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.

翻译：环境数据科学中的空间极值问题传统上严重依赖最大稳定过程。尽管这类模型在统计学家中的流行程度或许已达顶峰，但在众多应用领域中仍被视为"最前沿"技术。然而，虽然支撑最大稳定过程的渐近理论在数学上严谨且全面，我们认为在环境应用领域中，这类方法已被过度使用（甚至误用），从而阻碍了更具针对性且经过严格验证的模型的发展。本文系统梳理了最大稳定过程模型的主要局限性，强烈反对在环境研究中将其作为默认方法。我们探讨了基于变量超越恰当高阈值的更灵活框架的替代方案，并对未来研究进行了展望，着重阐述了前进方向以及机器学习与极值统计融合所带来的机遇。