# Pseudo-extended Markov chain Monte Carlo

arXiv: https://arxiv.org/abs/1708.05239 · HTML: https://mlsanity.com/paper/1708.05239/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2017.

## Built on by (most cited first, 3 of 3)

- [Tempered Guided Diffusion](https://mlsanity.com/paper/2605.03712/) (2026)
- [Continuously-Tempered PDMP Samplers](https://mlsanity.com/paper/2205.09559/) (2022)
- [Repelling-Attracting Hamiltonian Monte Carlo](https://mlsanity.com/paper/2403.04607/) (2024)

## Abstract (arXiv)

Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC method as a simple approach for improving the mixing of the MCMC sampler for multi-modal posterior distributions. The pseudo-extended method augments the state-space of the posterior using pseudo-samples as auxiliary variables. On the extended space, the modes of the posterior are connected, which allows the MCMC sampler to easily move between well-separated posterior modes. We demonstrate that the pseudo-extended approach delivers improved MCMC sampling over the Hamiltonian Monte Carlo algorithm on multi-modal posteriors, including Boltzmann machines and models with sparsity-inducing priors.