Neural Bayes estimators for censored inference with peaks-over-threshold models
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929390593507328 |
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| author | Richards, Jordan Sainsbury-Dale, Matthew Zammit-Mangion, Andrew Huser, Raphaël |
| author_facet | Richards, Jordan Sainsbury-Dale, Matthew Zammit-Mangion, Andrew Huser, Raphaël |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15642 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Neural Bayes estimators for censored inference with peaks-over-threshold models Richards, Jordan Sainsbury-Dale, Matthew Zammit-Mangion, Andrew Huser, Raphaël Methodology Machine Learning 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. |
| title | Neural Bayes estimators for censored inference with peaks-over-threshold models |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2306.15642 |