Modeling Nonstationary Extremal Dependence via Deep Spatial Deformations

TL;DR

This paper introduces deep compositional spatial models to effectively capture nonstationary extremal dependence in large-scale spatial data, overcoming computational and bijectivity challenges of traditional warping methods.

Contribution

It develops a novel deep learning-based approach for modeling nonstationary extremal dependence, enabling efficient estimation in high-dimensional spatial datasets.

Findings

Superior performance in estimating warped space demonstrated in simulations.

Efficient modeling of extremal dependence in UK precipitation extremes.

Able to handle data observed at thousands of locations.

Abstract

Modeling nonstationarity that often prevails in extremal dependence of spatial data can be challenging, and typically requires bespoke or complex spatial models that are difficult to estimate. Inference for stationary and isotropic models is considerably easier, but the assumptions that underpin these models are rarely met by data observed over large or topographically complex domains. A possible approach for accommodating nonstationarity in a spatial model is to warp the spatial domain to a latent space where stationarity and isotropy can be reasonably assumed. Although this approach is very flexible, estimating the warping function can be computationally expensive, and the transformation is not always guaranteed to be bijective, which may lead to physically unrealistic transformations when the domain folds onto itself. We overcome these challenges by developing deep compositional spatial models to capture nonstationarity in extremal dependence. Specifically, we focus on modeling high threshold exceedances of process functionals by leveraging efficient inference methods for limiting r-Pareto processes. A detailed high-dimensional simulation study demonstrates the superior performance of our model in estimating the warped space. We illustrate our method by modeling UK precipitation extremes and show that we can efficiently estimate the extremal dependence structure of data observed at thousands of locations.