Posterior consistency of logistic Gaussian process priors in density estimation
Journal Article (Journal Article)
We establish weak and strong posterior consistency of Gaussian process priors studied by Lenk [1988. The logistic normal distribution for Bayesian, nonparametric, predictive densities. J. Amer. Statist. Assoc. 83 (402), 509-516] for density estimation. Weak consistency is related to the support of a Gaussian process in the sup-norm topology which is explicitly identified for many covariance kernels. In fact we show that this support is the space of all continuous functions when the usual covariance kernels are chosen and an appropriate prior is used on the smoothing parameters of the covariance kernel. We then show that a large class of Gaussian process priors achieve weak as well as strong posterior consistency (under some regularity conditions) at true densities that are either continuous or piecewise continuous. © 2005 Elsevier B.V. All rights reserved.
Full Text
Duke Authors
Cited Authors
- Tokdar, ST; Ghosh, JK
Published Date
- January 1, 2007
Published In
Volume / Issue
- 137 / 1
Start / End Page
- 34 - 42
International Standard Serial Number (ISSN)
- 0378-3758
Digital Object Identifier (DOI)
- 10.1016/j.jspi.2005.09.005
Citation Source
- Scopus