# Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation

arXiv: https://arxiv.org/abs/1605.06376 · HTML: https://mlsanity.com/paper/1605.06376/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2016.

## Built on by (most cited first, 30 of 52)

- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
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- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference](https://mlsanity.com/paper/2210.05686/) (2022)
- [sbi reloaded: a toolkit for simulation-based inference workflows](https://mlsanity.com/paper/2411.17337/) (2024)
- [HNPE: Leveraging Global Parameters for Neural Posterior Estimation](https://mlsanity.com/paper/2102.06477/) (2021)
- [Learn-Morph-Infer: a new way of solving the inverse problem for brain tumor modeling](https://mlsanity.com/paper/2111.04090/) (2021)
- [Probabilistic Inference of Simulation Parameters via Parallel Differentiable Simulation](https://mlsanity.com/paper/2109.08815/) (2021)
- [Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2205.15784/) (2022)
- [Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2111.08030/) (2021)
- [Unifying Likelihood-free Inference with Black-box Optimization and Beyond](https://mlsanity.com/paper/2110.03372/) (2021)
- [Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport](https://mlsanity.com/paper/2206.11343/) (2022)
- [Balancing Simulation-based Inference for Conservative Posteriors](https://mlsanity.com/paper/2304.10978/) (2023)
- [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)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [Misspecification-robust Sequential Neural Likelihood for Simulation-based Inference](https://mlsanity.com/paper/2301.13368/) (2023)
- [Calibrating Agent-based Models to Microdata with Graph Neural Networks](https://mlsanity.com/paper/2206.07570/) (2022)
- [Variational Inference for Deblending Crowded Starfields](https://mlsanity.com/paper/2102.02409/) (2021)
- [Fitting summary statistics of neural data with a differentiable spiking network simulator](https://mlsanity.com/paper/2106.10064/) (2021)
- [Simulation-based Bayesian inference for multi-fingered robotic grasping](https://mlsanity.com/paper/2109.14275/) (2021)
- [Robust and integrative Bayesian neural networks for likelihood-free parameter inference](https://mlsanity.com/paper/2102.06521/) (2021)
- [ADAVI: Automatic Dual Amortized Variational Inference Applied To Pyramidal Bayesian Models](https://mlsanity.com/paper/2106.12248/) (2021)
- [FNOPE: Simulation-based inference on function spaces with Fourier Neural Operators](https://mlsanity.com/paper/2505.22573/) (2025)
- [Simulation-based Bayesian inference for robotic grasping](https://mlsanity.com/paper/2303.05873/) (2023)
- [Generative Bayesian Computation for Maximum Expected Utility](https://mlsanity.com/paper/2408.16101/) (2024)

## Abstract (arXiv)

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior over parameters by conditioning on data being inside an ε-ball around the observed data, which is only correct in the limit ε!rightarrow!0. Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters. These algorithms critically slow down as ε!rightarrow!0, and in practice draw samples from a broader distribution than the posterior. We propose a new approach to likelihood-free inference based on Bayesian conditional density estimation. Preliminary inferences based on limited simulation data are used to guide later simulations. In some cases, learning an accurate parametric representation of the entire true posterior distribution requires fewer model simulations than Monte Carlo ABC methods need to produce a single sample from an approximate posterior.