mlsanityData to 7 Oct 2026

The Statistical Accuracy of Neural Posterior and Likelihood Estimation

arXiv 2411.12068 ↗First posted 18 Nov 2024stat.ML cs.LG math.STcited by 15

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Abstract (arXiv)

Neural posterior estimation (NPE) and neural likelihood estimation (NLE) are machine learning approaches that provide accurate posterior, and likelihood, approximations in complex modeling scenarios, and in situations where conducting amortized inference is a necessity. While such methods have shown significant promise across a range of diverse scientific applications, the statistical accuracy of these methods is so far unexplored. In this manuscript, we give, for the first time, an in-depth exploration on the statistical behavior of NPE and NLE. We prove that these methods have similar theoretical guarantees to common statistical methods like approximate Bayesian computation (ABC) and Bayesian synthetic likelihood (BSL). While NPE and NLE methods are just as accurate as ABC and BSL, we prove that this accuracy can often be achieved at a vastly reduced computational cost, and will therefore deliver more attractive approximations than ABC and BSL in certain problems. We verify our results theoretically and in several examples from the literature.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 1 of its 42 references that are in the map. First posted on arXiv 18 Nov 2024.

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1 of 42 references.

References · 1

  1. 2022Investigating the Impact of Model Misspecification in Neural Simulation-based Inferencecited by 44

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 8; 2026: 7.

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  1. 2025Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Datacited by 11
  2. 2025Does Unsupervised Domain Adaptation Improve the Robustness of Amortized Bayesian Inference? A Systematic Evaluationcited by 10
  3. 2025Multifidelity Simulation-based Inference for Computationally Expensive Simulatorscited by 9
  4. 2025Simulation-based Bayesian inference under model misspecificationcited by 9
  5. 2025Diffusion Models in Simulation-Based Inference: A Tutorial Reviewcited by 8
  6. 2026BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Pythoncited by 7
  7. 2026Model Discovery Agent: LLM-assisted Bayesian experiment design for data-efficient discovery of mechanistic world modelscited by 6
  8. 2025Improving the Accuracy of Amortized Model Comparison with Self-Consistencycited by 5
  9. 2025Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Modelscited by 1
  10. 2025Improving the Accuracy of Amortized Model Comparison with Self-Consistencycited by 0
  11. 2026Preconditioned Robust Neural Posterior Estimation for Misspecified Simulatorscited by 0
  12. 2026Unsupervised Continual Learning for Amortized Bayesian Inferencecited by 0
3 more
  1. 2026A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problemscited by 0
  2. 2026Divide-and-Conquer: Towards Generalizable Amortized Bayesian Inference for the Drift Diffusion Modelcited by 0
  3. 2026Mitigating Representation Gaps in Amortized Bayesian Inference with Auxiliary Supervisioncited by 0