The Multiple-try Metropolis (MTM) method is an interesting extension of the classical Metropolis-Hastings algorithm. However, theoretical understandings of its convergence behavior as well as whether and how it may help are still unknown. This paper derives the exact convergence rate for Multiple-try Metropolis Independent sampler (MTM-IS) via an explicit eigen analysis. As a by-product, we prove that MTM-IS is less efficient than the simpler approach of repeated independent Metropolis-Hastings method at the same computational cost. We further explore more variations and find it possible to design more efficient MTM algorithms by creating correlated multiple trials.

翻译：多种尝试Metropolis（MTM）方法是经典Metropolis-Hastings算法的一种有趣扩展。然而，关于其收敛行为的理论理解，以及它是否以及如何提升性能，仍属未知。本文通过显式的特征分析，精确推导了多种尝试Metropolis独立采样器（MTM-IS）的收敛速率。作为副产品，我们证明了在相同计算成本下，MTM-IS的效率低于更简单的重复独立Metropolis-Hastings方法。我们进一步探索了更多的变体，发现通过创建相关的多次尝试，有可能设计出更高效的MTM算法。