# Towards Unifying Hamiltonian Monte Carlo and Slice Sampling

arXiv: https://arxiv.org/abs/1602.07800 · HTML: https://mlsanity.com/paper/1602.07800/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2016.

## Built on by (most cited first, 1 of 1)

- [Improving Gradient-guided Nested Sampling for Posterior Inference](https://mlsanity.com/paper/2312.03911/) (2023)

## Abstract (arXiv)

We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS). We provide a theoretical analysis of the mixing performance of such samplers, proving that in the limit of a single parameter, the MGS draws decorrelated samples from the desired target distribution. We further show that as this parameter tends toward this limit, performance gains are achieved at a cost of increasing numerical difficulty and some practical convergence issues. Our theoretical results are validated with synthetic data and real-world applications.