# Bayesian Synthetic Likelihood

arXiv: https://arxiv.org/abs/2305.05120 · HTML: https://mlsanity.com/paper/2305.05120/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2023.

## Built on by (most cited first, 29 of 29)

- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [PQMass: Probabilistic Assessment of the Quality of Generative Models using Probability Mass Estimation](https://mlsanity.com/paper/2402.04355/) (2024)
- [Preconditioned Neural Posterior Estimation for Likelihood-free Inference](https://mlsanity.com/paper/2404.13557/) (2024)
- [A Comprehensive Guide to Simulation-based Inference in Computational Biology](https://mlsanity.com/paper/2409.19675/) (2024)
- [Cost-aware simulation-based inference](https://mlsanity.com/paper/2410.07930/) (2024)
- [Multilevel neural simulation-based inference](https://mlsanity.com/paper/2506.06087/) (2025)
- [A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting](https://mlsanity.com/paper/2404.12219/) (2024)
- [A transport approach to sequential simulation-based inference](https://mlsanity.com/paper/2308.13940/) (2023)
- [A Likelihood-Free Approach to Goal-Oriented Bayesian Optimal Experimental Design](https://mlsanity.com/paper/2408.09582/) (2024)
- [Generalized Bayesian deep reinforcement learning](https://mlsanity.com/paper/2412.11743/) (2024)
- [Simulation-based inference for stochastic nonlinear mixed-effects models with applications in systems biology](https://mlsanity.com/paper/2504.11279/) (2025)
- [Wasserstein Gaussianization and Efficient Variational Bayes for Robust Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.14746/) (2023)
- [Structured Regularization for Constrained Optimization on the SPD Manifold](https://mlsanity.com/paper/2410.09660/) (2024)
- [Learning from Summarized Data: Gaussian Process Regression with Sample Quasi-Likelihood](https://mlsanity.com/paper/2412.17455/) (2024)
- [Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models](https://mlsanity.com/paper/2505.08683/) (2025)
- [A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios](https://mlsanity.com/paper/2512.23748/) (2025)
- [An efficient likelihood-free Bayesian inference method based on sequential neural posterior estimation](https://mlsanity.com/paper/2311.12530/) (2023)
- [Leveraging Nested MLMC for Sequential Neural Posterior Estimation with Intractable Likelihoods](https://mlsanity.com/paper/2401.16776/) (2024)
- [Neural Bayes estimation and selection for complex bivariate extremal dependence models](https://mlsanity.com/paper/2503.23156/) (2025)
- [Measuring the right thing: justifying metrics in AI impact assessments](https://mlsanity.com/paper/2504.05007/) (2025)
- [Flexible Selective Inference with Flow-based Transport Maps](https://mlsanity.com/paper/2506.01150/) (2025)
- [Recent Advances in Simulation-based Inference for Gravitational Wave Data Analysis](https://mlsanity.com/paper/2507.11192/) (2025)
- [Misspecification-robust amortised simulation-based inference using variational methods](https://mlsanity.com/paper/2509.05724/) (2025)
- [Fast and Robust Simulation-Based Inference With Optimization Monte Carlo](https://mlsanity.com/paper/2511.13394/) (2025)
- [Prequential posteriors](https://mlsanity.com/paper/2511.17721/) (2025)
- [Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators](https://mlsanity.com/paper/2602.18004/) (2026)
- [Amortized Neural Clustering of Time Series based on Statistical Features](https://mlsanity.com/paper/2605.13128/) (2026)
- [Amortized ratio-estimation importance sampling and localized simulation-based calibration for intractable likelihoods](https://mlsanity.com/paper/2609.39712/) (2026)

## Abstract (arXiv)

Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the construction of the resulting likelihood function. However, sometimes the model is so complicated that evaluation of the likelihood is infeasible, which renders exact Bayesian inference impossible. Bayesian synthetic likelihood (BSL) is a posterior approximation procedure that can be used to conduct inference in situations where the likelihood is intractable, but where simulation from the model is straightforward. In this entry, we give a high-level presentation of BSL, and its extensions aimed at delivering scalable and robust posterior inferences.