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.

翻译：测地线切片采样（Durmus 等人，2024 年提出）是一种基于切片采样的马尔可夫链蒙特卡洛方法，用于在黎曼流形上近似采样。我们证明，对于具有紧支撑且相对于黎曼测度具有有界密度的分布，该方法是均匀遍历的。收敛界中的常数可显式给出，我们研究了这些常数对测地线切片采样器的超参数、目标分布以及底层定义域的依赖性。