Exploration and inference in spatial extremes using empirical basis functions

TL;DR

This paper introduces a novel data-driven method using empirical basis functions to explore and model spatial extremal dependence in large datasets, enhancing visualization and Bayesian modeling of spatial extremes.

Contribution

It proposes a new approach based on empirical pairwise extremal coefficients to estimate basis functions for spatial extremes, addressing a gap in large dataset inference.

Findings

Effective visualization of extremal dependence patterns.

Successful application to extreme precipitation data.

Enhanced Bayesian modeling of spatial extremes.

Abstract

Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to explore and model spatial extremal dependence. Based on a low-rank max-stable model we propose a data-driven approach to estimate meaningful basis functions using empirical pairwise extremal coefficients. These spatial empirical basis functions can be used to visualize the main trends in extremal dependence. In addition to exploratory analysis, we describe how these functions can be used in a Bayesian hierarchical model to model spatial extremes of large datasets. We illustrate our methods on extreme precipitations in eastern U.S.