Realistic and Fast Modeling of Spatial Extremes Over Large Geographical Domains

• Activity Number: 238 - Advances in Spatial and Temporal Models for Complex Environmental Systems
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Arnab Hazra and Raphael Huser* and David Bolin
• Companies: Indian Institute of Technology Kanpur and King Abdullah University of Science and Technology (KAUST) and King Abdullah University of Science and Technology (KAUST)
• Keywords: Asymptotic dependence and independence; Gaussian scale mixture process; Heavy tails; Low-rank process; Stochastic partial differential equation; Spatial extreme event

Abstract

Various natural phenomena exhibit spatial extremal dependence at short distances only, while it fades away as the distance between sites increases arbitrarily. However, the available models proposed in the literature for spatial extremes generally assume that spatial extremal dependence persists across the entire spatial domain. This is a clear limitation when modeling extremes over large geographical domains, but surprisingly, it has been mostly overlooked in the literature. We here develop a more realistic Bayesian framework based on a novel Gaussian scale mixture model, where the Gaussian process component is defined by a stochastic partial differential equation that yields a sparse precision matrix, and the random scale component is modeled as a low-rank Pareto-tailed or Weibull-tailed spatial process determined by compactly supported basis functions. We show that our proposed model can capture a wide range of extremal dependence structures as a function of distance, and that its sparse structure allows fast Bayesian computations in high spatial dimensions. Our new methodology is illustrated by application to precipitation extremes during the monsoon season in Bangladesh.