  Hamiltonian Monte Carlo provides efficient Markov transitions at the expense
of introducing two free parameters: a step size and total integration time.
Because the step size controls discretization error it can be readily tuned to
achieve certain accuracy criteria, but the total integration time is left
unconstrained. Recently Hoffman and Gelman proposed a criterion for tuning the
integration time in certain systems with their No U-Turn Sampler, or NUTS. In
this paper I investigate the dynamical basis for the success of NUTS and
generalize it to Riemannian Manifold Hamiltonian Monte Carlo.
