# Misspecification-robust amortised simulation-based inference using variational methods

arXiv: https://arxiv.org/abs/2509.05724 · HTML: https://mlsanity.com/paper/2509.05724/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 68 references that are in the map.
- First posted on arXiv 6 Sep 2025.

## Builds on (most cited first, 30 of 40)

- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [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)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [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)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [Likelihood-free inference with emulator networks](https://mlsanity.com/paper/1805.09294/) (2018)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [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)
- [Variational methods for simulation-based inference](https://mlsanity.com/paper/2203.04176/) (2022)
- [Doubly Reparameterized Gradient Estimators for Monte Carlo Objectives](https://mlsanity.com/paper/1810.04152/) (2018)
- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
- [Reinterpreting Importance-Weighted Autoencoders](https://mlsanity.com/paper/1704.02916/) (2017)
- [Sequential Neural Posterior and Likelihood Approximation](https://mlsanity.com/paper/2102.06522/) (2021)
- [Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.05120/) (2023)
- [Amortized Variational Inference: When and Why?](https://mlsanity.com/paper/2307.11018/) (2023)
- [Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference](https://mlsanity.com/paper/2210.05686/) (2022)
- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation](https://mlsanity.com/paper/1404.7063/) (2014)
- [Adversarial robustness of amortized Bayesian inference](https://mlsanity.com/paper/2305.14984/) (2023)
- [Robust Approximate Bayesian Inference with Synthetic Likelihood](https://mlsanity.com/paper/1904.04551/) (2019)

## Abstract (arXiv)

Recent advances in neural density estimation have enabled powerful simulation-based inference (SBI) methods that can flexibly approximate Bayesian inference for intractable stochastic models. Although these methods have demonstrated reliable posterior estimation when the simulator accurately represents the underlying data generative process (DGP), recent work has shown that they perform poorly in the presence of model misspecification. This poses a significant issue for their use in real-world problems, due to simulators always misrepresenting the true DGP to a certain degree. In this paper, we introduce robust variational neural posterior estimation (RVNP), a method which addresses the problem of misspecification in amortised SBI by bridging the simulation-to-reality gap using variational inference and error modelling. We test RVNP on multiple benchmark tasks, including using real data from astronomy, and show that it can recover robust posterior inference in a data-driven manner without adopting hyperparameters or priors governing the misspecification influence.