An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning
Maximilian Dax, Theo Heimel, Gilles Louppe
cs.LG, astro-ph.CO, astro-ph.GA, hep-ex, hep-ph, stat.ML
Submitted: 2026-08-21
Updated: 2026-08-24
Comments: 39 pages, 13 figures
Code: https://github.com/smsharma/awesome-neural-sbi
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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
Terminology
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.
Sources
- Simulation-Based Inference: A Practical Guide
- The frontier of simulation-based inference
- Simulation-based inference methods for particle physics
- Machine Learning Techniques for Astrophysics and Cosmology: Simulation-Based Inference
- Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference
- Fast $\epsilon$-free Inference of Simulation Models with Bayesian Conditional Density Estimation
- Approximating the Likelihood in Approximate Bayesian Computation
- Variational Inference with Normalizing Flows
- Consistency Models for Scalable and Fast Simulation-Based Inference
- Density estimation using Real NVP
- Flow Matching for Scalable Simulation-Based Inference
- Auto-Encoding Variational Bayes
- Real-time gravitational-wave inference for binary neutron stars using machine learning
- Approximating Likelihood Ratios with Calibrated Discriminative Classifiers
- Learning Likelihood Ratios with Neural Network Classifiers
- Mining gold from implicit models to improve likelihood-free inference
- A Guide to Constraining Effective Field Theories with Machine Learning
- OmniFold: A Method to Simultaneously Unfold All Observables
- The Landscape of Unfolding with Machine Learning
- Invertible Networks or Partons to Detector and Back Again
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