# Simulation-based Bayesian inference under model misspecification

arXiv: https://arxiv.org/abs/2503.12315 · HTML: https://mlsanity.com/paper/2503.12315/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 79 of its 157 references that are in the map.
- First posted on arXiv 16 Mar 2025.

## Builds on (most cited first, 30 of 79)

- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [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)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [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)
- [Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models](https://mlsanity.com/paper/1501.03291/) (2015)
- [Likelihood-free inference with emulator networks](https://mlsanity.com/paper/1805.09294/) (2018)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Bayesian Workflow](https://mlsanity.com/paper/2011.01808/) (2020)
- [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)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)

## Built on by (most cited first, 9 of 9)

- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [G-Sim: Generative Simulations with Large Language Models and Gradient-Free Calibration](https://mlsanity.com/paper/2506.09272/) (2025)
- [Minimum Distance Summaries for Robust Neural Posterior Estimation](https://mlsanity.com/paper/2602.09161/) (2026)
- [Representative, Informative, and De-Amplifying: Requirements for Robust Bayesian Active Learning under Model Misspecification](https://mlsanity.com/paper/2506.07805/) (2025)
- [Flow Matching Calibration for Simulation-Based Inference under Model Misspecification](https://mlsanity.com/paper/2509.23385/) (2025)
- [Scalable Simulation-Based Model Inference with Test-Time Complexity Control](https://mlsanity.com/paper/2603.15292/) (2026)
- [Misspecification-robust amortised simulation-based inference using variational methods](https://mlsanity.com/paper/2509.05724/) (2025)
- [Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators](https://mlsanity.com/paper/2602.18004/) (2026)
- [Mixed neural posterior estimation for simulators with discrete and continuous parameters](https://mlsanity.com/paper/2605.13551/) (2026)

## Abstract (arXiv)

Simulation-based Bayesian inference (SBI) methods are widely used for parameter estimation in complex models where evaluating the likelihood is challenging but generating simulations is relatively straightforward. However, these methods commonly assume that the simulation model accurately reflects the true data-generating process, an assumption that is frequently violated in realistic scenarios. In this paper, we focus on the challenges faced by SBI methods under model misspecification. We consolidate recent research aimed at mitigating the effects of misspecification, highlighting three key strategies: i) robust summary statistics, ii) generalised Bayesian inference, and iii) error modelling and adjustment parameters. To illustrate both the vulnerabilities of popular SBI methods and the effectiveness of misspecification-robust alternatives, we present empirical results on an illustrative example.