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We introduce an approach to quickly and accurately approximate the cumulativedistribution function of multivariate Gaussian distributions arising fromspatial Gaussian processes. This approximation is trivially parallelizable andsimple to implement using standard software. We demonstrate its accuracy andcomputational efficiency in a series of simulation experiments and apply it toanalyzing the joint tail of a large precipitation dataset using arecently-proposed scale mixture model for spatial extremes. This dataset ismany times larger than what was previously considered possible to fit usingpreferred inferential techniques.

A Vecchia Approximation for High-Dimensional Gaussian Cumulative Distribution Functions Arising from Spatial Data