# Robust Approximate Bayesian Inference with Synthetic Likelihood

arXiv: https://arxiv.org/abs/1904.04551 · HTML: https://mlsanity.com/paper/1904.04551/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2019.

## Built on by (most cited first, 14 of 14)

- [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)
- [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)
- [Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data](https://mlsanity.com/paper/2501.13483/) (2025)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [Misspecification-robust Sequential Neural Likelihood for Simulation-based Inference](https://mlsanity.com/paper/2301.13368/) (2023)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigation](https://mlsanity.com/paper/2406.03154/) (2024)
- [A Comprehensive Guide to Simulation-based Inference in Computational Biology](https://mlsanity.com/paper/2409.19675/) (2024)
- [Meta-Uncertainty in Bayesian Model Comparison](https://mlsanity.com/paper/2210.07278/) (2022)
- [Minimum Distance Summaries for Robust Neural Posterior Estimation](https://mlsanity.com/paper/2602.09161/) (2026)
- [Wasserstein Gaussianization and Efficient Variational Bayes for Robust Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.14746/) (2023)
- [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)

## Abstract (arXiv)

Bayesian synthetic likelihood (BSL) is now an established method for conducting approximate Bayesian inference in models where, due to the intractability of the likelihood function, exact Bayesian approaches are either infeasible or computationally too demanding. Implicit in the application of BSL is the assumption that the data generating process (DGP) can produce simulated summary statistics that capture the behaviour of the observed summary statistics. We demonstrate that if this compatibility between the actual and assumed DGP is not satisfied, i.e., if the model is misspecified, BSL can yield unreliable parameter inference. To circumvent this issue, we propose a new BSL approach that can detect the presence of model misspecification, and simultaneously deliver useful inferences even under significant model misspecification. Two simulated and two real data examples demonstrate the performance of this new approach to BSL, and document its superior accuracy over standard BSL when the assumed model is misspecified.