[Paper Review] Hierarchical space-time modeling of exceedances with an application to rainfall data

Jean-Noël Bacro, Carlo Gaetan+2 more|arXiv (Cornell University)|Aug 8, 2017

Financial Risk and Volatility Modeling47 references3 citations

TL;DR

This paper proposes a novel hierarchical space-time model for asymptotically independent exceedances using a space-time Gamma process convolution to model the rate of an exponential process, enabling physically interpretable anisotropic dependence via moving geometric objects. The model improves upon censored Gaussian random fields in modeling hourly rainfall extremes in Southern France, with fast and accurate inference via weighted pairwise likelihood.

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.

Motivation & Objective

• To develop a physically interpretable space-time model for high threshold exceedances in environmental extremes, particularly for rainfall data.
• To address the limitations of classical max-stable and Gaussian models in capturing asymptotic independence, which is common in environmental data.
• To model complex spatio-temporal dependence structures in high-dimensional, continuous space-time data with realistic tail behavior.
• To enable fast and accurate inference for large-scale environmental datasets using composite likelihood methods.
• To improve simulation and prediction capabilities for flash flood risk by better capturing joint tail decay rates in precipitation events.

Proposed method

• The model uses a space-time Gamma random field to define the rate parameter of an exponential process, inducing asymptotic independence in the extremes.
• The Gamma process is constructed via convolution with a kernel that depends on space-time distance and a velocity vector, enabling anisotropic, physically motivated dependence.
• The dependence structure is driven by geometric objects (e.g., storm cells) moving through space-time with a fixed velocity, reflecting physical storm dynamics.
• Inference is performed using weighted pairwise likelihood, which is computationally efficient and shown to be accurate for high-dimensional data.
• The model is embedded in a hierarchical framework, allowing for flexible marginal and dependence structure modeling while maintaining interpretability.
• The Laplace transform of the underlying random measure is derived to facilitate likelihood computation, with explicit formulas for univariate and bivariate Laplace transforms.

Experimental results

Research questions

• RQ1 Can a physically interpretable space-time model capture asymptotic independence in environmental extremes more effectively than classical models?
• RQ2 How well can a Gamma process convolution model represent the spatio-temporal dependence of high rainfall threshold exceedances?
• RQ3 Does the use of a velocity-driven geometric object framework improve the modeling of storm dynamics in space-time extremes?
• RQ4 Can weighted pairwise likelihood provide fast and accurate inference for large-scale space-time extreme value models?
• RQ5 How does the proposed model compare to censored Gaussian random fields in predicting extreme rainfall events?

Key findings

• The proposed model significantly improves fit to hourly rainfall data from Southern France compared to a censored Gaussian space-time random field model.
• Empirical analysis confirms asymptotic independence in the data, supporting the need for models beyond classical max-stable or asymptotically dependent limits.
• The model captures relatively fast joint tail decay rates, which classical limit models fail to represent accurately.
• Weighted pairwise likelihood inference is both computationally efficient and accurate, enabling application to large datasets.
• The velocity-driven geometric structure provides a physically interpretable mechanism for storm propagation, enhancing model interpretability.
• The model's ability to handle asymptotic independence with smooth transition to dependence allows for more realistic simulation of extreme rainfall events.