# Advances in Statistical Modeling of Spatial Extremes

arXiv: https://arxiv.org/abs/2007.00774 · HTML: https://mlsanity.com/paper/2007.00774/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 12 of 12)

- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [Deep graphical regression for jointly moderate and extreme Australian wildfires](https://mlsanity.com/paper/2308.14547/) (2023)
- [Fast parameter estimation of Generalized Extreme Value distribution using Neural Networks](https://mlsanity.com/paper/2305.04341/) (2023)
- [Neural Bayes estimators for censored inference with peaks-over-threshold models](https://mlsanity.com/paper/2306.15642/) (2023)
- [Regular Variation in Hilbert Spaces and Principal Component Analysis for Functional Extremes](https://mlsanity.com/paper/2308.01023/) (2023)
- [Capturing Extreme Events in Turbulence using an Extreme Variational Autoencoder (xVAE)](https://mlsanity.com/paper/2502.04685/) (2025)
- [Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networks](https://mlsanity.com/paper/2505.03034/) (2025)
- [A2 Copula-Driven Spatial Bayesian Neural Network For Modeling Non-Gaussian Dependence: A Simulation Study](https://mlsanity.com/paper/2505.24006/) (2025)
- [Modeling Spatio-temporal Extremes via Conditional Variational Autoencoders](https://mlsanity.com/paper/2512.06348/) (2025)
- [Multi-output Extreme Spatial Model for Complex Aircraft Production Systems](https://mlsanity.com/paper/2604.22548/) (2026)

## Abstract (arXiv)

The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or r-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often suggests that such asymptotic models are too rigidly constrained, and that they do not adequately capture the frequent situation where more severe events tend to be spatially more localized. In other words, these asymptotic models have a strong tail dependence that persists at increasingly high levels, while data usually suggest that it should weaken instead. Another well-known limitation of classical spatial extremes models is that they are either computationally prohibitive to fit in high dimensions, or they need to be fitted using less efficient techniques. In this review paper, we describe recent progress in the modeling and inference for spatial extremes, focusing on new models that have more flexible tail structures that can bridge asymptotic dependence classes, and that are more easily amenable to likelihood-based inference for large datasets. In particular, we discuss various types of random scale constructions, as well as the conditional spatial extremes model, which have recently been getting increasing attention within the statistics of extremes community. We illustrate some of these new spatial models on two different environmental applications.