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arXiv · 0807.2734

Lower bounds for posterior rates with Gaussian process priors

Ismaël Castillo
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Abstract

Upper bounds for rates of convergence of posterior distributions associated to Gaussian process priors are obtained by van der Vaart and van Zanten in [14] and expressed in terms of a concentration function involving the Reproducing Kernel Hilbert Space of the Gaussian prior. Here lower-bound counterparts are obtained. As a corollary, we obtain the precise rate of convergence of posteriors for Gaussian priors in various settings. Additionally, we extend the upper-bound results of [14] about Riemann-Liouville priors to a continuous family of parameters.

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Ismaël Castillo. 2008-12-22. Lower bounds for posterior rates with Gaussian process priors. https://doi.org/10.1214/08-ejs273

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