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We compare numerically the performance of reversible and non-reversibleMarkov Chain Monte Carlo algorithms for high dimensional oil reservoirproblems; because of the nature of the problem at hand, the target measuresfrom which we sample are supported on bounded domains. We compare twostrategies to deal with bounded domains, namely reflecting proposals off theboundary and rejecting them when they fall outside of the domain. We observethat for complex high dimensional problems reflection mechanisms outperformrejection approaches and that the advantage of introducing non-reversibility inthe Markov Chain employed for sampling is more and more visible as thedimension of the parameter space increases.

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