# On skew-symmetric distributions and their use in Monte Carlo sampling algorithms: coordinate-free, Gibbs-style and manifold versions of the Barker proposal

arXiv: https://arxiv.org/abs/2610.01448 · HTML: https://mlsanity.com/paper/2610.01448/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 8 of 8)

- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Langevin diffusions and the Metropolis-adjusted Langevin algorithm](https://mlsanity.com/paper/1309.2983/) (2013)
- [Auxiliary gradient-based sampling algorithms](https://mlsanity.com/paper/1610.09641/) (2016)
- [The Barker proposal: combining robustness and efficiency in gradient-based MCMC](https://mlsanity.com/paper/1908.11812/) (2019)
- [Information-geometric Markov Chain Monte Carlo methods using Diffusions](https://mlsanity.com/paper/1403.7957/) (2014)
- [Optimal design of the Barker proposal and other locally-balanced Metropolis-Hastings algorithms](https://mlsanity.com/paper/2201.01123/) (2022)
- [A fresh take on 'Barker dynamics' for MCMC](https://mlsanity.com/paper/2012.09731/) (2020)
- [On randomized step sizes in Metropolis-Hastings algorithms](https://mlsanity.com/paper/2601.19710/) (2026)

## Abstract (arXiv)

Skew-symmetric probability distributions provide a principled mechanism for incorporating gradient information into Markov chain Monte Carlo algorithms. Here we review the (preconditioned) Barker proposal, a Metropolis--Hastings algorithm built on skew-symmetric distributions, and motivate its design. We then introduce three natural extensions. First, we propose coordinate-free variants of the Barker algorithm. Second, we introduce a Gibbs-style Barker algorithm that re-evaluates the gradient at each partially updated coordinate. Third, we derive a simplified manifold Barker algorithm, producing a manifold sampler with enhanced robustness compared to natural comparators. Numerical experiments demonstrate that the Gibbs-style variant improves raw sampling efficiency on correlated targets, that the coordinate-free variants offer limited practical advantage over the standard Barker proposal once computational costs are accounted for, and that the simplified manifold Barker algorithm can achieve significant advantages over simplified manifold MALA when the local geometric structure of the target is irregular or unreliable.