First, I'll just say that I am a CS guy, and not a mathematician by any means, don't monitor any MCMC conferences and have been using pretty outdated MCMC methods so far and just recently started learning MCMC more seriously.
So, I have stumbled across a few articles about Irreversible MCMC[1][2], and I am trying to apply it in my research project (computer graphics) but I am not sure if it's applicable.
In my case, I've got a continuous mutation space. I can draw samples from some function and basically the same but normalized samples are used as target distribution.
Also I am using just Metropolis algorithm at the moment and not Metropolis-Hastings. I mean, MH could be used too, but it's got some serious implementation flaws and almost all state off the art extensions are built on top of just Metropolis with equal transition probabilities.
So, here's the question: Does it make any sense to use Irreversible MCMC based on just Metropolis algorithm with continuous mutation space? The articles mentioned above use examples with discreet cases (graphs, e.t.c.) and Metropolis-Hastings with arbitrary transition probabilities. And I believe you can't do the same thing with continuous case.
And if not, are there any similar approaches, based on the idea of driving the sampler more "clever" which could be used in my use-case?