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.

翻译：多提议MCMC算法因其在提升性能方面的潜力而备受关注，尤其可通过现代硬件的并行实现发挥作用。本文提出立体多点梅特罗波利斯算法（SMTM），这是一种专为高维分布采样设计的新型无梯度算法族。通过将多点梅特罗波利斯（MTM）与立体MCMC框架相结合，SMTM突破了传统MTM的局限性，特别是其在高维情况下常出现的病态收敛行为。对于轻尾与重尾目标分布，SMTM不仅优于经典MTM和现有立体随机游走梅特罗波利斯算法，还展现出对参数调优的强鲁棒性。这些优势得到高维尺度分析的支持，并通过大量仿真研究得到验证。