# The Apogee to Apogee Path Sampler

arXiv: https://arxiv.org/abs/2112.08187 · HTML: https://mlsanity.com/paper/2112.08187/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2021.

## Built on by (most cited first, 5 of 5)

- [GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlo](https://mlsanity.com/paper/2404.15253/) (2024)
- [Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentration](https://mlsanity.com/paper/2410.06978/) (2024)
- [On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplers](https://mlsanity.com/paper/2307.03460/) (2023)
- [The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler](https://mlsanity.com/paper/2506.18746/) (2025)
- [Scalable Monte Carlo for Bayesian Learning](https://mlsanity.com/paper/2407.12751/) (2024)

## Abstract (arXiv)

Amongst 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, T. When integrating both forward and backward in time using the same leapfrog integration step as HMC, the set of local maxima in the potential along a path, or apogees, is the same whatever point (position and momentum) along the path is chosen to initialise the integration. We present the Apogee to Apogee Path Sampler (AAPS), which utilises 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.