mlsanityData to 7 Oct 2026

Likelihood-Free Parameter Estimation with Neural Bayes Estimators

arXiv 2208.12942 ↗First posted 27 Aug 2022stat.ME stat.MLcited by 31

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Abstract (arXiv)

Neural point estimators are neural networks that map data to parameter point estimates. They are fast, likelihood free and, due to their amortised nature, amenable to fast bootstrap-based uncertainty quantification. In this paper, 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 making inference from replicated data, which we address in the neural setting using permutation-invariant neural networks. Through extensive simulation studies we show that these neural point estimators can quickly and optimally (in a Bayes sense) estimate parameters in weakly-identified and highly-parameterised models with relative ease. We demonstrate 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.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 21 of its 78 references that are in the map. First posted on arXiv 27 Aug 2022.

Builds on

21 of 78 references.

References · 21

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  2. 2017Deep Setscited by 1,394
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  4. 2020BayesFlow: Learning complex stochastic models with invertible neural networkscited by 139
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9 more
  1. 2022Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimizationcited by 14
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 9; 2025: 6; 2026: 11.

31 papers.

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  1. 2024Neural Methods for Amortized Inferencecited by 36
  2. 2023Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networkscited by 13
  3. 2023Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoodscited by 10
  4. 2023Fast parameter estimation of Generalized Extreme Value distribution using Neural Networkscited by 7
  5. 2026BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Pythoncited by 7
  6. 2023Towards black-box parameter estimationcited by 6
  7. 2023Neural Bayes estimators for censored inference with peaks-over-threshold modelscited by 6
  8. 2024Paired Autoencoders for Likelihood-free Estimation in Inverse Problemscited by 6
  9. 2024Generative Bayesian Computation for Maximum Expected Utilitycited by 3
  10. 2024Deep Optimal Experimental Design for Parameter Estimation Problemscited by 2
  11. 2024Deep Generative Quantile Bayescited by 1
  12. 2025Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networkscited by 1
19 more
  1. 2025LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Datacited by 1
  2. 2025Theoretical guarantees for neural estimators in parametric statisticscited by 1
  3. 2025Trustworthy scientific inference with generative modelscited by 1
  4. 2026It Just Takes Two: Scaling Amortized Inference to Large Setscited by 1
  5. 2024Latent Variable Sequence Identification for Cognitive Models with Neural Network Estimatorscited by 0
  6. 2024Modeling Spatial Extremal Dependence of Precipitation Using Distributional Neural Networkscited by 0
  7. 2024A Generalized Unified Skew-Normal Process with Neural Bayes Inferencecited by 0
  8. 2024When the whole is greater than the sum of its parts: Scaling black-box inference to large data settings through divide-and-conquercited by 0
  9. 2025Neural Bayes estimation and selection for complex bivariate extremal dependence modelscited by 0
  10. 2025Fast Likelihood-Free Parameter Estimation for L'evy Processescited by 0
  11. 2026Neural Architectures for Amortized Bayesian Inference: Statistical Foundations and Empirical Assessmentscited by 0
  12. 2026Amortized Bayesian inference for actigraph time sheet data from mobile devicescited by 0
  13. 2026Permutation-preserving Functions and Neural Vecchia Covariance Kernelscited by 0
  14. 2026Keeping Score: Adaptive, Tuning-Free Loss Weighting for Score-Augmented Neural Ratio Estimationcited by 0
  15. 2026Benchmark of Likelihood-Free Inference Methods based on Neural and Optimal Transport Approachescited by 0
  16. 2026The Simulacrum: Decision-Theoretic Pretraining for Near-Optimal Time-Series Forecasting and Inferencecited by 0
  17. 2026Stochastic generator of trajectories from record data: application to the fluctuations of a glacier's frontal position from a sample of morainescited by 0
  18. 2026Amortized Inference for Sampling Distributions Where the Bootstrap Failscited by 0
  19. 2026Mitigating Representation Gaps in Amortized Bayesian Inference with Auxiliary Supervisioncited by 0