Efficient Modeling of Spatial Extremes over Large Geographical Domains

TL;DR

This paper introduces a novel Bayesian Gaussian scale mixture model for spatial extremes that captures local dependence structures over large domains, enabling efficient computation and improved fit for heavy rainfall data.

Contribution

It develops a new sparse Bayesian model with a stochastic PDE Gaussian process and low-rank tail processes, addressing limitations of existing models for large-scale spatial extremes.

Findings

Model outperforms competitors in rainfall data fitting

Captures a wide range of extremal dependence structures

Enables fast Bayesian inference in high dimensions

Abstract

Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is a strong limitation when modeling extremes over large geographical domains, and yet it has been mostly overlooked in the literature. We here develop a more realistic Bayesian framework based on a novel Gaussian scale mixture model, with the Gaussian process component defined by a stochastic partial differential equation yielding a sparse precision matrix, and the random scale component modeled as a low-rank Pareto-tailed or Weibull-tailed spatial process determined by compactly-supported basis functions. We show that our proposed model is approximately tail-stationary and that it can capture a wide range of extremal dependence structures. Its inherently sparse structure allows fast Bayesian computations in high spatial dimensions based on a customized Markov chain Monte Carlo algorithm prioritizing calibration in the tail. We fit our model to analyze heavy monsoon rainfall data in Bangladesh. Our study shows that our model outperforms natural competitors and that it fits precipitation extremes well. We finally use the fitted model to draw inference on long-term return levels for marginal precipitation and spatial aggregates.