The multiple-try Metropolis (MTM) algorithm uses a compound proposal with multiple candidate draws to improve local sampling efficiency. While several methodological works have continued to develop MTM and the multi-candidate mechanism that characterizes it, the literature lacks a unified comparison of these components. This paper presents a structured formulation of MTM within the involutive MCMC framework, providing a principled approach for deriving valid acceptance probabilities based on the proposal mechanism. Through a comprehensive simulation experiment, we evaluate the impact of MTM configurations on non-Gaussian and multimodal target distributions. Our results reveal that while weight functions are a focus of several methodological developments, their impact on stationary sampling efficiency is secondary to the configuration of the proposal distribution. Furthermore, we find that while increasing the number of candidates enhances per-iteration efficiency, the realized performance gains are offset by computational overhead introduced by multiple candidacy unless parallelize computing is used. Our findings offer practical guidance for configuring an MTM algorithm for complex and non-Gaussian targets.

翻译：多次尝试Metropolis（MTM）算法通过使用包含多个候选样本的复合提议机制来提升局部采样效率。尽管已有若干方法论研究持续发展MTM及其标志性的多候选机制，但现有文献缺乏对这些组件的统一比较。本文在类对合MCMC框架内构建了MTM的结构化形式，提供了一种基于提议机制推导有效接受概率的原则性方法。通过全面的模拟实验，我们评估了MTM配置对非高斯和多模态目标分布的影响。研究结果表明：尽管权重函数是若干方法论研究的焦点，但其对平稳采样效率的影响次于提议分布的配置作用。此外，我们发现增加候选数量虽能提升单次迭代效率，但实际性能提升会因多候选机制引入的计算开销而抵消（除非采用并行计算）。我们的发现为面向复杂非高斯目标的MTM算法配置提供了实践指导。