08 - Contraction rates of posteriors based on Gaussian - Harry VAN ZANTEN

Contraction rates of posterior distributions on nonparametric models are derived for Gaussian process priors. We show that the convergence rate depends on the small ball probabilities of the Gaussian process and on the position of the true parameter relative to the reproducing kernel Hilbert space of the Gaussian process. Explicit examples are given for various statistical settings, including density estimation, nonparametric regression, and classification. We also discuss how rescaling of the prior process affects the contraction rates and how random rescaling can yield rate-adaptive procedures. This is based on joint work with Aad van der Vaart. Harry VAN ZANTEN. Vrije Universiteit. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750607556 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 34 mn