Electronic Journal of Statistics

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

Jan van Waaij and Harry van Zanten

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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

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

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

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Zentralblatt MATH identifier

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

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


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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