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A diffusion approach to Stein's method on Riemannian manifolds

Le, Huiling; Lewis, Alexander; Bharath, Karthik; Fallaize, Christopher

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Authors

Huiling Le

Alexander Lewis



Abstract

We detail an approach to developing Stein’s method for bounding integral metrics on probability measures defined on a Riemannian manifold M. Our approach exploits the relationship between the generator of a diffusion on M having a target invariant measure and its characterising Stein operator. We consider a pair of such diffusions with different starting points, and through analysis of the distance process between the pair, derive Stein factors, which bound the solution to the Stein equation and its derivatives. The Stein factors contain curvature-dependent terms and reduce to those currently available for Rm, and moreover imply that the bounds for Rm remain valid when M is a flat manifold.

Citation

Le, H., Lewis, A., Bharath, K., & Fallaize, C. (2024). A diffusion approach to Stein's method on Riemannian manifolds. Bernoulli, 30(2), 1079-1104. https://doi.org/10.3150/23-bej1625

Journal Article Type Article
Acceptance Date Apr 21, 2023
Publication Date May 1, 2024
Deposit Date May 10, 2023
Publicly Available Date May 1, 2024
Journal Bernoulli
Print ISSN 1350-7265
Electronic ISSN 1573-9759
Publisher Bernoulli Society for Mathematical Statistics and Probability
Peer Reviewed Peer Reviewed
Volume 30
Issue 2
Pages 1079-1104
DOI https://doi.org/10.3150/23-bej1625
Keywords Coupling; integral metrics; Stein equation; stochastic flow; Wasserstein distance
Public URL https://nottingham-repository.worktribe.com/output/20560259
Publisher URL https://projecteuclid.org/journals/bernoulli/volume-30/issue-2/A-diffusion-approach-to-Steins-method-on-Riemannian-manifolds/10.3150/23-BEJ1625.full

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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/

Copyright Statement
This research was funded, in whole or in part, by [Engineering and Physical Sciences Research Council (EPSRC), UK, EPSRC EP/V048104/1]. A CC BY 4.0 license is applied to this article arising from this submission, in accordance with the grant’s open access conditions






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