Scaling analysis of multiple-try MCMC methods
The authors consider multiple-try Markov chain Monte Carlo (MCMC) algorithms. These are distinguished from standard MCMC algorithms in that the next state in the chain is chosen from a pool of proposals. In this study multiple proposals with a dependence structure are considered, extending work on independently distributed multiple proposals. In particular, the authors focus on an extreme dependence structure such that all proposals are generated from one random vector, i.e., each proposal value in the pool can be used to calculate the remaining values in the pool. The considered efficiency measure for the algorithms is the speed the algorithms converge weakly to a diffusion process (asymptotic scaling), which, as is argued in the paper, is appropriate for high-dimensional target distributions. The authors prove convergence results of this type for multiple-try MCMC algorithms with dependencies in the proposals. The authors use scaling analysis to investigate the speed of the algorithms with respect to the number of proposal and the dependence structure of the proposals. A numerical example for a multivariate normal distribution is presented illustrating the theoretical findings. The authors conclude that introducing multiple proposals results in an increase in speed of the algorithm, which is further increased choosing dependent proposals over independent proposal. Hence, the algorithm might be practically more efficient for certain implementations, however, the study does not present a definitive answer.
scientific article; zbMATH DE number 6017603