# The Statistical Accuracy of Neural Posterior and Likelihood Estimation

arXiv: https://arxiv.org/abs/2411.12068 · HTML: https://mlsanity.com/paper/2411.12068/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 42 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Builds on (most cited first, 1 of 1)

- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)

## Built on by (most cited first, 18 of 18)

- [Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data](https://mlsanity.com/paper/2501.13483/) (2025)
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- [Does Unsupervised Domain Adaptation Improve the Robustness of Amortized Bayesian Inference? A Systematic Evaluation](https://mlsanity.com/paper/2502.04949/) (2025)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Python](https://mlsanity.com/paper/2602.07098/) (2026)
- [Model Discovery Agent: LLM-assisted Bayesian experiment design for data-efficient discovery of mechanistic world models](https://mlsanity.com/paper/2608.09696/) (2026)
- [Improving the Accuracy of Amortized Model Comparison with Self-Consistency](https://mlsanity.com/paper/2508.20614/) (2025)
- [Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models](https://mlsanity.com/paper/2505.08683/) (2025)
- [Improving the Accuracy of Amortized Model Comparison with Self-Consistency](https://mlsanity.com/paper/2512.14308/) (2025)
- [Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators](https://mlsanity.com/paper/2602.18004/) (2026)
- [Unsupervised Continual Learning for Amortized Bayesian Inference](https://mlsanity.com/paper/2602.22884/) (2026)
- [A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems](https://mlsanity.com/paper/2607.06252/) (2026)
- [Divide-and-Conquer: Towards Generalizable Amortized Bayesian Inference for the Drift Diffusion Model](https://mlsanity.com/paper/2608.03566/) (2026)
- [Mitigating Representation Gaps in Amortized Bayesian Inference with Auxiliary Supervision](https://mlsanity.com/paper/2609.39525/) (2026)
- [Learning Decision-Stump Thresholds in Context: Dynamics of Softmax Attention](https://mlsanity.com/paper/2610.07074/) (2026)
- [Two-way Guidance: Simultaneous Learning of Summary Statistics for Generative Bayes](https://mlsanity.com/paper/2610.12850/) (2026)
- [Sample-Size Extrapolation in Simulation-Based Inference via Statistical Scaling](https://mlsanity.com/paper/2610.16820/) (2026)

## 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.