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Geodesic Monte Carlo on embedded manifolds
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Byrne, Simon and Girolami, Mark (2013) Geodesic Monte Carlo on embedded manifolds. Scandinavian Journal of Statistics, Volume 40 (Number 4). pp. 825-845. doi:10.1111/sjos.12036
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Official URL: http://dx.doi.org/10.1111/sjos.12036
Abstract
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science > Statistics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Geodesics (Mathematics), Riemannian manifolds, Stiefel manifolds, Monte Carlo method | ||||||||||||
| Journal or Publication Title: | Scandinavian Journal of Statistics | ||||||||||||
| Publisher: | John Wiley & Sons Ltd | ||||||||||||
| ISSN: | 0303-6898 | ||||||||||||
| Official Date: | December 2013 | ||||||||||||
| Dates: |
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| Date of first compliant deposit: | 28 December 2015 | ||||||||||||
| Volume: | Volume 40 | ||||||||||||
| Number: | Number 4 | ||||||||||||
| Number of Pages: | 20 | ||||||||||||
| Page Range: | pp. 825-845 | ||||||||||||
| DOI: | 10.1111/sjos.12036 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access |
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