# Synthetic likelihood in misspecified models

arXiv: https://arxiv.org/abs/2104.03436 · HTML: https://mlsanity.com/paper/2104.03436/

## Key facts

- Cited by 5 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 8 Apr 2021.

## Built on by (most cited first, 5 of 5)

- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)
- [Misspecification-robust Sequential Neural Likelihood for Simulation-based Inference](https://mlsanity.com/paper/2301.13368/) (2023)
- [A Comprehensive Guide to Simulation-based Inference in Computational Biology](https://mlsanity.com/paper/2409.19675/) (2024)
- [Misspecification-robust amortised simulation-based inference using variational methods](https://mlsanity.com/paper/2509.05724/) (2025)

## Abstract (arXiv)

Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the Bayesian synthetic likelihood posterior when the assumed model differs from the actual data generating process. We demonstrate that the Bayesian synthetic likelihood posterior can display a wide range of non-standard behaviours depending on the level of model misspecification, including multimodality and asymptotic non-Gaussianity. Our results suggest that likelihood tempering, a common approach for robust Bayesian inference, fails for synthetic likelihood whilst recently proposed robust synthetic likelihood approaches can ameliorate this behavior and deliver reliable posterior inference under model misspecification. All results are illustrated using a simple running example.