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Adaptive Bayesian credible bands in regression with a Gaussian process prior
Suzanne Sniekers1, Aad van der Vaart1
1Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands.
Abstract:
A credible band is the set of all functions between a lower and an upper bound that are constructed so that the set has prescribed mass under the posterior distribution. In a Bayesian analysis such a band is used to quantify the remaining uncertainty on the unknown function in a similar manner as a confidence band. We investigate the validity of a credible band in the nonparametric regression model with the prior distribution on the function given by a Gaussian process. We show that there are many true regression functions for which the credible band has the correct order of magnitude to be used as a confidence set. We also exhibit functions for which the credible band is misleading.
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