Translator Disclaimer
2015 Adaptive Bayesian credible sets in regression with a Gaussian process prior
Suzanne Sniekers, Aad van der Vaart
Electron. J. Statist. 9(2): 2475-2527 (2015). DOI: 10.1214/15-EJS1078

Abstract

We investigate two empirical Bayes methods and a hierarchical Bayes method for adapting the scale of a Gaussian process prior in a nonparametric regression model. We show that all methods lead to a posterior contraction rate that adapts to the smoothness of the true regression function. Furthermore, we show that the corresponding credible sets cover the true regression function whenever this function satisfies a certain extrapolation condition. This condition depends on the specific method, but is implied by a condition of self-similarity. The latter condition is shown to be satisfied with probability one under the prior distribution.

Citation

Download Citation

Suzanne Sniekers. Aad van der Vaart. "Adaptive Bayesian credible sets in regression with a Gaussian process prior." Electron. J. Statist. 9 (2) 2475 - 2527, 2015. https://doi.org/10.1214/15-EJS1078

Information

Received: 1 April 2015; Published: 2015
First available in Project Euclid: 19 November 2015

zbMATH: 1327.62300
MathSciNet: MR3425364
Digital Object Identifier: 10.1214/15-EJS1078

Subjects:
Primary: 62G05, 62G15
Secondary: 62G20

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

JOURNAL ARTICLE
53 PAGES


SHARE
Vol.9 • No. 2 • 2015
Back to Top