# Reversibility of elliptical slice sampling revisited

arXiv: https://arxiv.org/abs/2301.02426 · HTML: https://mlsanity.com/paper/2301.02426/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 6 Jan 2023.

## Builds on (most cited first, 6 of 6)

- [Dimension-independent likelihood-informed MCMC](https://mlsanity.com/paper/1411.3688/) (2014)
- [Perturbation theory for Markov chains via Wasserstein distance](https://mlsanity.com/paper/1503.04123/) (2015)
- [Integrals over Gaussians under Linear Domain Constraints](https://mlsanity.com/paper/1910.09328/) (2019)
- [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)
- [Efficient Bayesian shape-restricted function estimation with constrained Gaussian process priors](https://mlsanity.com/paper/1902.04701/) (2019)

## Built on by (most cited first, 3 of 3)

- [ESS-Flow: Training-free guidance of flow-based models as inference in source space](https://mlsanity.com/paper/2510.05849/) (2025)
- [Gibbsian polar slice sampling](https://mlsanity.com/paper/2302.03945/) (2023)
- [Parallel Affine Transformation Tuning of Markov Chain Monte Carlo](https://mlsanity.com/paper/2401.16567/) (2024)

## Abstract (arXiv)

We extend elliptical slice sampling, a Markov chain transition kernel suggested in Murray, Adams and MacKay 2010, to infinite-dimensional separable Hilbert spaces and discuss its well-definedness. We point to a regularity requirement, provide an alternative proof of the desirable reversibility property and show that it induces a positive semi-definite Markov operator. Crucial within the proof of the formerly mentioned results is the analysis of a shrinkage Markov chain that may be interesting on its own.