# Likelihood-free inference with emulator networks

arXiv: https://arxiv.org/abs/1805.09294 · HTML: https://mlsanity.com/paper/1805.09294/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 30 of 61)

- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Compositional Score Modeling for Simulation-based Inference](https://mlsanity.com/paper/2209.14249/) (2022)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [Variational methods for simulation-based inference](https://mlsanity.com/paper/2203.04176/) (2022)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [Conditional Optimal Transport on Function Spaces](https://mlsanity.com/paper/2311.05672/) (2023)
- [Position: The Future of Bayesian Prediction Is Prior-Fitted](https://mlsanity.com/paper/2505.23947/) (2025)
- [On minimax density estimation via measure transport](https://mlsanity.com/paper/2207.10231/) (2022)
- [Generalized Bayesian Inference for Scientific Simulators via Amortized Cost Estimation](https://mlsanity.com/paper/2305.15208/) (2023)
- [Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2205.15784/) (2022)
- [Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Models](https://mlsanity.com/paper/2504.17660/) (2025)
- [Likelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning for Reliable Simulator-Based Inference](https://mlsanity.com/paper/2107.03920/) (2021)
- [Unifying Likelihood-free Inference with Black-box Optimization and Beyond](https://mlsanity.com/paper/2110.03372/) (2021)
- [Approximate Bayesian Computation with Domain Expert in the Loop](https://mlsanity.com/paper/2201.12090/) (2022)
- [Neural Posterior Estimation with Differentiable Simulators](https://mlsanity.com/paper/2207.05636/) (2022)
- [Sourcerer: Sample-based Maximum Entropy Source Distribution Estimation](https://mlsanity.com/paper/2402.07808/) (2024)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Python](https://mlsanity.com/paper/2602.07098/) (2026)
- [Deep Bayesian Active Learning for Accelerating Stochastic Simulation](https://mlsanity.com/paper/2106.02770/) (2021)
- [Contrastive Neural Ratio Estimation for Simulation-based Inference](https://mlsanity.com/paper/2210.06170/) (2022)
- [A generative flow for conditional sampling via optimal transport](https://mlsanity.com/paper/2307.04102/) (2023)
- [Generative Bayesian Inference with GANs](https://mlsanity.com/paper/2208.12113/) (2022)

## Abstract (arXiv)

Approximate Bayesian Computation (ABC) provides methods for Bayesian inference in simulation-based stochastic models which do not permit tractable likelihoods. We present a new ABC method which uses probabilistic neural emulator networks to learn synthetic likelihoods on simulated data -- both local emulators which approximate the likelihood for specific observed data, as well as global ones which are applicable to a range of data. Simulations are chosen adaptively using an acquisition function which takes into account uncertainty about either the posterior distribution of interest, or the parameters of the emulator. Our approach does not rely on user-defined rejection thresholds or distance functions. We illustrate inference with emulator networks on synthetic examples and on a biophysical neuron model, and show that emulators allow accurate and efficient inference even on high-dimensional problems which are challenging for conventional ABC approaches.