The Apogee to Apogee Path Sampler

Abstract

Among Markov chain Monte Carlo algorithms, Hamiltonian Monte Carlo (HMC) is often the algorithm of choice for complex, high-dimensional target distributions; however, its efficiency is notoriously sensitive to the choice of the integration-time tuning parameter. When integrating both forward and backward in time using the same leapfrog integration step as HMC, the set of apogees, local maxima in the potential along a path, is the same whatever point (position and momentum) along the path is chosen to initialize the integration. We present the Apogee to Apogee Path Sampler (AAPS), which uses this invariance to create a simple yet generic methodology for constructing a path, proposing a point from it and accepting or rejecting that proposal so as to target the intended distribution. We demonstrate empirically that AAPS has a similar efficiency to HMC but is much more robust to the setting of its equivalent tuning parameter, the number of apogees that the path crosses. Supplementary materials for this article are available online.

KEYWORDS:

• Hamiltonian Monte Carlo
• Leapfrog step
• Markov chain Monte Carlo
• Robustness to tuning

Supplementary Materials

Appendices A–I are contained in the supplementary materials.

Data Availability Statement

Code is available from https://github.com/ChrisGSherlock/AAPS

Disclosure Statement

There are no financial or nonfinancial conflicts of interest to declare.

Acknowledgments

We are grateful to two anonymous reviewers for comments and suggestions that have materially improved the article.

Additional information

Funding

All three authors gratefully acknowledge funding through EPSRC grant EP/P033075/1.