Geodesic Monte Carlo on embedded manifolds
File(s)
Published version
Author(s)
Byrne, Simon
Girolami, Mark
Type
Journal Article
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.
Date Issued
2013-12-01
Date Acceptance
2013-06-21
Citation
Scandinavian Journal of Statistics, 2013, 40 (4), pp.825-845
ISSN
0303-6898
Publisher
Wiley
Start Page
825
End Page
845
Journal / Book Title
Scandinavian Journal of Statistics
Volume
40
Issue
4
Copyright Statement
© 2013 The Authors. Scandinavian Journal of Statistics published by John Wiley & Sons Ltd on behalf of The Board of the Foundation of the Scandinavian Journal of Statistics. This is an open access article under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/3.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000327258100011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
directional statistics
geodesic
Hamiltonian Monte Carlo
Riemannian manifold
Stiefel manifold
PROBABILISTIC MODEL
UNCERTAINTY
Publication Status
Published
Date Publish Online
2013-09-13