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.

可逆链如 Gibbs sampler 和 Metropolis Hasting 在 Markov chain Monte Carlo 算法中很流行。然而，已经表明，通过添加反对称扰动可以很容易地改进它们。由于受扰动的马尔可夫链不再可逆，因此不能保证添加另一个反对称扰动会更好。Chen and Hwang (2013) 提出了一种多重加速的方法。但是，他们的证明存在错误，并且该陈述并不总是成立。在本文中，我们将首先指出错误并给出一个反例。然后我们将给出保证多次加速的充分条件。