Neural Bayes Estimators for Censored Inference with Peaks-over-threshold Models

Oregon Convention Center 

Making inference with spatial extremal dependence models can be computationally costly as they involve intractable and/or censored likelihoods. Building upon recent advances in likelihood-free inference with neural 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. Simulation studies show massive gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when fitting popular extremal dependence models, such as max-stable, 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 high PM2.5 concentration over the whole of Saudi Arabia.