  The classical Metropolis-Hastings (MH) algorithm can be extended to generate
non-reversible Markov chains. This is achieved by means of a modification of
the acceptance probability, using the notion of vorticity matrix. The resulting
Markov chain is non-reversible. Results from the literature on asymptotic
variance, large deviations theory and mixing time are mentioned, and in the
case of a large deviations result, adapted, to explain how non-reversible
Markov chains have favorable properties in these respects.
  We provide an application of NRMH in a continuous setting by developing the
necessary theory and applying, as first examples, the theory to Gaussian
distributions in three and nine dimensions. The empirical autocorrelation and
estimated asymptotic variance for NRMH applied to these examples show
significant improvement compared to MH with identical stepsize.
