Posterior consistency of Gaussian process prior for nonparametric binary regression
| dc.creator | Ghosal, Subhashis | |
| dc.creator | Roy, Anindya | |
| dc.date | 2007-02-23 | |
| dc.date.accessioned | 2026-07-07T08:08:45Z | |
| dc.date.available | 2026-07-07T08:08:45Z | |
| dc.description | 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. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053606000000795 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0702686 | |
| dc.identifier | http://arxiv.org/abs/math/0702686 | |
| dc.identifier | Annals of Statistics 2006, Vol. 34, No. 5, 2413-2429 | |
| dc.identifier | doi:10.1214/009053606000000795 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131371 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G08, 62G20 (Primary) | |
| dc.title | Posterior consistency of Gaussian process prior for nonparametric binary regression | |
| dc.type | text |