Implement Unbiased Hamiltonian Monte Carlo with couplings

[AdrienCorenflos]

Ideally implement these two different papers

• https://arxiv.org/abs/1709.00404
• https://arxiv.org/abs/2104.05134

They both build on this https://rss.onlinelibrary.wiley.com/doi/full/10.1111/rssb.12336 and can be used to compute unbiased estimates of expectations. I don't really think these methods are implemented in any Python library (I don't think it's in Stan either?) and would be a cool show case.

[rlouf]

CC @pierrejacob

[rlouf]

https://arxiv.org/abs/2104.05134

[rlouf]

https://arxiv.org/abs/2206.07202