Stereographic Multiple-Try Metropolis

Zhihao Wang; Jun Yang

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arXiv · 2505.12487

Stereographic Multiple-Try Metropolis

Zhihao Wang·Jun Yang

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Abstract

Multiple-proposal MCMC algorithms have recently gained attention for their potential to improve performance, especially through parallel implementation on modern hardware. We introduce Stereographic Multiple-Try Metropolis (SMTM), a novel family of gradient-free algorithms designed for sampling high-dimensional distributions. By integrating multiple-try Metropolis (MTM) with the stereographic MCMC framework, SMTM overcomes the traditional limitations of MTM, particularly its pathological convergence behavior often observed in high dimensions. For both light-tailed and heavy-tailed targets, SMTM not only outperforms classical MTM and the existing stereographic random-walk Metropolis but also demonstrates strong robustness to tuning. These advantages are supported by high-dimensional scaling analysis and validated through extensive simulation studies.

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Zhihao Wang, Jun Yang. 2026-04-30. Stereographic Multiple-Try Metropolis. https://arxiv.org/abs/2505.12487

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