Stereographic Multiple-Try Metropolis

TL;DR

The paper introduces SMTM, a new gradient-free MCMC algorithm that improves high-dimensional sampling efficiency and robustness over existing methods, with strong theoretical and empirical support.

Contribution

It combines multiple-try Metropolis with stereographic MCMC to overcome convergence issues in high dimensions, offering a robust and efficient sampling method.

Findings

SMTM outperforms classical MTM and stereographic random-walk Metropolis in high dimensions.

SMTM demonstrates robustness to tuning parameters.

High-dimensional scaling analysis supports SMTM's efficiency.

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.