  In this paper, we propose irreversible versions of the Metropolis Hastings
(MH) and Metropolis adjusted Langevin algorithm (MALA) with a main focus on the
latter. For the former, we show how one can simply switch between different
proposal and acceptance distributions upon rejection to obtain an irreversible
jump sampler (I-Jump). The resulting algorithm has a simple implementation akin
to MH, but with the demonstrated benefits of irreversibility. We then show how
the previously proposed MALA method can also be extended to exploit
irreversible stochastic dynamics as proposal distributions in the I-Jump
sampler. Our experiments explore how irreversibility can increase the
efficiency of the samplers in different situations.
