Fast and Scalable Inference for Spatial Extreme Value Models

TL;DR

This paper introduces a fast, scalable inference method for spatial GEV models using Laplace approximation combined with sparsity techniques, enabling accurate predictions for large spatial datasets.

Contribution

It presents a novel combination of Laplace approximation and sparsity-inducing covariance for efficient spatial GEV inference, surpassing traditional MCMC and INLA methods.

Findings

Accurately estimates Bayesian predictive distributions.

Scales to thousands of spatial locations.

Significantly faster than MCMC methods.

Abstract

The generalized extreme value (GEV) distribution is a popular model for analyzing and forecasting extreme weather data. To increase prediction accuracy, spatial information is often pooled via a latent Gaussian process (GP) on the GEV parameters. Inference for GEV-GP models is typically carried out using Markov chain Monte Carlo (MCMC) methods, or using approximate inference methods such as the integrated nested Laplace approximation (INLA). However, MCMC becomes prohibitively slow as the number of spatial locations increases, whereas INLA is only applicable in practice to a limited subset of GEV-GP models. In this paper, we revisit the original Laplace approximation for fitting spatial GEV models. In combination with a popular sparsity-inducing spatial covariance approximation technique, we show through simulations that our approach accurately estimates the Bayesian predictive distribution of extreme weather events, is scalable to several thousand spatial locations, and is several orders of magnitude faster than MCMC. A case study in forecasting extreme snowfall across Canada is presented.