A hierarchical Bayesian non-asymptotic extreme value model for spatial data

TL;DR

This paper introduces a hierarchical Bayesian model for spatial extreme precipitation data that relaxes traditional asymptotic assumptions, capturing variability and spatial dependence to improve estimation accuracy.

Contribution

It presents a novel non-asymptotic Bayesian hierarchical approach for spatial extremes, incorporating latent processes and spatial structure, advancing beyond traditional extreme value models.

Findings

Reduces estimation uncertainty compared to existing methods

Successfully applied to North Carolina rainfall data

Improves spatial extreme modeling accuracy

Abstract

Spatial maps of extreme precipitation are crucial in flood protection. With the aim of producing maps of precipitation return levels, we propose a novel approach to model a collection of spatially distributed time series where the asymptotic assumption, typical of the traditional extreme value theory, is relaxed. We introduce a Bayesian hierarchical model that accounts for the possible underlying variability in the distribution of event magnitudes and occurrences, which are described through latent temporal and spatial processes. Spatial dependence is characterized by geographical covariates and effects not fully described by the covariates are captured by spatial structure in the hierarchies. The performance of the approach is illustrated through simulation studies and an application to daily rainfall extremes across North Carolina (USA). The results show that we significantly reduce the estimation uncertainty with respect to state of the art techniques.