Neural Inference Methods for Spatial Extremes in High Dimensions

Raphael Huser

KAUST - King Abdullah University of Science and Technology

Monday 10th February 2025

14:30:00

Room 16B.0.1, Building 16B, Via Bonardi, 9

Neural Bayes estimators are neural networks that approximate Bayes estimators. They are thus likelihood-free, extremely fast to evaluate, and amenable to rapid uncertainty quantification, while also (approximately) inheriting the appealing large-sample properties of Bayes estimators. Neural Bayes estimators are therefore ideal to use with spatial extremes models observed in high dimensions, where estimation is often a computational bottleneck. In this seminar, I will summarize our research progress in that area and explain how, for any spatial model that can be simulated from, a single neural Bayes estimator can be trained to make fast inference with new data that involve varying sample sizes, varying spatial configurations of observed locations, and varying censoring levels used in peaks-over-threshold modeling. This methodology will be illustrated by application to sea surface temperature extremes over the Red Sea, and air pollution extremes over the whole Arabic peninsula. Joint work with Jordan Richards, Matthew Sainsbury-Dale, and Andrew Zammit-Mangion. This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk. Contact: alessandra.menafoglio@polimi.it