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Communicating likelihoods with normalising flows.

Jack Y Araz^1,2,3, Anja Beck⁴, Méril Reboud⁵

¹Department of Physics and Astronomy, University College London, London, WC1E 6B UK.

The European Physical Journal. C, Particles and Fields

|July 15, 2026

Summary

This study introduces a machine learning workflow to model unbinned likelihoods from data samples. The method validates learned likelihoods with statistical tests, enabling reliable sharing for high-energy physics analyses.

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Area of Science:

Machine Learning
Statistical Modeling
High-Energy Physics

Background:

Modeling unbinned likelihoods is crucial for data analysis in physics.
Existing methods lack rigorous validation of learned likelihoods.
Reliable communication of likelihoods between analyses is challenging.

Purpose of the Study:

To develop a machine-learning-based workflow for modeling unbinned likelihoods.
To introduce rigorous statistical validation for learned likelihood models.
To facilitate the reliable sharing of experimental and phenomenological likelihoods.

Main Methods:

Utilized machine learning to model unbinned likelihoods from samples.
Employed rigorous statistical tests, including the Kolmogorov-Smirnov test, for validation.
Demonstrated the workflow's effectiveness in three high-energy physics case studies.

Main Results:

Successfully modeled unbinned likelihoods using a machine learning approach.
Validated the learned likelihoods using statistical tests, ensuring reliability.
Showcased the workflow's applicability and effectiveness in high-energy physics.

Conclusions:

The proposed machine learning workflow provides a validated method for modeling unbinned likelihoods.
This approach enhances the reliability and communication of likelihoods for subsequent analyses.
An open-source implementation, nabu, is provided to encourage broader adoption.