论文标题
非参数贝叶斯推断，用于可逆的多维扩散
Nonparametric Bayesian inference for reversible multi-dimensional diffusions
论文作者
论文摘要
我们研究非参数贝叶斯模型，用于周期性漂移的可逆多维扩散。对于连续的观察路径，利用可逆性证明在近似理论条件下，在不变性测量的先验上，在近似理论条件下，漂移梯度矢量场的一般后验收缩率定理。将一般定理应用于高斯先生和$ p $ - 指示先验，这些先验显示出在任何维度上以sobolev平滑度类别的最小值最佳速率收敛到真理。
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.
