Computationally efficient spatial modeling using recursive skeletonization factorizations

Recursive skeletonization factorization techniques can evaluate an accurate approximation to the log-likelihood for irregularly sited two-dimensional spatial data under a Gaussian process in O(n^3∕2) time and O(nlogn) storage. We demonstrate the application of these techniques to data on the surface of a sphere by fitting a Matérn model to approximately 87,000 total column ozone observations obtained from a single orbit of a polar-orbiting satellite. We then demonstrate that this fit can be improved by allowing either the range or scale parameters of the process to vary with latitude, but that the latter form of nonstationarity can be accommodated using skeletonization factorizations that do not need to be redone when optimizing over the parameters describing nonstationarity.