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Geodesic Monte Carlo on embedded manifolds

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Title: Geodesic Monte Carlo on embedded manifolds
Authors: Byrne, S
Girolami, M
Item 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.
Issue Date: 1-Dec-2013
Date of Acceptance: 21-Jun-2013
URI: http://hdl.handle.net/10044/1/66027
DOI: https://dx.doi.org/10.1111/sjos.12036
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.
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
directional statistics
Hamiltonian Monte Carlo
Riemannian manifold
Stiefel manifold
geodesic, Hamiltonian Monte Carlo
0104 Statistics
Publication Status: Published
Online Publication Date: 2013-09-13
Appears in Collections:Mathematics
Faculty of Natural Sciences