可逆馬可夫鏈之多重加速

Abstract

Chen and Hwang, 2013 proposed to improve a reversible Markov chain by adding an antisymmetric perturbation on a cycle. Since the perturbed Markov chain is no longer reversible, one can not iteratively apply this antisymmetric perturbation method on different cycles. Chen and Hwang, 2013 also showed that the method works on disjoint cycles. In this paper, we further investigate the case of two cycles sharing the same vertex. We will show that the method can work on two cycles under some additional conditions. In addition to the theory, we implement the antisymmetric perturbation method on the Ising model.