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Dimension‐independent Markov chain Monte Carlo on the sphere
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Lie, Han Cheng, Rudolf, Daniel, Sprungk, Björn and Sullivan, T. J. (2023) Dimension‐independent Markov chain Monte Carlo on the sphere. Scandinavian Journal of Statistics . doi:10.1111/sjos.12653 ISSN 0303-6898. (In Press)
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Official URL: https://doi.org/10.1111/sjos.12653
Abstract
We consider Bayesian analysis on high-dimensional spheres with angular central Gaussian priors. These priors model antipodally symmetric directional data, are easily defined in Hilbert spaces and occur, for instance, in Bayesian density estimation and binary level set inversion. In this paper we derive efficient Markov chain Monte Carlo methods for approximate sampling of posteriors with respect to these priors. Our approaches rely on lifting the sampling problem to the ambient Hilbert space and exploit existing dimension-independent samplers in linear spaces. By a push-forward Markov kernel construction we then obtain Markov chains on the sphere which inherit reversibility and spectral gap properties from samplers in linear spaces. Moreover, our proposed algorithms show dimension-independent efficiency in numerical experiments.
| Item Type: | Journal Article | |||||||||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| SWORD Depositor: | Library Publications Router | |||||||||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Markov processes , Monte Carlo method, Mathematical statistics, Distribution (Probability theory), Manifolds (Mathematics) | |||||||||||||||||||||||||||
| Journal or Publication Title: | Scandinavian Journal of Statistics | |||||||||||||||||||||||||||
| Publisher: | Wiley-Blackwell Publishing Ltd. | |||||||||||||||||||||||||||
| ISSN: | 0303-6898 | |||||||||||||||||||||||||||
| Official Date: | 24 April 2023 | |||||||||||||||||||||||||||
| Dates: |
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| DOI: | 10.1111/sjos.12653 | |||||||||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||||||||
| Publication Status: | In Press | |||||||||||||||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||||||||||||||
| Date of first compliant deposit: | 27 July 2023 | |||||||||||||||||||||||||||
| Date of first compliant Open Access: | 28 July 2023 | |||||||||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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