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Activity Number: 392
Type: Invited
Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #314196 View Presentation
Title: Coverage of Credible Sets Based on Gaussian Process Priors
Author(s): Aad van der Vaart*
Companies: Leiden University
Keywords: posterior ; coverage ; Gaussian ; credible set ; nonparametric ; adaptation
Abstract:

In the Bayesian framework one may model an unknown function a priori as a sample path of a Gaussian process. The posterior mode or mean then gives a nonparametric estimator of the function. The posterior spread could be used as a measure of the quality of this estimator. A particular case is that of integrated Brownian motion priors, which lead to penalized spline estimators. In this talk we focus on the second aspect of the posterior, which we approach by investigating the coverage of posterior credible sets. This is a delicate issue, in particular when the length scale of the Gaussian process (its smoothness) is set in an adaptive way by an empirical or hieararchical Bayes scheme.


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