Uniform ergodicity of geodesic slice sampling

2025/10/08 by Mareike Hasenpflug, Hasenpflug, Mareike
Mathematics · #53Z50 (Secondary) #65C05 (Primary) 60J05 #FOS: Mathematics #Morphological variations and asymmetry #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2510.06748

openalex publication_date 2025/10/08 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

Geodesic slice sampling, introduced in Durmus et al., 2024, is a slice sampling based Markov chain Monte Carlo method for approximate sampling from distributions on Riemannian manifolds. We prove that it is uniformly ergodic for distributions with compact support that have a bounded density with respect to the Riemannian measure. The constants in our convergence bound are available explicitly, and we investigate their dependence on the hyperparameters of the geodesic slice sampler, the target distribution and the underlying domain.

Citations

• Efficient Sampling on Riemannian Manifolds via Langevin MCMC
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• Reversibility of elliptical slice sampling revisited
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• Simple Monte Carlo and the Metropolis Algorithm
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• Slice Sampling

Related

• Geodesic slice sampling on Riemannian manifolds
• Geodesic slice sampling on the sphere
• Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature
• Sampling From A Manifold
• On the Geometric Ergodicity of Two-Variable Gibbs Samplers