Neural Bayes estimators for censored inference with peaks-over-threshold models

• URL: http://arxiv.org/abs/2306.15642v4
• Date: Tue, 18 Jun 2024 13:55:37 GMT
• Title: Neural Bayes estimators for censored inference with peaks-over-threshold models
• Authors: Jordan Richards, Matthew Sainsbury-Dale, Andrew Zammit-Mangion, Raphaël Huser,
• Abstract summary: Building on advances in likelihood-free inference with neural Bayes estimators, we develop highly efficient estimators for censored peaks-over-threshold models. Our new method challenges traditional censored likelihood-based inference methods for spatial extremal dependence models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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