# Simulation-based Bayesian inference under model misspecification

**Authors:** Ryan P. Kelly, David J. Warne, David T. Frazier, David J. Nott, Michael U. Gutmann, Christopher Drovandi  
**arXiv:** [2503.12315](https://arxiv.org/abs/2503.12315)  
**Date:** 2025-03-16  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2503.12315v1/

## Key points

- Simulation-based Bayesian inference (SBI) methods are commonly used for parameter estimation in complex models with challenging likelihood evaluation.
- Challenges arise when the simulation model does not accurately represent the true data-generating process, leading to model misspecification.
- One key strategy to address model misspecification is the use of robust summary statistics that capture relevant features while filtering out irrelevant noise or artifacts.
- Constructing robust summary statistics is crucial in SBI research to differentiate between relevant and irrelevant model misfit and focus on essential features for analysis objectives.
- Inference based on summary statistics shifts the focus from standard Bayesian posterior using full datasets to partial posterior conditioned on selected summaries, enhancing robustness through strategies like M-estimators or Bayesian restricted likelihood approaches.
- Alternative strategies such as Bayesian data selection and generalised Bayesian inference offer innovative ways to handle model misspecification by identifying compatible parts of data with assumed parametric models or incorporating expert knowledge through sequential experimental design.

## Summary

Simulation-based Bayesian inference (SBI) methods are widely used for parameter estimation in complex models where evaluating the likelihood is challenging. However, these methods often assume that the simulation model accurately represents the true data-generating process. In realistic scenarios, this may not always be the case. This paper delves into the challenges faced by SBI methods when dealing with model misspecification and explores strategies to mitigate its effects. One key strategy highlighted in this study is the use of robust summary statistics. When using summaries instead of the full dataset, model misspecification can manifest as an inability to reproduce observed summaries rather than the entire dataset. By carefully selecting robust summaries that capture relevant features while disregarding irrelevant noise or artifacts, researchers can focus on aspects crucial for inferential goals. The construction of summary statistics has been a focal point in SBI research, with an emphasis on creating summaries that are resilient to model misspecification. Adhering to a principled Bayesian workflow, researchers differentiate between relevant and irrelevant model misfit. Instead of striving for an exact match between the assumed model and the true data-generating process, attention is directed towards summarizing data into features essential for analysis objectives while filtering out irrelevant elements. Robust summary statistics play a vital role in capturing relevant features effectively even in cases of minor deviations from model assumptions. Inference based on summary statistics shifts the focus from standard Bayesian posterior based on full datasets to partial posterior conditioned on selected summaries. This approach aims to enhance robustness by focusing on relevant features through robust summary statistics such as M-estimators or Bayesian restricted likelihood approaches that are insensitive to undesirable perturbations. Additionally, alternative strategies like Bayesian data selection and generalised Bayesian inference offer innovative ways to handle model misspecification by identifying compatible parts of data with assumed parametric models or incorporating expert knowledge through sequential experimental design. Overall, this paper underscores the importance of addressing model misspecification in SBI methods and presents various strategies aimed at enhancing robustness and accuracy in parameter estimation within complex models. Through empirical results on illustrative examples, it demonstrates how these strategies can effectively mitigate the impact of misspecification and improve inference outcomes.