Posterior consistency of Gaussian process prior for nonparametric binary regression

• 成果类型: Article
• 署名作者: Ghosal, Subhashis; Roy, Anindya
• 署名单位: North Carolina State University; University System of Maryland; University of Maryland Baltimore County
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000795
• 发表日期: 2006
• 页码: 2413-2429
• 关键词: DENSITY-ESTIMATION

摘要

Consider binary observations whose response probability is an unknown smooth function of a set of covariates. Suppose that a prior on the response probability function is induced by a Gaussian process mapped to the unit interval through a link function. In this paper we study consistency of the resulting posterior distribution. If the covariance kernel has derivatives up to a desired order and the bandwidth parameter of the kernel is allowed to take arbitrarily small values, we show that the posterior distribution is consistent in the L-1-distance. As an auxiliary result to our proofs, we show that, under certain conditions, a Gaussian process assigns positive probabilities to the uniform neighborhoods of a continuous function. This result may be of independent interest in the literature for small ball probabilities of Gaussian processes.