As I understand things, the numerical imprecisions lead to problems when integrating the hamiltonian flow. This is exactly why a metropolis hastings steps is done to the generated proposals. Hence, the MH step is exactly there to get rid of the problems implied by numerical imprecisions. Apparently this does not seem to be enough to get rid of bias as Mike has now repeatedly reported.
As discussed during the Stan meeting this is a very hard problem to solve rigorously. However, I am wondering if there are some case studies around which would shed some light on this? My main motivation would be to understand if the bias is practically relevant or not. This can probably not be answered in general, but having strategies to detect a real bias would be great.
If we could collect some ideas on this, it would help us all a lot to get some clarity on the matter.