rank, scalable deformation function written as a linear combination of the tensor product of B-spline basis. This approach addresses two important weaknesses in current computational aspects. First, it allows one to constrain estimated 2D deformations to be non-folding (bijective) in 2D. This requirement of the model has, up to now,been addressed only by arbitrary levels of spatial smoothing. Second, basis functions with compact support enable the application to large datasets of spatial monitoring sites of environmental data. An application to rainfall data in southeastern Brazil illustrates the method