Modeling non-stationary extreme dependence with stationary max-stable processes and multidimensional scaling

TL;DR

This paper introduces a flexible approach using multidimensional scaling to model non-stationary extreme weather dependence with max-stable processes, improving fit over traditional methods.

Contribution

The study proposes a novel method that warps spatial data into a latent space via MDS, enhancing modeling of non-stationary extremal dependence.

Findings

Proposed methods better reproduce extremal coefficients.

Approach captures complex spatial dependence more effectively.

Compared favorably to classical climate space models.

Abstract

Modeling the joint distribution of extreme weather events in multiple locations is a challenging task with important applications. In this study, we use max-stable models to study extreme daily precipitation events in Switzerland. The non-stationarity of the spatial process at hand involves important challenges, which are often dealt with by using a stationary model in a so-called climate space, with well-chosen covariates. Here, we instead chose to warp the weather stations under study in a latent space of higher dimension using multidimensional scaling (MDS). The advantage of this approach is its improved flexibility to reproduce highly non-stationary phenomena, while keeping a tractable stationary spatial model in the latent space. Two model fitting approaches, which both use MDS, are presented and compared to a classical approach that relies on composite likelihood maximization in a climate space. Results suggest that the proposed methods better reproduce the observed extremal coefficients and their complex spatial dependence.