# Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes

arXiv: https://arxiv.org/abs/2401.17430 · HTML: https://mlsanity.com/paper/2401.17430/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2024.

## Built on by (most cited first, 8 of 8)

- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Flexible Tails for Normalizing Flows](https://mlsanity.com/paper/2406.16971/) (2024)
- [Deep Learning of Multivariate Extremes via a Geometric Representation](https://mlsanity.com/paper/2406.19936/) (2024)
- [Deep learning joint extremes of metocean variables using the SPAR model](https://mlsanity.com/paper/2412.15808/) (2024)
- [Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networks](https://mlsanity.com/paper/2505.03034/) (2025)
- [Modeling Nonstationary Extremal Dependence via Deep Spatial Deformations](https://mlsanity.com/paper/2505.12548/) (2025)
- [Modeling Spatial Extremal Dependence of Precipitation Using Distributional Neural Networks](https://mlsanity.com/paper/2407.08668/) (2024)
- [Modelling non-stationary extremal dependence through a geometric approach](https://mlsanity.com/paper/2509.22501/) (2025)

## Abstract (arXiv)

Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the `state-of-the-art' in many applied fields. However, while the asymptotic theory supporting the use of max-stable processes is mathematically rigorous and comprehensive, we think that it has also been overused, if not misused, in environmental applications, to the detriment of more purposeful and meticulously validated models. In this paper, we review the main limitations of max-stable process models, and strongly argue against their systematic use in environmental studies. Alternative solutions based on more flexible frameworks using the exceedances of variables above appropriately chosen high thresholds are discussed, and an outlook on future research is given, highlighting recommendations moving forward and the opportunities offered by hybridizing machine learning with extreme-value statistics.