Ok. That makes perfect sense.

]]>I know nothing, but I do not think so.

]]>Dan, you should have been at the workshop where I discussed exactly this point in detail! To summarize, Hamiltonian flow and the modified Hamiltonian flow of a symplectic integrator are both non-reversible hence effective at exploring the target. But if we want to unbias with a Metropolis the samples then we have to augment the flow (say with a momentum flip before and then a momentum resampling after) to make it reversible. The problem is that such an augmentation compromises the performance of the flow — for example if we apply corrections with a high frequency then we devolve into a Langevin diffusion. Only by integrating for long enough can we resolve that tension, and formalizing that idea very naturally motivates algorithms like NUTS.

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