Likelihood-Free Parameter Estimation with Neural Bayes Estimators

Matthew Sainsbury-Dale*, Andrew Zammit-Mangion, Raphaël Huser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Neural Bayes estimators are neural networks that approximate Bayes estimators. They are fast, likelihood-free, and amenable to rapid bootstrap-based uncertainty quantification. In this article, we aim to increase the awareness of statisticians to this relatively new inferential tool, and to facilitate its adoption by providing user-friendly open-source software. We also give attention to the ubiquitous problem of estimating parameters from replicated data, which we address using permutation-invariant neural networks. Through extensive simulation studies we demonstrate that neural Bayes estimators can be used to quickly estimate parameters in weakly identified and highly parameterized models with relative ease. We illustrate their applicability through an analysis of extreme sea-surface temperature in the Red Sea where, after training, we obtain parameter estimates and bootstrap-based confidence intervals from hundreds of spatial fields in a fraction of a second.

Original languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalAmerican Statistician
Issue number1
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023 The Author(s). Published with license by Taylor & Francis Group, LLC.


  • Amortized inference
  • Deep learning
  • Exchangeable data
  • Extreme-value model
  • Permutation invariant
  • Point estimation
  • Spatial statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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