Neural Bayes Estimators for Censored Inference with Peaks-over-threshold Models
Conference
Format: IPS Abstract
Keywords: deep neural networks, extremes, likelihood-free, spatial statistics
Session: Invited Session 8A - Bayesian Models And Methods In Environmental Applications
Wednesday 4 December 1 p.m. - 2:30 p.m. (Australia/Adelaide)
Abstract
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. Joint work with Jordan Richards, Matthew Sainsbury-Dale, and Andrew Zammit-Mangion.