An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning

2026-07-23

AI Summary

This work addresses inverse problems in science and engineering—such as parameter inference and detector response unfolding—by proposing a unified simulation-based inference (SBI) framework that systematically integrates Bayesian and frequentist perspectives. Leveraging machine learning techniques, including neural posterior estimation and neural likelihood estimation, the framework enables efficient and general-purpose parameter inference, with extensions to empirical Bayes and unfolding tasks. The paper provides a comprehensive review of SBI methodologies and their application paradigms, while also offering a thorough analysis of validation strategies and inherent limitations. By clarifying best practices and pitfalls, this study advances the reliable deployment and innovative application of SBI in scientific domains.

Abstract

Simulation-based inference (SBI) with machine learning is an increasingly important tool for solving inverse problems in science and engineering, including parameter inference and the inversion of detector effects. We provide an overview of the Bayesian and frequentist statistical frameworks, describe how machine-learning-based SBI methods, such as neural posterior estimation and neural likelihood estimation, can be used for parameter estimation within these frameworks, and show that the same methods can also be applied to Empirical Bayes or unfolding tasks. We also discuss how to validate inference results and the limitations of SBI with machine learning.

Problem

• simulation-based inference
• inverse problems
• parameter inference
• detector effects
• machine learning

Innovation

• simulation-based inference
• neural posterior estimation
• neural likelihood estimation
• Bayesian inference
• Empirical Bayes