Curvature-based rejection sampling

TL;DR

This paper introduces curvature-based rejection sampling (CURS), a geometric method for exact sampling from probability densities on Riemannian manifolds that depend only on distance, with moderate computational costs for low-dimensional cases.

Contribution

The paper presents a novel geometric rejection sampling method, CURS, that leverages volume comparison on Riemannian manifolds for efficient exact sampling.

Findings

CURS effectively samples from distance-dependent densities on Riemannian manifolds.

The method has moderate computational costs under certain geometric conditions.

CURS is suitable for low-dimensional applications where traditional methods may be less efficient.

Abstract

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.