Neural Bayes estimators for likelihood-free and amortised inference for spatial extremes

Likelihood-based inference with spatial extremal dependence models is often infeasible in moderate or high dimensions due to an intractable likelihood function and/or the need for computationally expensive censoring to reduce estimation bias. Neural Bayes estimators are a promising recent approach to inference that uses neural networks to transform data into parameter estimates. They are likelihood-free, inherit the optimality properties of Bayes estimators, and are substantially faster than classical methods. Neural Bayes estimators are adapted for peaks-over-threshold dependence models; in particular, a methodology is developed for coping with the computational challenges often encountered when modelling spatial extremes (e.g., censoring). Substantial improvements are demonstrated in computational and statistical efficiency relative to conventional likelihood-based approaches using popular extremal dependence models, including max-stable and r-Pareto processes and random scale mixtures. The application to Arabian PM2.5 concentrations illustrates the significant computational advantages of using the estimator over traditional likelihood-based techniques, as it requires fitting over 100 million spatial extremal dependence models.