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:多宗大都会方法(MTM)是古典大都会-哈斯廷斯算法的一个有趣的延伸。 但是,对于其趋同行为以及是否和如何帮助的理论理解仍然未知。 本文通过明确的伊根分析得出了多宗大都会独立采样器(MTM-IS)的确切趋同率。 作为副产品,我们证明MTM-IS比以同样的计算成本重复独立大都会-哈斯廷斯方法的简单方法效率要低。 我们进一步探索更多的变异性,并发现通过创建相关多重试验来设计更高效的MTM算法是可能的。