关于偏斜对称分布及其在蒙特卡洛采样算法中的应用：Barker提议的坐标无关、Gibbs风格与流形版本
On skew-symmetric distributions and their use in Monte Carlo sampling algorithms: coordinate-free, Gibbs-style and manifold versions of the Barker proposal
- University of Oxford（牛津大学）
- University College London（伦敦大学学院）
- MRC Biostatistics Unit, University of Cambridge（剑桥大学医学研究理事会生物统计学单元）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文回顾了基于偏斜对称分布的Barker提议，并提出三种扩展：坐标无关、Gibbs风格和简化流形版本，实验表明Gibbs风格提升相关目标采样效率，流形版本在几何不规则时优于MALA。
AI中文摘要：
偏斜对称概率分布为将梯度信息纳入马尔可夫链蒙特卡洛算法提供了一种原则性机制。在此，我们回顾（预条件化的）Barker提议，这是一种基于偏斜对称分布的Metropolis-Hastings算法，并阐述其设计动机。随后，我们引入三种自然扩展。首先，我们提出Barker算法的坐标无关变体。其次，我们引入一种Gibbs风格的Barker算法，该算法在每次部分更新的坐标处重新评估梯度。第三，我们推导出一种简化的流形Barker算法，与自然比较对象相比，该算法生成的流形采样器具有更强的鲁棒性。数值实验表明，在相关目标上，Gibbs风格变体提高了原始采样效率；在考虑计算成本后，坐标无关变体相对于标准Barker提议提供的实际优势有限；而当目标的局部几何结构不规则或不可靠时，简化的流形Barker算法相较于简化的流形MALA能够取得显著优势。
英文摘要：
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.
