Professor Reza Ramezan

Title: Revisiting Laplace Approximation: A Scalable Bayesian Computational Framework for Spatial GEV Models

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), or approximately via 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. Here we revisit the original Laplace approximation GEV-GP models. In combination with a sparsity-inducing basis expansion, we show through simulations that our approach accurately estimates the Bayesian predictive distribution of extreme weather events, is scalable to thousands of spatial locations, and is orders of magnitude faster than MCMC. A case study on extreme snowfall in Canada is presented.