Posterior consistency of Gaussian process prior for nonparametric binary regression

Ghosal, Subhashis ; Roy, Anindya

Ann. Statist., Tome 34 (2006) no. 1, p. 2413-2429 / Harvested from Project Euclid

Résumé

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 L₁-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.

Détail

Publié le : 2006-10-14
Classification:  Binary regression,  Gaussian process,  Karhunen–Loeve expansion,  maximal inequality,  posterior consistency,  reproducing kernel Hilbert space,  62G08,  62G20