# Modeling Spatial Extremal Dependence of Precipitation Using Distributional Neural Networks

arXiv: https://arxiv.org/abs/2407.08668 · HTML: https://mlsanity.com/paper/2407.08668/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 57 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Builds on (most cited first, 16 of 16)

- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2112.08217/) (2021)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [Neural Networks for Parameter Estimation in Intractable Models](https://mlsanity.com/paper/2107.14346/) (2021)
- [Generative machine learning methods for multivariate ensemble post-processing](https://mlsanity.com/paper/2211.01345/) (2022)
- [Fast covariance parameter estimation of spatial Gaussian process models using neural networks](https://mlsanity.com/paper/2012.15339/) (2020)
- [Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2205.15784/) (2022)
- [Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes](https://mlsanity.com/paper/2401.17430/) (2024)
- [Fast parameter estimation of Generalized Extreme Value distribution using Neural Networks](https://mlsanity.com/paper/2305.04341/) (2023)
- [Towards black-box parameter estimation](https://mlsanity.com/paper/2303.15041/) (2023)
- [Full likelihood inference for max-stable data](https://mlsanity.com/paper/1703.08665/) (2017)
- [Higher-dimensional spatial extremes via single-site conditioning](https://mlsanity.com/paper/1912.06560/) (2019)
- [Statistical Post-Processing of Forecasts for Extremes Using Bivariate Brown-Resnick Processes with an Application to Wind Gusts](https://mlsanity.com/paper/1312.4584/) (2013)
- [Bayesian inference for the Brown-Resnick process, with an application to extreme low temperatures](https://mlsanity.com/paper/1506.07836/) (2015)
- [A comparative tour through the simulation algorithms for max-stable processes](https://mlsanity.com/paper/1809.09042/) (2018)

## Abstract (arXiv)

In this work, we propose a simulation-based estimation approach using generative neural networks to determine dependencies of precipitation maxima and their underlying uncertainty in time and space. Within the common framework of max-stable processes for extremes under temporal and spatial dependence, our methodology allows estimating the process parameters and their respective uncertainty, but also delivers an explicit nonparametric estimate of the spatial dependence through the pairwise extremal coefficient function. We illustrate the effectiveness and robustness of our approach in a thorough finite sample study where we obtain good performance in complex settings for which closed-form likelihood estimation becomes intractable. We use the technique for studying monthly rainfall maxima in Western Germany for the period 2021-2023, which is of particular interest since it contains an extreme precipitation and consecutive flooding event in July 2021 that had a massive deadly impact. Beyond the considered setting, the presented methodology and its main generative ideas also have great potential for other applications.