Spatial deformation for non-stationary extremal dependence

TL;DR

This paper extends a location deformation method to model non-stationary extremal dependence in spatial data, enabling more accurate analysis of extreme events over complex domains.

Contribution

It introduces a least squares based deformation approach for non-stationary extremal dependence, improving modeling flexibility without requiring prior covariate knowledge.

Findings

Effective in simulations with varying non-stationarity levels

Improves extremal dependence modeling in temperature and precipitation data

Outperforms naive stationary models

Abstract

Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for modelling non-stationarity in extremal dependence rely on models that are either computationally difficult to fit or require prior knowledge of covariates. Sampson and Guttorp (1992) proposed a simple technique for handling non-stationarity in spatial dependence by smoothly mapping the sampling locations of the process from the original geographical space to a latent space where stationarity can be reasonably assumed. We present an extension of this method to a spatial extremes framework by considering least squares minimisation of pairwise theoretical and empirical extremal dependence measures. Along with some practical advice on applying these deformations, we provide a detailed simulation study in which we propose three spatial processes with varying degrees of non-stationarity in their extremal and central dependence structures. The methodology is applied to Australian summer temperature extremes and UK precipitation to illustrate its efficacy compared to a naive modelling approach.