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This paper establishes machine learning as a critical tool for simulation-based inference in high-energy physics and cosmology, bridging Bayesian and frequentist frameworks to solve complex inverse problems. By detailing methods like neural posterior estimation and validating their limitations, the work offers essential insights into advancing scientific discovery through advanced statistical modeling rather than consumer applications or general software updates.
An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning
arXiv:2607.21702v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Cosmology and Nongalactic Astrophysics (astro-ph.CO); Astrophysics of Galaxies (astro-ph.GA); High Energy Physics - Experiment (hep-ex); High Energy Physics - Phenomenology (hep-ph); Machine Learning (stat.ML)
arXiv:2607.21702 [cs.LG]
(or arXiv:2607.21702v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.21702 arXiv-issued DOI via DataCite (pending registration)
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