Likelihood-Free Inference for Multivariate Generalized Pareto Models

2026-05-26

AI Summary

This study addresses the challenge of accurately inferring marginal tails and dependence structures in multivariate generalized Pareto models when likelihood-based inference is infeasible, the support is discrete, or exceedance samples are sparse. To overcome these limitations, the authors propose AW–NBE, a two-stage likelihood-free method: it first obtains initial parameter estimates via neural Bayesian estimation trained on simulated data, then refines these estimates by locally aligning the empirical distributions of observed and simulated samples using an optimal transport step based on Sinkhorn divergence. The approach innovatively integrates neural Bayesian estimation with optimal transport and introduces novel multivariate Q–Q plots and potential-based diagnostic tools for model validation. Experiments on financial returns and Swiss drought data demonstrate that AW–NBE substantially outperforms existing methods, achieving higher tail inference accuracy while preserving dependence structure.

Abstract

Likelihood-based inference for multivariate extreme-value models is often unreliable or infeasible when likelihoods are intractable or supports are discrete. This challenge is particularly acute for multivariate discrete generalized Pareto models, where both marginal tail behavior and dependence must be inferred from sparse exceedance samples. We propose a two-stage likelihood-free inference procedure, termed AW--NBE (Adaptive Wasserstein Neural Bayes Estimator), that combines neural Bayes estimation with a targeted optimal transport refinement step based on the Sinkhorn discrepancy. In the first stage, a neural Bayes estimator trained on simulated data provides fast and stable initial parameter estimates. In the second stage, these estimates are locally refined by minimizing the Sinkhorn divergence between the empirical distributions of observed and simulated exceedances. This refinement reduces the Sinkhorn discrepancy between the empirical distributions of observed and simulated exceedances, while preserving dependence features learned by the neural estimator. Model adequacy is assessed using new optimal transport based multivariate Q--Q and potential diagnostics. Applications to financial log-returns and Swiss dry spell exceedances suggest that AW--NBE can improve parameter inferences compared to estimation using solely, either the Sinkhorn discrepancy, or the standard neural Bayes estimators and censored likelihood estimation.

Problem

• likelihood-free inference
• multivariate generalized Pareto models
• extreme-value analysis
• discrete support
• sparse exceedance samples

Innovation

• likelihood-free inference
• neural Bayes estimation
• Sinkhorn discrepancy
• optimal transport
• multivariate generalized Pareto models