Adaptive Bayesian multivariate density estimation with Dirichlet mixtures
Journal Article
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient conditions on the prior specification that guarantee convergence to a true density at a rate that is minimax optimal for the smoothness class to which the true density belongs. No prior knowledge of smoothness is assumed. The sufficient conditions are shown to hold for the Dirichlet location mixture-of-normals prior with a Gaussian base measure and an inverse Wishart prior on the covariance matrix parameter. Locally Hölder smoothness classes and their anisotropic extensions are considered. Our study involves several technical novelties, including sharp approximation of finitely differentiable multivariate densities by normal mixtures and a new sieve on the space of such densities. © 2013 Biometrika Trust.
Full Text
Duke Authors
Cited Authors
- Shen, W; Tokdar, ST; Ghosal, S
Published Date
- 2013
Published In
Volume / Issue
- 100 / 3
Start / End Page
- 623 - 640
International Standard Serial Number (ISSN)
- 0006-3444
Digital Object Identifier (DOI)
- 10.1093/biomet/ast015