A Flexible Bayesian Hierarchical Modeling Framework for Spatially Dependent Peaks-Over-Threshold Data

• Activity Number: 380 - Advances in Bayesian Extreme Value Analysis
• Type: Topic Contributed
• Date/Time: Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Rishikesh Yadav* and Raphael Huser and Thomas Opitz
• Companies: King Abdullah University of Science and Technology and King Abdullah University of Science and Technology (KAUST) and INRAe
• Keywords: Bayesian hierarchical modeling ; extreme event; stochastic gradient Langevin dynamics; sub-asymptotic modeling; threshold exceedance.

Abstract

In this work, we develop a constructive modeling framework for extreme spatial threshold exceedances, based on general product mixtures of random fields possessing light or heavy-tailed margins and various spatial dependence characteristics, which are suitably designed to provide high flexibility in the tail and at pre-asymptotic levels. Our proposed model is akin to a recently proposed Gamma-Gamma model, but it possesses a higher degree of flexibility in its joint tail structure, capturing strong dependence more easily. Thanks to the model’s hierarchical formulation, the inference may be conveniently performed based on Markov chain Monte Carlo (MCMC) methods, and we demonstrate how the stochastic gradient Langevin dynamics (SGLD) algorithm can be exploited to fit our model very efficiently in relatively high spatio-temporal dimensions, while simultaneously censoring non-threshold exceedances and performing spatial prediction at multiple sites. We explore the theoretical properties of the proposed model, and illustrate the proposed methodology by simulation and application to daily precipitation data from Eastern Spain measured at about 100 stations over the period 2011-2020.