Byrne, S;
Girolami, M;
(2013)
Geodesic Monte Carlo on Embedded Manifolds.
SCANDINAVIAN JOURNAL OF STATISTICS
, 40
(4)
825 - 845.
10.1111/sjos.12036.
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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.
| Type: | Article |
|---|---|
| Title: | Geodesic Monte Carlo on Embedded Manifolds |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1111/sjos.12036 |
| Publisher version: | http://dx.doi.org/10.1111/sjos.12036 |
| Additional information: | © 2013 Board of the Foundation of the Scandinavian Journal of Statistics. Full text made available to UCL Discovery by kind permission of Wiley. |
| Keywords: | directional statistics, geodesic, Hamiltonian Monte Carlo, Riemannian manifold, Stiefel manifold |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1403377 |
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