The Metropolis-Hastings algorithm is extended to 'non-reversible Metropolis Hastings' so that it can generate non-reversible Markov chains, using the notion of a vorticity matrix. It is universal, in the sense that any finite Markov chain (reversible or non-reversible) satisfying a very mild condition on its directed graph structure, can be generated by the new approach. The method is based on the novel notion of the 'vorticity matrix' of a Markov chain. It can be shown that any chain obtained from Metropolis-Hastings, given a suitable vorticity matrix, can be altered quite elegantly into a non-reversible chain that performs at least as well as the original chain in terms of asymptotic variance. This can be done without loss of the practical properties that make Metropolis-Hastings successful. A numerical experiment on the n-cycle illustrates the promise of this approach. Mixing times on the cycle typically reduce significantly as compared to classical Metropolis-Hastings, and the relative effectiveness increases as a function of the problem size. The non-reversible nature of the resulting chains helps especially to overcome multi-modality in the target distribution.
In the non-reversible MH algorithm REF , a vorticity function (or matrix) is added to the MH procedure.
Non-reversible Metropolis-Hastings
Mathematics Computer Science