AI 中文总结
针对复杂目标分布中 MTM 局部最优转移不足的问题，提出复合辅助 metropolis（CAM）方法，将链局部状态与辅助信息纳入多候选框架，通过定义辅助变量灵活抽样，经测试其性能优于 MTM 及 No-U-Turn Sampler。
AI 中文摘要
多尝试 metropolis（MTM）算法通过每次迭代评估多个候选抽样来提高局部转移效率，但对于复杂的目标分布，局部最优转移可能不足以进行有效的全局探索。本文提出复合辅助 metropolis（CAM），一种通用的多候选 MCMC 方法，它将链的局部状态和辅助信息纳入 MTM 的多候选框架。通过辅助生成分布，CAM 能灵活定义辅助信息。考虑了三种辅助变量并针对具有挑战性的分布进行测试，以 MTM 为基线评估辅助信息的效果，结果表明 CAM 能有效抽样，且与 No-U-Turn Sampler 相比，在温和测试分布中性能相似，在最困难设置下表现更好。
英文摘要
Multiple-try Metropolis (MTM) is a Markov chain Monte Carlo (MCMC) algorithm that improves local transition efficiency by evaluating multiple candidate draws at each iteration. However, for complicated target distributions exhibiting severely non-Gaussian topography or multiple well-separated modes, locally optimal transitions may be insufficient for effective global exploration. In this work, we propose compound auxiliary Metropolis (CAM), a general multi-candidate MCMC method that incorporates both the local state of the chain and auxiliary information into the multi-candidate framework of MTM. Using an auxiliary generating distribution, CAM accommodates a flexible definition of auxiliary information. As examples, we consider three different auxiliary variables: one that promotes state-independent exploration and two that use a reference distribution to improve mixing. These auxiliaries are tested against distributions that present challenging targets for modern MCMC methods. In particular, we focus on the challenges presented by multiple well-separated modes and topography that requires long mixing for local MCMC moves. We find that CAM is able to sample effectively from these distributions, using MTM as a baseline to evaluate the benefit introduced by the auxiliary information. CAM also compares favourably with the No-U-Turn Sampler, showing similar performance for milder test distributions and better performance for the most difficult settings.
