Hierarchical Space-Time Modeling of Asymptotically Independent Exceedances With an Application to Precipitation Data

Jean-Noël Bacro,Carlo Gaetan,Thomas Opitz,Gwladys Toulemonde

doi:10.1080/01621459.2019.1617152

Abstract

The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of high-dimensional data, we propose a novel hierarchical model for high threshold exceedances defined over continuous space and time by embedding a space-time Gamma process convolution for the rate of an exponential variable, leading to asymptotic independence in space and time. Its physically motivated anisotropic dependence structure is based on geometric objects moving through space-time according to a velocity vector. We demonstrate that inference based on weighted pairwise likelihood is fast and accurate. The usefulness of our model is illustrated by an application to hourly precipitation data from a study region in Southern France, where it clearly improves on an alternative censored Gaussian space-time random field model. While classical limit models based on threshold-stability fail to appropriately capture relatively fast joint tail decay rates between asymptotic dependence and classical independence, strong empirical evidence from our application and other recent case studies motivates the use of more realistic asymptotic independence models such as ours. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Highlights

The French Mediterranean area is subject to heavy rainfall events occurring mainly in the fall season
This has motivated the development of more flexible dependence models, such as max-mixtures of max-stable and asymptotically independent processes (Wadsworth and Tawn, 2012; Bacro et al, 2016) or max-infinitely divisible constructions (Huser et al, 2018) for maxima data, or Gaussian scale mixture processes (Opitz, 2016; Huser et al, 2017) for threshold exceedances, capable to accommodate asymptotic dependence, asymptotic independence and Gaussian dependence with a smooth transition
We develop statistical inference based on pairwise likelihood

Summary

INTRODUCTION

The French Mediterranean area is subject to heavy rainfall events occurring mainly in the fall season. The results from the empirical spatio-temporal exploration of our French rainfall data in Section 6.2 are strongly in favor of asymptotic independence, which appears to be characteristic for many environmental data sets (Davison et al, 2013; Thibaud et al, 2013; Tawn et al, 2018) and may arise from physical laws such as the conservation of mass This has motivated the development of more flexible dependence models, such as max-mixtures of max-stable and asymptotically independent processes (Wadsworth and Tawn, 2012; Bacro et al, 2016) or max-infinitely divisible constructions (Huser et al, 2018) for maxima data, or Gaussian scale mixture processes (Opitz, 2016; Huser et al, 2017) for threshold exceedances, capable to accommodate asymptotic dependence, asymptotic independence and Gaussian dependence with a smooth transition.

A HIERARCHICAL MODEL FOR SPATIO-TEMPORAL EXCEEDANCES

JOINT TAIL BEHAVIOR OF THE HIERARCHICAL PROCESS

COMPOSITE LIKELIHOOD INFERENCE

SIMULATION STUDY

Findings

CONCLUSIONS