A unified framework for multiple-try Metropolis algorithms

The multiple-try Metropolis (MTM) algorithm is a generalization of the Metropolis-Hastings algorithm in which the transition kernel uses a compound proposal consisting of multiple candidate draws. Since its seminal paper there have been several extensions to this algorithm. This paper presents a general framework that encompasses many of these extensions, as well as an independent comparison. To facilitate this, a deterministic Metropolis transition kernel is used to develop a procedure that derives valid acceptance probabilities for reversible Markov chain Monte Carlo algorithms, given only the proposal mechanism. Several configurations of MTM are explored in full factorial simulation experiment that compares the sampling performance of MTM algorithms with respect to non-Gaussian target distributions, multimodal sampling, and Monte Carlo error. We find that the form of the proposal distribution is the most important factor in determining algorithm performance, while the form of the weight function has negligible impact. A large number of candidate draws can improve the per-iteration performance, though improvement of the overall performance is limited by the additional computational burden introduced by multiple candidacy.