# Ensemble preconditioning for Markov chain Monte Carlo simulation

arXiv: https://arxiv.org/abs/1607.03954 · HTML: https://mlsanity.com/paper/1607.03954/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2016.

## Built on by (most cited first, 16 of 16)

- [Sampling via Gradient Flows in the Space of Probability Measures](https://mlsanity.com/paper/2310.03597/) (2023)
- [Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance](https://mlsanity.com/paper/2302.11024/) (2023)
- [Optimal Preconditioning and Fisher Adaptive Langevin Sampling](https://mlsanity.com/paper/2305.14442/) (2023)
- [Scalable Bayesian Learning with posteriors](https://mlsanity.com/paper/2406.00104/) (2024)
- [Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods](https://mlsanity.com/paper/2104.03384/) (2021)
- [Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions](https://mlsanity.com/paper/2110.00610/) (2021)
- [Second Order Ensemble Langevin Method for Sampling and Inverse Problems](https://mlsanity.com/paper/2208.04506/) (2022)
- [Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusion](https://mlsanity.com/paper/2305.05014/) (2023)
- [Ensemble-Based Annealed Importance Sampling](https://mlsanity.com/paper/2401.15645/) (2024)
- [New affine invariant ensemble samplers and their dimensional scaling](https://mlsanity.com/paper/2505.02987/) (2025)
- [A Langevin sampling algorithm inspired by the Adam optimizer](https://mlsanity.com/paper/2504.18911/) (2025)
- [Constrained Ensemble Langevin Monte Carlo](https://mlsanity.com/paper/2102.04279/) (2021)
- [A Complete Decomposition of Stochastic Differential Equations](https://mlsanity.com/paper/2601.07834/) (2026)
- [Time-Inhomogeneous Preconditioned Langevin Dynamics](https://mlsanity.com/paper/2605.06091/) (2026)
- [Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics](https://mlsanity.com/paper/2606.26881/) (2026)
- [Gradient-free Riemannian Langevin Sampler](https://mlsanity.com/paper/2607.07519/) (2026)

## Abstract (arXiv)

We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics thus providing a practical approach to difficult anisotropic sampling problems in high dimensions. Numerical experiments with model problems demonstrate that dramatic potential speedups, compared to various alternative schemes, are attainable.