Electronic Journal of Statistics

Gaussian process methods for one-dimensional diffusions: Optimal rates and adaptation

Jan van Waaij and Harry van Zanten

Full-text: Open access

Abstract

We study the performance of nonparametric Bayes procedures for one-dimensional diffusions with periodic drift. We improve existing convergence rate results for Gaussian process (GP) priors with fixed hyper parameters. Moreover, we exhibit several possibilities to achieve adaptation to smoothness. We achieve this by considering hierarchical procedures that involve either a prior on a multiplicative scaling parameter, or a prior on the regularity parameter of the GP.

Article information

Source
Electron. J. Statist. Volume 10, Number 1 (2016), 628-645.

Dates
Received: September 2015
First available in Project Euclid: 7 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1457382316

Digital Object Identifier
doi:10.1214/16-EJS1117

Mathematical Reviews number (MathSciNet)
MR3471991

Zentralblatt MATH identifier
06554160

Subjects
Primary: 62M99: None of the above, but in this section 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Nonparametric inference for diffusions Bayesian inference asymptotic performance Gaussian process prior adaptation to smoothness

Citation

van Waaij, Jan; van Zanten, Harry. Gaussian process methods for one-dimensional diffusions: Optimal rates and adaptation. Electron. J. Statist. 10 (2016), no. 1, 628--645. doi:10.1214/16-EJS1117. https://projecteuclid.org/euclid.ejs/1457382316


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