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  • Open Access

Residual neural likelihood estimation and its application to gravitational-wave astronomy

Mattia Emma*

Gregory Ashton

  • Department of Physics, Royal Holloway University of London, Egham, TW20 0EX, United Kingdom and Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom

  • *Contact author: mattia.emma@ligo.org
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Phys. Rev. D 113, 124064 – Published 22 June, 2026

DOI: https://doi.org/10.1103/f5df-cxyg

Abstract

Simulation-based inference provides a powerful framework for Bayesian inference when the likelihood is analytically intractable or computationally prohibitive. By leveraging machine-learning techniques and neural density estimators, it enables flexible likelihood or posterior modeling directly from simulations. We introduce residual neural likelihood estimation (RNLE), a modification of neural likelihood estimation (NLE) that learns the likelihood of non-Gaussian noise in gravitational-wave detector data. Exploiting the additive structure of the signal and noise generation processes, RNLE directly models the noise distribution, substantially reducing the number of simulations required for accurate parameter estimation and improving robustness to realistic noise artifacts. The performance of RNLE is demonstrated using a toy model, simulated gravitational-wave signals, and real detector noise from ground based interferometers. In the presence of loud non-Gaussian transients, we find that RNLE can improve robustness of parameter recovery when trained on appropriately constructed datasets. We further assess the stability of the method by quantifying the variability introduced by retraining the conditional density estimator on statistically identical datasets with different optimization seeds, referred to as training noise, and investigate evidence-weighted combinations of independently trained RNLE realizations as a diagnostic of this variability. An implementation of RNLE is publicly available in the sbilby package, enabling its deployment within gravitational-wave astronomy and a broad range of scientific applications requiring flexible, simulation-based likelihood estimation.

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Phys. Rev. D 113, 124064– Published 22 June, 2026
  • Received 21 January 2026
  • Accepted 20 May 2026
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