Benchmark of Likelihood-Free Inference Methods based on Neural and Optimal Transport Approaches

2026-05-28

AI Summary

This study addresses the lack of systematic evaluation of likelihood-free inference methods under complex data structures, particularly heavy-tailed or discrete distributions. Focusing on such challenging scenarios for the first time, the authors conduct comprehensive simulation experiments comparing four representative approaches—maximum likelihood estimation (MLE), neural Bayes estimator (NBE), entropy-regularized optimal transport (EOT), and adaptive weighting NBE (AW–NBE)—with special attention to their performance in the presence of extreme values and discrete observations. The findings reveal distinct strengths and limitations of each method when handling non-standard data, underscore the critical influence of evaluation metric choice on conclusions, and fill a notable gap in existing benchmarking efforts. This work provides empirical guidance for selecting appropriate inference methods in practical applications involving heavy-tailed or discrete data.

Abstract

Simulation-based inference (SBI) has become an increasingly important framework for parameter estimation in models for which simulation is feasible, including cases where likelihood evaluation is unavailable or costly. While recent work has introduced benchmark frameworks to compare likelihood-free methods, these studies often do not account for structural features such as heavy-tails or discreteness. In this article, we investigate how the performance of likelihood-free inference methods depends on these structural properties. We consider four approaches: MLE, NBE, EOT and AW--NBE and evaluate them using simulations. This study highlights the importance of carefully selecting evaluation tools in the presence of extremes and discrete data.

Problem

• simulation-based inference
• likelihood-free inference
• heavy-tailed data
• discrete data
• benchmarking

Innovation

• likelihood-free inference
• simulation-based inference
• heavy-tailed data
• discrete data
• optimal transport