Nonparametric Bayesian inference for reversible multidimensional diffusions
研究了可逆多维扩散的非参数贝叶斯模型，利用可逆性证明漂移梯度向量场的后验收缩率定理，并应用于高斯先验和p指数先验，在任意维数下达到最优非参数速率。
We study nonparametric Bayesian models for reversible multidimensional 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 optimal nonparametric rate over Sobolev smoothness classes in any dimension.