# Bayesian inference for misspecified generative models

arXiv: https://arxiv.org/abs/2305.08429 · HTML: https://mlsanity.com/paper/2305.08429/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2023.

## Built on by (most cited first, 11 of 11)

- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [G-Sim: Generative Simulations with Large Language Models and Gradient-Free Calibration](https://mlsanity.com/paper/2506.09272/) (2025)
- [A Comprehensive Guide to Simulation-based Inference in Computational Biology](https://mlsanity.com/paper/2409.19675/) (2024)
- [Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach](https://mlsanity.com/paper/2504.20319/) (2025)
- [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)
- [Bayesian Decision Making around Experts](https://mlsanity.com/paper/2510.08113/) (2025)
- [BOCO: Bayesian Online Contextual Optimization for Decision-Focused Online Learning](https://mlsanity.com/paper/2511.20413/) (2025)
- [Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance](https://mlsanity.com/paper/2601.16425/) (2026)
- [Simulation-Based Quantum System Inference with Neural Posterior Estimation](https://mlsanity.com/paper/2609.34995/) (2026)

## Abstract (arXiv)

Bayesian inference is a powerful tool for combining information in complex settings, a task of increasing importance in modern applications. However, Bayesian inference with a flawed model can produce unreliable conclusions. This review discusses approaches to performing Bayesian inference when the model is misspecified, where by misspecified we mean that the analyst is unwilling to act as if the model is correct. Much has been written about this topic, and in most cases we do not believe that a conventional Bayesian analysis is meaningful when there is serious model misspecification. Nevertheless, in some cases it is possible to use a well-specified model to give meaning to a Bayesian analysis of a misspecified model and we will focus on such cases. Three main classes of methods are discussed - restricted likelihood methods, which use a model based on a non-sufficient summary of the original data; modular inference methods which use a model constructed from coupled submodels and some of the submodels are correctly specified; and the use of a reference model to construct a projected posterior or predictive distribution for a simplified model considered to be useful for prediction or interpretation.