Making inference with spatial extremal dependence models can be computationally burdensome since they involve intractable and/or censored likelihoods. Building on recent advances in likelihood-free inference with neural Bayes estimators, that is, neural networks that approximate Bayes estimators, we develop highly efficient estimators for censored peaks-over-threshold models that {use data augmentation techniques} to encode censoring information in the neural network {input}. Our new method provides a paradigm shift that challenges traditional censored likelihood-based inference methods for spatial extremal dependence models. Our simulation studies highlight significant gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when applying our novel estimators to make inference with popular extremal dependence models, such as max-stable, $r$-Pareto, and random scale mixture process models. We also illustrate that it is possible to train a single neural Bayes estimator for a general censoring level, precluding the need to retrain the network when the censoring level is changed. We illustrate the efficacy of our estimators by making fast inference on hundreds-of-thousands of high-dimensional spatial extremal dependence models to assess extreme particulate matter 2.5 microns or less in diameter (${\rm PM}_{2.5}$) concentration over the whole of Saudi Arabia.

翻译：利用空间极值依赖模型进行推断可能计算负担沉重，因为这些模型涉及难以处理的和/或截断的似然函数。基于近期在无似然推断与神经贝叶斯估计器（即近似贝叶斯估计器的神经网络）方面的进展，我们针对截断峰值超阈值模型开发了高效估计器，该估计器通过数据增强技术将截断信息编码至神经网络输入中。我们的新方法提供了范式转变，对传统基于截断似然的空间极值依赖模型推断方法提出了挑战。模拟研究表明，在将我们的新型估计器应用于常见极值依赖模型（如最大稳定过程、$r$-帕累托过程及随机尺度混合过程模型）进行推断时，相较于基于似然的竞争方法，我们在计算效率与统计效率方面均取得了显著提升。我们还证明，可以为通用截断水平训练单一的神经贝叶斯估计器，从而避免在截断水平改变时重新训练网络。我们通过对数十万个高维空间极值依赖模型进行快速推断，评估沙特阿拉伯全境直径小于等于2.5微米的细颗粒物（${\rm PM}_{2.5}$）浓度极端值，展示了所提估计器的有效性。