  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.
