Bayesian inference with rescaled Gaussian process priors

Details Bayesian inference with rescaled Gaussian process priors Bayesian inference with rescaled Gaussian process priors

2007-10-19

arxiv.org/abs/0710.3679v1

Electronic Journal of Statistics 2007, Vol. 1, 433-448

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-EJS098 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/07-EJS098

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit rescaled Gaussian process priors yielding posteriors that contract around the true parameter at optimal convergence rates. To derive our results we establish bounds on small deviation probabilities for smooth stationary Gaussian processes.

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