Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.09097 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914970843742208 |
|---|---|
| author | Schär, Philip Stier, Thilo D. |
| author_facet | Schär, Philip Stier, Thilo D. |
| contents | We theoretically analyze the properties of a geodesic random walk on the Euclidean $d$-sphere. Specifically, we prove that the random walk's transition kernel is Wasserstein contractive with a contraction rate which can be bounded from above independently of the dimension $d$. Our result is of particular interest due to its implications regarding the potential for dimension-independent performance of both geodesic slice sampling on the sphere and Gibbsian polar slice sampling, which are Markov chain Monte Carlo methods for approximate sampling from essentially arbitrary distributions on their respective state spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09097 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Dimension-Independent Bound on the Wasserstein Contraction Rate of a Geodesic Random Walk on the Sphere Schär, Philip Stier, Thilo D. Statistics Theory Probability 60G50 (Primary) 60J05, 65C05 (Secondary) We theoretically analyze the properties of a geodesic random walk on the Euclidean $d$-sphere. Specifically, we prove that the random walk's transition kernel is Wasserstein contractive with a contraction rate which can be bounded from above independently of the dimension $d$. Our result is of particular interest due to its implications regarding the potential for dimension-independent performance of both geodesic slice sampling on the sphere and Gibbsian polar slice sampling, which are Markov chain Monte Carlo methods for approximate sampling from essentially arbitrary distributions on their respective state spaces. |
| title | A Dimension-Independent Bound on the Wasserstein Contraction Rate of a Geodesic Random Walk on the Sphere |
| topic | Statistics Theory Probability 60G50 (Primary) 60J05, 65C05 (Secondary) |
| url | https://arxiv.org/abs/2309.09097 |