Strong consistency of nonparametric Bayes density estimation on compact metric spaces with applications to specific manifolds.

Published

Journal Article

This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any continuous density. The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. These conditions are verified on compact Euclidean spaces using multivariate Gaussian kernels, on the hypersphere using a von Mises-Fisher kernel and on the planar shape space using complex Watson kernels.

Full Text

Duke Authors

Cited Authors

  • Bhattacharya, A; Dunson, DB

Published Date

  • August 2012

Published In

Volume / Issue

  • 64 / 4

Start / End Page

  • 687 - 714

PubMed ID

  • 22984295

Pubmed Central ID

  • 22984295

Electronic International Standard Serial Number (EISSN)

  • 1572-9052

International Standard Serial Number (ISSN)

  • 0020-3157

Digital Object Identifier (DOI)

  • 10.1007/s10463-011-0341-x

Language

  • eng