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October 2006 Posterior consistency of Gaussian process prior for nonparametric binary regression
Subhashis Ghosal, Anindya Roy
Ann. Statist. 34(5): 2413-2429 (October 2006). DOI: 10.1214/009053606000000795


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.


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Subhashis Ghosal. Anindya Roy. "Posterior consistency of Gaussian process prior for nonparametric binary regression." Ann. Statist. 34 (5) 2413 - 2429, October 2006.


Published: October 2006
First available in Project Euclid: 23 January 2007

zbMATH: 1106.62039
MathSciNet: MR2291505
Digital Object Identifier: 10.1214/009053606000000795

Primary: 62G08 , 62G20

Keywords: binary regression , Gaussian process , Karhunen–Loeve expansion , maximal inequality , posterior consistency , ‎reproducing kernel Hilbert ‎space

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 5 • October 2006
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