Rates of contraction of posterior distributions based on Gaussian process priors

  title={Rates of contraction of posterior distributions based on Gaussian process priors},
  author={Aad W. Vaart and J. H. van Zanten},
  journal={Annals of Statistics},
We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the position of the true parameter relative to the reproducing kernel Hilbert space of the Gaussian process and the small ball probabilities of the Gaussian process. We determine these quantities for a range of examples of Gaussian priors and in several statistical settings. For instance, we consider the rate of… 

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