On multiple acceleration of reversible Markov chain

Abstract

Reversible chains such as Gibbs sampler and Metropolis Hasting are popular in Markov chain Monte Carlo algorithms. However, it has been shown that they can be easily improved by adding an antisymmetric perturbation. Since the perturbed Markov chain is no longer reversible, adding another antisymmetric perturbation is not guaranteed to be better. Chen and Hwang (2013) proposed a way for multiple acceleration. However, there is a mistake in their proof, and the statement does not always hold. In this paper, we will first point out the mistake and show a counterexample. Then we will give a sufficient condition such that multiple acceleration is guaranteed.