# Likelihood-free approximate Gibbs sampling

arXiv: https://arxiv.org/abs/1906.04347 · HTML: https://mlsanity.com/paper/1906.04347/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2019.

## Built on by (most cited first, 8 of 8)

- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
- [GATSBI: Generative Adversarial Training for Simulation-Based Inference](https://mlsanity.com/paper/2203.06481/) (2022)
- [Contrastive Neural Ratio Estimation for Simulation-based Inference](https://mlsanity.com/paper/2210.06170/) (2022)
- [Improving the Accuracy of Marginal Approximations in Likelihood-Free Inference via Localisation](https://mlsanity.com/paper/2207.06655/) (2022)
- [A Gradient Flow Perspective on Minimum MMD Estimation](https://mlsanity.com/paper/2607.03871/) (2026)
- [An efficient likelihood-free Bayesian inference method based on sequential neural posterior estimation](https://mlsanity.com/paper/2311.12530/) (2023)
- [Semi-Amortized Bayesian Inference with Reusable Local Posteriors](https://mlsanity.com/paper/2610.18945/) (2026)

## Abstract (arXiv)

Likelihood-free methods such as approximate Bayesian computation (ABC) have extended the reach of statistical inference to problems with computationally intractable likelihoods. Such approaches perform well for small-to-moderate dimensional problems, but suffer a curse of dimensionality in the number of model parameters. We introduce a likelihood-free approximate Gibbs sampler that naturally circumvents the dimensionality issue by focusing on lower-dimensional conditional distributions. These distributions are estimated by flexible regression models either before the sampler is run, or adaptively during sampler implementation. As a result, and in comparison to Metropolis-Hastings based approaches, we are able to fit substantially more challenging statistical models than would otherwise be possible. We demonstrate the sampler's performance via two simulated examples, and a real analysis of Airbnb rental prices using a intractable high-dimensional multivariate non-linear state space model containing 13,140 parameters, which presents a real challenge to standard ABC techniques.