Symmetrically processed splitting integrators for enhanced Hamiltonian Monte Carlo sampling

TL;DR

This paper introduces symmetrically processed splitting integrators for Hamiltonian Monte Carlo that significantly increase acceptance rates without sacrificing sample quality, using a modified processing technique.

Contribution

It presents a new class of integrators based on modified processing, improving HMC sampling efficiency and enabling high-order splitting with positive coefficients.

Findings

Up to five times more accepted proposals at the same computational cost

Integrators are easy to implement and do not impair sample quality

Modified processing technique has potential for broader applications

Abstract

We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver five times as many accepted proposals as standard leapfrog/Verlet without impairing in any way the quality of the samples. They are based on a suitable modification of the processing technique first introduced by J.C. Butcher. The idea of modified processing may also be useful for other purposes, like the construction of high-order splitting integrators with positive coefficients.