The multiple-try Metropolis (MTM) algorithm is an extension of the Metropolis-Hastings (MH) algorithm by selecting the proposed state among multiple trials according to some weight function. Although MTM has gained great popularity owing to its faster empirical convergence and mixing than the standard MH algorithm, its theoretical mixing property is rarely studied in the literature due to its complex proposal scheme. We prove that MTM can achieve a mixing time bound smaller than that of MH by a factor of the number of trials under a general setting applicable to high-dimensional model selection problems with discrete state spaces. Our theoretical results motivate a new class of weight functions called locally balanced weight functions and guide the choice of the number of trials, which leads to improved performance over standard MTM algorithms. We support our theoretical results by extensive simulation studies and real data applications with several Bayesian model selection problems.
翻译:多重大都会算法(MTM)是大都会-哈斯廷斯(MH)算法(MH)的延伸,它根据某些重量函数在多重试验中选择了拟议状态。虽然MTM因其比标准MH算法更快的经验趋同和混合而赢得了很大支持,但其理论混合属性却很少在文献中研究,因为其复杂的提议方案。我们证明MTM能够实现比MH更小的混合时间,在适用于与离散国家空间有关的高维模式选择问题的一般情况下,在适用于高维模式选择问题的一般情况下,将审判次数从一个因素上看。我们的理论结果激励了一种新的重量函数类别,叫做本地平衡的重量函数,并指导了审判次数的选择,从而改善了标准MTM算法的性。我们通过广泛的模拟研究和实际数据应用以及几个巴耶斯模式选择问题来支持我们的理论结果。