Sampling From A Manifold

TL;DR

This paper introduces algorithms for sampling from distributions on submanifolds in high-dimensional spaces, with applications in topological statistics, goodness of fit testing, and Neyman's smooth test, supported by geometric measure theory tools.

Contribution

It develops novel algorithms for sampling on manifolds and provides an accessible introduction to geometric measure theory techniques.

Findings

Algorithms successfully sample from distributions on submanifolds

Applications demonstrate effectiveness in statistical testing

Provides foundational tools for geometric measure theory in statistics

Abstract

We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to Neyman's smooth test. This article is partially expository, giving an introduction to the tools of geometric measure theory.