  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.

Methodology;Machine Learning