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Nonparametric Bayesian density estimation on manifolds with applications to planar shapes.

Publication ,  Journal Article
Bhattacharya, A; Dunson, DB
Published in: Biometrika
December 2010

Statistical analysis on landmark-based shape spaces has diverse applications in morphometrics, medical diagnostics, machine vision and other areas. These shape spaces are non-Euclidean quotient manifolds. To conduct nonparametric inferences, one may define notions of centre and spread on this manifold and work with their estimates. However, it is useful to consider full likelihood-based methods, which allow nonparametric estimation of the probability density. This article proposes a broad class of mixture models constructed using suitable kernels on a general compact metric space and then on the planar shape space in particular. Following a Bayesian approach with a nonparametric prior on the mixing distribution, conditions are obtained under which the Kullback-Leibler property holds, implying large support and weak posterior consistency. Gibbs sampling methods are developed for posterior computation, and the methods are applied to problems in density estimation and classification with shape-based predictors. Simulation studies show improved estimation performance relative to existing approaches.

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Published In

Biometrika

DOI

EISSN

1464-3510

ISSN

0006-3444

Publication Date

December 2010

Volume

97

Issue

4

Start / End Page

851 / 865

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
 

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Bhattacharya, A., & Dunson, D. B. (2010). Nonparametric Bayesian density estimation on manifolds with applications to planar shapes. Biometrika, 97(4), 851–865. https://doi.org/10.1093/biomet/asq044
Bhattacharya, Abhishek, and David B. Dunson. “Nonparametric Bayesian density estimation on manifolds with applications to planar shapes.Biometrika 97, no. 4 (December 2010): 851–65. https://doi.org/10.1093/biomet/asq044.
Bhattacharya A, Dunson DB. Nonparametric Bayesian density estimation on manifolds with applications to planar shapes. Biometrika. 2010 Dec;97(4):851–65.
Bhattacharya, Abhishek, and David B. Dunson. “Nonparametric Bayesian density estimation on manifolds with applications to planar shapes.Biometrika, vol. 97, no. 4, Dec. 2010, pp. 851–65. Epmc, doi:10.1093/biomet/asq044.
Bhattacharya A, Dunson DB. Nonparametric Bayesian density estimation on manifolds with applications to planar shapes. Biometrika. 2010 Dec;97(4):851–865.
Journal cover image

Published In

Biometrika

DOI

EISSN

1464-3510

ISSN

0006-3444

Publication Date

December 2010

Volume

97

Issue

4

Start / End Page

851 / 865

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics