A Bayesian Gaussian spatial-scale mixture model for short-range extremal dependence and long-range extremal independence, with application to heavy rainfall in Bangladesh

• Activity Number: 504 - Spatial Modeling on the Sphere and Over Large Domains
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Arnab Hazra* and Raphael Huser and David Bolin
• Companies: King Abdullah University of Science and Technology and King Abdullah University of Science and Technology (KAUST) and King Abdullah University of Science and Technology
• Keywords: Asymptotic dependence and independence; Extreme precipitation; Gaussian spatial-scale mixture process; Hierarchical Bayesian model; Random scale model; Stochastic Partial differential equation

Abstract

Spatial extremal dependence in precipitation generally fades away as the spatial distance increases. Max-stable processes satisfying the properties of extreme precipitation are scarce and they are also computationally intensive. As an alternative, a few researchers have considered location and/or scale mixtures of Gaussian processes which are computationally advantageous and also allow easier interpretation. However, these models generally have a downside of nonzero spatial extremal dependence throughout the spatial domain which is unrealistic for extreme precipitation over a large region. In this paper, we propose a hierarchical Bayesian Gaussian spatial-scale mixture process that bridges short-range extremal dependence and long-range extremal independence. The construction of the spatial random scale process is driven by stochastic partial differential equations. We discuss the properties of the model, Bayesian computational details using Markov chain Monte Carlo along with the computational efficiency based on simulation studies. We fit the proposed model to analyze monsoon rainfall in Bangladesh and draw inferences about the long-term return levels and the extremal dependence.