# Gibbsian polar slice sampling

arXiv: https://arxiv.org/abs/2302.03945 · HTML: https://mlsanity.com/paper/2302.03945/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 21 references that are in the map.
- First posted on arXiv 8 Feb 2023.

## Builds on (most cited first, 4 of 4)

- [Geometric convergence of elliptical slice sampling](https://mlsanity.com/paper/2105.03308/) (2021)
- [Convergence of hybrid slice sampling via spectral gap](https://mlsanity.com/paper/1409.2709/) (2014)
- [Geodesic slice sampling on the sphere](https://mlsanity.com/paper/2301.08056/) (2023)
- [Reversibility of elliptical slice sampling revisited](https://mlsanity.com/paper/2301.02426/) (2023)

## Built on by (most cited first, 2 of 2)

- [Parallel Affine Transformation Tuning of Markov Chain Monte Carlo](https://mlsanity.com/paper/2401.16567/) (2024)
- [Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling](https://mlsanity.com/paper/2609.08172/) (2026)

## Abstract (arXiv)

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.