HMC: avoiding rejections by not using leapfrog and some results on the acceptance rate
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We give numerical evidence that the standard leapfrog algorithm may not be the best integrator to use within the Hamiltonian Monte Carlo (HMC) method and its variants. When the dimensionality of the target distribution is high, the number of accepted proposals obtained with a given computational effort may be multiplied by a factor of three or more by switching to alternative integrators very similar to leapfrog. Such integrators have appeared in the numerical analysis and molecular dynamics literature rather than in the statistics literature. In addition, we provide some theoretical results on the acceptance rate of HMC.
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