On the application of higher order symplectic integrators in Hamiltonian Monte Carlo

TL;DR

This paper investigates new higher order symplectic integrators for Hamiltonian Monte Carlo, demonstrating their superior efficiency over the traditional leapfrog method in various models.

Contribution

It introduces and tests new symplectic integrators based on optimal acceptance probability, outperforming the standard leapfrog method in HMC sampling.

Findings

New integrators achieve higher acceptance probabilities.

New methods produce more efficient samples per computational time.

Leapfrog is less effective than proposed schemes.

Abstract

We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Two integration schemes from Blanes et al. (2014), and a new scheme based on optimal acceptance probability, are considered as candidates to the commonly used leapfrog method. All integration schemes are tested within the framework of the No-U-Turn sampler (NUTS), both for a logistic regression model and a student $t$-model. The results show that the leapfrog method is inferior to all the new methods both in terms of asymptotic expected acceptance probability for a model problem and the and efficient sample size per computing time for the realistic models.