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.
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. https://doi.org/10.1214/16-EJS1117