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2016 Gaussian process methods for one-dimensional diffusions: Optimal rates and adaptation
Jan van Waaij, Harry van Zanten
Electron. J. Statist. 10(1): 628-645 (2016). DOI: 10.1214/16-EJS1117


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.


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Jan van Waaij. Harry van Zanten. "Gaussian process methods for one-dimensional diffusions: Optimal rates and adaptation." Electron. J. Statist. 10 (1) 628 - 645, 2016.


Received: 1 September 2015; Published: 2016
First available in Project Euclid: 7 March 2016

zbMATH: 06554160
MathSciNet: MR3471991
Digital Object Identifier: 10.1214/16-EJS1117

Primary: 62C10 , 62M99

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

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.10 • No. 1 • 2016
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