We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure. The general theorem is applied to Gaussian priors and $p$-exponential priors, which are shown to converge to the truth at the minimax optimal rate over Sobolev smoothness classes in any dimension

翻译：我们研究的是非参数性贝叶斯模型,以进行周期性漂移的可逆多维扩散。对于连续观测路径,可逆性被利用来证明在变量测量之前诱导的近似理论条件下,在近似理论条件下,对漂渐梯矢量场的一般后退速率理论。一般理论适用于高森前科和美元丰度前科,这些前科显示在任何层面的索博勒夫平滑等级上的最低最大最佳速率上与事实一致。