一维扩散的高斯过程方法：最优速率和自适应
Gaussian process methods for one-dimensional diffusions: optimal rates and adaptation
摘要：
我们研究了一维周期漂移扩散的非参数贝叶斯过程的性能。我们改进了现有的收敛速度的结果高斯过程（GP）先验与固定的超参数。此外，我们展示了几种可能性，以实现适应平滑。我们实现这一点，考虑分层的程序，涉及到一个乘法缩放参数的先验，或先验的GP的正则性参数。
英文摘要：
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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