Theoretical guarantees for neural likelihood-free estimators in spatial extremes

Establish theoretical accuracy guarantees for neural likelihood-free parameter estimation methods used in extreme-value applications, specifically characterizing how estimation error depends on the chosen neural network architecture and the number of training samples when modeling spatial or spatio-temporal extremes.

Background

The paper highlights growing interest in neural, likelihood-free inference methods (e.g., neural Bayes estimators) to overcome computational hurdles in spatial extreme-value models where likelihoods are expensive or intractable. While these amortized approaches can provide rapid parameter estimates after training, the authors note that formal theoretical guarantees are lacking.

In particular, the relationship between estimator accuracy, neural network architecture, and training data size remains unspecified for extreme-value applications. Formalizing these guarantees would underpin the reliability of neural estimators when extrapolating to rare-event regimes central to environmental risk assessment.