  We propose a methodology to parallelize Hamiltonian Monte Carlo estimators.
Our approach constructs a pair of Hamiltonian Monte Carlo chains that are
coupled in such a way that they meet exactly after some random number of
iterations. These chains can then be combined so that resulting estimators are
unbiased. This allows us to produce independent replicates in parallel and
average them to obtain estimators that are consistent in the limit of the
number of replicates, instead of the usual limit of the number of Markov chain
iterations. We investigate the scalability of our coupling in high dimensions
on a toy example. The choice of algorithmic parameters and the efficiency of
our proposed methodology are then illustrated on a logistic regression with 300
covariates, and a log-Gaussian Cox point processes model with low to fine
grained discretizations.
