Reversible and non-reversible Markov Chain Monte Carlo algorithms for reservoir simulation problems.

We compare numerically the performance of reversible and non-reversible Markov Chain Monte Carlo algorithms for high dimensional oil reservoir problems; because of the nature of the problem at hand, the target measures from which we sample are supported on bounded domains. We compare two strategies to deal with bounded domains, namely reflecting proposals off the boundary and rejecting them when they fall outside of the domain. We observe that for complex high dimensional problems reflection mechanisms outperform rejection approaches and that the advantage of introducing non-reversibility in the Markov Chain employed for sampling is more and more visible as the dimension of the parameter space increases.