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 encode censoring information in the neural network architecture. 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 (PM2.5) concentration over the whole of Saudi Arabia.

翻译：利用空间极值依赖模型进行推断时，由于涉及难以处理的和/或截断的似然函数，计算负担通常较重。基于似然自由推断与神经贝叶斯估计量（即近似贝叶斯估计量的神经网络）的最新进展，我们开发了针对截断峰值超阈值模型的高效估计量，通过将截断信息编码到神经网络架构中实现。我们的新方法提供了范式转变，挑战了传统基于截断似然的空间极值依赖模型推断方法。仿真研究显示，相比基于似然的竞争方法，应用我们提出的估计量对主流极值依赖模型（如最大稳定过程、$r$-Pareto过程及随机尺度混合过程模型）进行推断时，在计算效率和统计效率上均取得显著提升。我们还证明，可为通用截断水平训练单一神经贝叶斯估计量，从而避免在改变截断水平时重新训练网络。通过评估沙特阿拉伯全境直径≤2.5微米的极端颗粒物（PM2.5）浓度，我们利用该估计量对数十万个高维空间极值依赖模型进行快速推断，验证了其有效性。