On skew-symmetric distributions and their use in Monte Carlo sampling algorithms: coordinate-free, Gibbs-style and manifold versions of the Barker proposal
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.
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BibTeX
@misc{vu2026skewsymmetric,
title = {{On skew-symmetric distributions and their use in Monte Carlo sampling algorithms: coordinate-free, Gibbs-style and manifold versions of the Barker proposal}},
author = {Minh Vu and Samuel Livingstone and Pantelis Samartsidis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01448},
eprint = {2610.01448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01448},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On skew-symmetric distributions and their use in Monte Carlo sampling algorithms: coordinate-free, Gibbs-style and manifold versions of the Barker proposal
AU - Minh Vu
AU - Samuel Livingstone
AU - Pantelis Samartsidis
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01448
UR - https://arxiv.org/abs/2610.01448
AB - 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.
ER -