Inference for spatial extremal dependence models can be computationally burdensome in moderate-to-high dimensions due to their reliance on intractable and/or censored likelihoods. Exploiting recent advances in likelihood-free inference with neural Bayes estimators (that is, neural estimators that target Bayes estimators), we develop a novel approach to construct highly efficient estimators for censored peaks-over-threshold models by encoding censoring information in the neural network architecture. Our new method provides a paradigm shift that challenges traditional censored likelihood-based inference for spatial extremes. Our simulation studies highlight significant gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when applying our novel estimators for inference of popular extremal dependence models, such as max-stable, $r$-Pareto, and random scale mixture processes. We also illustrate that it is possible to train a single estimator for a general censoring level, obviating the need to retrain 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 particulate matter 2.5 microns or less in diameter (PM2.5) concentration over the whole of Saudi Arabia.

翻译：针对空间极值依赖模型的推断，在中高维度场景下常因依赖难解和/或截断似然而面临计算负担。利用最近基于似然自由推断与神经贝叶斯估计量（即针对贝叶斯估计量的神经估计器）的进展，我们通过将截断信息编码至神经网络架构，提出了一种构建高效截断峰值超阈值模型估计量的新方法。该方法彻底改变了传统基于截断似然的空间极值推断范式。模拟研究表明，相较于基于似然的竞争方法，我们提出的新型估计量在推断流行极值依赖模型（如最大稳定过程、$r$-Pareto过程和随机尺度混合过程）时，在计算效率与统计效率方面均取得显著提升。同时，我们证明可针对通用截断水平训练单个估计量，从而避免因截断水平变化需重新训练的问题。通过快速推断构建覆盖沙特阿拉伯全境、规模达数十万的高维空间极值依赖模型，我们评估了直径≤2.5微米的颗粒物（PM2.5）浓度，验证了该估计量的有效性。