Title: Vecchia approximations of Gaussian-process predictions,
Abstract: Gaussian processes (GPs) are highly flexible function estimators used for
geospatial analysis, nonparametric regression, and machine learning, but they
are computationally infeasible for large datasets. Vecchia approximations of
GPs have been used to enable fast evaluation of the likelihood for parameter
inference. Here, we study Vecchia approximations of spatial predictions at
observed and unobserved locations, including obtaining joint predictive
distributions at large sets of locations. We propose a general Vecchia
framework for GP predictions, which contains some novel and some existing
special cases. We study the accuracy and computational properties of these
approaches theoretically and numerically. We show that our new approaches
exhibit linear computational complexity in the total number of spatial
locations. We also apply our methods to a satellite dataset of chlorophyll
fluorescence.