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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. 

We discuss the use of neural Bayes estimators for spatial extremal dependence models; in particular, methodologies are developed for coping with the computational challenges often encountered when modelling censored or irregularly-sampled spatial data. Substantial improvements are demonstrated in computational and statistical efficiency relative to conventional likelihood-based approaches using popular spatial extremal dependence models, including max-stable and r-Pareto processes, and random scale mixtures. We showcase the significant computational advantages of using the estimator via an application to Saudi Arabian PM2.5 extremes, which requires fitting over 100 million spatial extremal dependence models, as well as a comparison with competing Bayesian inference approaches using sparse Gaussian process approximations. We also illustrate practical implementation of neural Bayes estimators via the NeuralEstimators R package.

Co-authors (alphabetical order): Raphael Huser, Ben Seiyon Lee,  Reetam Majumder, Matthew Sainsbury-Dale, Emma Simpson, Andrew Zammit-Mangion, Likun Zhang

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