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

TL;DR

This paper presents a fast, parallelizable approximation method for high-dimensional Gaussian CDFs from spatial data, enabling analysis of large datasets previously infeasible with existing techniques.

Contribution

It introduces a novel Vecchia approximation approach that is simple to implement, highly accurate, and computationally efficient for large-scale spatial Gaussian process data.

Findings

Accurately approximates high-dimensional Gaussian CDFs

Demonstrates efficiency on large spatial datasets

Enables analysis of datasets previously too large for existing methods

Abstract

We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to implement using standard software. We demonstrate its accuracy and computational efficiency in a series of simulation experiments and apply it to analyzing the joint tail of a large precipitation dataset using a recently-proposed scale mixture model for spatial extremes. This dataset is many times larger than what was previously considered possible to fit using preferred inferential techniques.