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arXiv · 1504.07972

Adaptive Bayesian credible sets in regression with a Gaussian process prior

Suzanne Sniekers·Aad van der Vaart
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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.

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Suzanne Sniekers, Aad van der Vaart. 2015-04-29. Adaptive Bayesian credible sets in regression with a Gaussian process prior. https://arxiv.org/abs/1504.07972

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