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

2026-10-01

AI Summary

This study addresses the inefficiency of gradient utilization and inadequate adaptation to manifold geometry in Markov chain Monte Carlo (MCMC) sampling. Grounded in skew-symmetric distribution theory, this work proposes a coordinate-free Barker proposal algorithm along with its Gibbs and manifold variants. Methodologically, a Gibbs re-evaluation mechanism is introduced to enhance sampling efficiency for highly correlated targets, while a simplified manifold framework is constructed to improve robustness against irregular geometric structures. Experimental results demonstrate that the proposed Gibbs variant significantly improves sampling performance on correlated targets. Furthermore, when local geometric information is unreliable, the manifold-based Barker algorithm substantially outperforms the Metropolis-adjusted Langevin algorithm (MALA), offering a novel paradigm for efficient sampling in spaces with complex geometries.

Abstract

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.

Problem

• Markov chain Monte Carlo
• skew-symmetric distributions
• Barker proposal
• manifold sampling
• gradient information

Innovation

• Skew-symmetric distributions
• Barker proposal
• Markov chain Monte Carlo
• Manifold sampler
• Gibbs-style sampling