Recent methods in modeling spatial extreme events have focused on utilizing parametric max-stable processes and their underlying dependence structure. In this work, we provide a unified approach for analyzing spatial extremes with little available data by estimating the distribution of model parameters or the spatial dependence directly. By employing recent developments in generative neural networks we predict a full sample-based distribution, allowing for direct assessment of uncertainty regarding model parameters or other parameter dependent functionals. We validate our method by fitting several simulated max-stable processes, showing a high accuracy of the approach, regarding parameter estimation, as well as uncertainty quantification. Additional robustness checks highlight the generalization and extrapolation capabilities of the model, while an application to precipitation extremes across Western Germany demonstrates the usability of our approach in real-world scenarios.

翻译：近年来，建模空间极端事件的方法主要集中于利用参数化最大稳定过程及其底层依赖结构。本研究提出了一种统一方法，用于在可用数据极少的情况下分析空间极值，通过直接估计模型参数的分布或空间依赖性来实现。借助生成神经网络的最新进展，我们预测了基于完整样本的分布，从而能够直接评估模型参数或其他参数依赖函数的不确定性。我们通过拟合多个模拟的最大稳定过程验证了该方法，结果显示该方法在参数估计和不确定性量化方面均具有高精度。额外的稳健性检验突显了模型的泛化与外推能力，而对德国西部极端降水数据的应用则证明了该方法在实际场景中的可用性。