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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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
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:	Date Event December 2013 Published 13 September 2013 Available 21 June 2013 Accepted 12 June 2013 Modified 25 January 2013 Submitted
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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