Convergence rate of multiple-try Metropolis independent sampler

Abstract The multiple-try Metropolis method is an interesting extension of the classical Metropolis–Hastings algorithm. However, theoretical understanding about its usefulness and convergence behavior still lacking. We here derive exact rate for Independent sampler (MTM-IS) via explicit eigen analysis. As a by-product, we prove that naive application MTM-IS less efficient than using simpler approach “thinned” independent at same computational cost. further explore more variants find it possible to design algorithms by applying MTM part target distribution or creating correlated multiple trials.