Split Hamiltonian Monte Carlo revisited

We study Hamiltonian Monte Carlo (HMC) samplers based on splitting the Hamiltonian H as H0(θ,p)+U1(θ), where H0 is quadratic and U1 small. We show that, in general, such samplers suffer from stepsize stability restrictions similar to those of algorithms based on the standard leapfrog integrator. The restrictions may be circumvented by preconditioning the dynamics. Numerical experiments show that, when the H0(θ,p)+U1(θ) splitting is combined with preconditioning, it is possible to construct samplers far more efficient than standard leapfrog HMC.This work has been supported by Ministerio de Ciencia e Innovación (Spain) through project PID2019-104927GB-C21, MCIN/AEI/10.13039/501100011033, ERDF ("A way of making Europe")