Convergence Rate of Multiple-try Metropolis Independent sampler

TL;DR

This paper analyzes the convergence rate of the Multiple-try Metropolis Independent sampler, revealing it is less efficient than repeated independent Metropolis-Hastings, and suggests potential improvements through correlated trials.

Contribution

It provides the first explicit eigen analysis of MTM-IS convergence rate and compares its efficiency to simpler methods, proposing new variations for better performance.

Findings

MTM-IS has a specific convergence rate derived analytically.

MTM-IS is less efficient than repeated independent Metropolis-Hastings at same cost.

Correlated trials can lead to more efficient MTM algorithms.

Abstract

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.