I know that the deterministic dynamics in Hamiltonian Monte Carlo/Hybrid Monte Carlo are reversible and the numerical integrators one uses to approximate them are reversible too. But HMC consists of 2 steps:
- Sample velocity
- Run Hamiltonian Dynamics with accept/reject
From the reversibility of the integrator and the form of the accept/reject ratio I guess one can show that the step 2 is reversible. But is the full algorithm with step 1 and step 2 reversible with respect to the measure one wants to sample?
