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

Jan van Waaij, Harry van Zanten

Research output: Contribution to JournalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)628-645
Number of pages18
JournalElectronic Journal of Statistics
Volume10
Issue number1
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes

Keywords

  • Adaptation to smoothness
  • Asymptotic performance
  • Bayesian inference
  • Gaussian process prior
  • Nonparametric inference for diffusions

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