Sampling from a manifold. (English) Zbl 1356.62015

Diaconis, Persi; Holmes, Susan; Shahshahani, Mehrdad

Jones, Galin (ed.) et al., Advances in modern statistical theory and applications. A Festschrift in honor of Morris L. Eaton. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-84-3). Institute of Mathematical Statistics Collections 10, 102-125 (2013).

Summary: We develop algorithms for sampling from a probability distribution on a submanifold embedded in \(\mathbb{R}^n\). 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.
For the entire collection see [Zbl 1319.62004].

MSC:

62D05	Sampling theory, sample surveys
62H11	Directional data; spatial statistics
62G10	Nonparametric hypothesis testing
62B10	Statistical aspects of information-theoretic topics
49Q15	Geometric measure and integration theory, integral and normal currents in optimization

Keywords:

manifold; conditional distribution; geometric measure theory; sampling; submanifold; topological statistics; Neyman’s smooth test