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

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Bhattacharya, A; Dunson, DB

Published Date

  • December 2010

Published In

Volume / Issue

  • 97 / 4

Start / End Page

  • 851 - 865

PubMed ID

  • 22822255

Pubmed Central ID

  • 22822255

Electronic International Standard Serial Number (EISSN)

  • 1464-3510

International Standard Serial Number (ISSN)

  • 0006-3444

Digital Object Identifier (DOI)

  • 10.1093/biomet/asq044

Language

  • eng