Symmetry and Bayesian Function Estimation1
2005 ◽
Vol 56
(1-4)
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pp. 57-80
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Summary This paper develops Bayesian function estimation on compact Riemannian manifolds. The approach is to combine Bayesian methods along with aspects of spectral geometry associated with the Laplace-Beltrami operator on Riemannian manifolds. Although frequentist nonparametric function estimation in Euclidean space abound, to date, no attempt has been made with respect to Bayesian function estimation on a general Riemannian manifold. The Bayesian approach to function estimation is very natural for manifolds because one can elicit very specific prior information on the possible symmetries in question . One can then establish Bayes estimators that possess built in symmetries. A detailed analysis for the 2–sphere is provided.
2000 ◽
Vol 95
(450)
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pp. 520-534
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2010 ◽
Vol 23
(6)
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pp. 1245-1253
1993 ◽
Vol 21
(2)
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pp. 1040-1057
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2020 ◽
Vol 36
(2)
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pp. 314-331
2011 ◽
Vol 161
(2)
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pp. 166-181
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2011 ◽
Vol 25
(1)
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pp. 280-309
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2018 ◽
Vol 137
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pp. 326-330
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