Rates of contraction of posterior distributions based on Gaussian process priors

• 成果类型: Article
• 署名作者: Van Der Wart, A. W.; Van Zanten, J. H.
• 署名单位: Vrije Universiteit Amsterdam
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000613
• 发表日期: 2008
• 页码: 1435-1463
• 关键词: fractional brownian-motion; convergence-rates; STOCHASTIC-PROCESSES; series expansion; regression; REPRESENTATION; densities

摘要

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 contraction of the posterior distribution based on sampling from a smooth density model when the prior models the log density as a (fractionally integrated) Brownian motion. We also consider regression with Gaussian errors and smooth classification under a logistic or probit link function combined with various priors.