# Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators

arXiv: https://arxiv.org/abs/2602.18004 · HTML: https://mlsanity.com/paper/2602.18004/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 68 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Understanding Random Forests: From Theory to Practice](https://mlsanity.com/paper/1407.7502/) (2014)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)
- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)
- [BayesFlow: Amortized Bayesian Workflows With Neural Networks](https://mlsanity.com/paper/2306.16015/) (2023)
- [Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.05120/) (2023)
- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [The Statistical Accuracy of Neural Posterior and Likelihood Estimation](https://mlsanity.com/paper/2411.12068/) (2024)
- [Robust Approximate Bayesian Inference with Synthetic Likelihood](https://mlsanity.com/paper/1904.04551/) (2019)
- [Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference](https://mlsanity.com/paper/2310.04395/) (2023)
- [ABC random forests for Bayesian parameter inference](https://mlsanity.com/paper/1605.05537/) (2016)
- [Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data](https://mlsanity.com/paper/2501.13483/) (2025)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [Preconditioned Neural Posterior Estimation for Likelihood-free Inference](https://mlsanity.com/paper/2404.13557/) (2024)
- [Efficient identification of informative features in simulation-based inference](https://mlsanity.com/paper/2210.11915/) (2022)
- [Field-level simulation-based inference with galaxy catalogs: the impact of systematic effects](https://mlsanity.com/paper/2310.15234/) (2023)
- [Improving the Accuracy of Marginal Approximations in Likelihood-Free Inference via Localisation](https://mlsanity.com/paper/2207.06655/) (2022)

## Abstract (arXiv)

Simulation-based inference (SBI) enables parameter estimation for complex stochastic models with intractable likelihoods when model simulation is feasible. Neural posterior estimation (NPE) is a popular SBI approach that often achieves accurate inference with far fewer simulations than classical approaches. But in practice, neural approaches can be unreliable for two reasons: incompatible data summaries arising from model misspecification yield unreliable posteriors due to extrapolation, and prior-predictive draws can produce extreme summaries that lead to difficulties in obtaining an accurate posterior for the observed data of interest. Existing preconditioning schemes target well-specified settings, and their behaviour under misspecification remains unexplored. We study preconditioning under misspecification and propose preconditioned robust neural posterior estimation, which computes data-dependent weights that focus training near the observed summaries and fits a robust neural posterior approximation. We also introduce a forest-proximity preconditioning approach that uses tree-based proximity scores to down-weight outlying simulations and concentrate computation around the observed dataset. Across two synthetic examples and one real example with incompatible summaries and extreme prior-predictive behaviour, we demonstrate that preconditioning combined with robust NPE increases stability and improves accuracy, calibration, and posterior-predictive fit over standard baseline methods.