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Abstract Details
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Activity Number:
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74
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Type:
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Contributed
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Date/Time:
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Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #302265 |
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Title:
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Density Estimation on Riemannian Manifolds
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Author(s):
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Justin Jacobs*+
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Companies:
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University of Maryland at Baltimore County
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Address:
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1000 Hilltop Circle, Baltimore, MD, 21250,
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Keywords:
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Density Estimation ;
Riemannian Manifolds ;
Nonparametrics ;
Bayesian
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Abstract:
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The spectral properties of the Laplace-Beltrami operator on positive curvature Riemannian manifolds provide a general framework for identifying orthonormal bases that can be used to identify continuous densities on the given manifold. In this talk, we explore nonparametric Bayesian methodology for estimating probability densities on Riemannian manifolds. We use a Kaurhunen-Loeve expansion of the density in the logistic-normal form using the orthonormal basis induced by the Laplace-Beltrami operator on the manifold. The Gausssian process representation naturally lends itself to specification of priors on the density. For illustration, we will analyze Monte-Carlo simulations of various distributions on the sphere and circle. We will also take a look at a real-life application in meteorlogical tracking.
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Authors who are presenting talks have a * after their name.
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