The present work introduces curvature-based rejection sampling (CURS). This is a method for sampling from a general class of probability densities defined on Riemannian manifolds. It can be used to sample from any probability density which ``depends only on distance". The idea is to combine the statistical principle of rejection sampling with the geometric principle of volume comparison. CURS is an exact sampling method and (assuming the underlying Riemannian manifold satisfies certain technical conditions) it has a particularly moderate computational cost. The aim of the present work is to show that there are many applications where CURS should be the user's method of choice for dealing with relatively low-dimensional scenarios.

翻译：本文提出了一种基于曲率的拒绝采样方法（CURS）。该方法适用于在黎曼流形上定义的一类广泛概率密度分布中进行采样，可用于从任何“仅依赖于距离”的概率密度中抽取样本。其核心思想是将拒绝采样的统计原理与体积比较的几何原理相结合。CURS是一种精确采样方法，且（在假设基础黎曼流形满足特定技术条件的前提下）具有相对较低的计算成本。本文旨在证明，在处理相对低维场景时，CURS应成为用户在众多应用中的首选方法。