Estimating a density near an unknown manifold: A Bayesian nonparametric approach
未知流形邻域中的密度估计：贝叶斯非参数方法
We study the Bayesian density estimation of data living in the offset of an unknown submanifold of the Euclidean space. In this perspective, we introduce a new notion of anisotropic Hölder for the underlying density and obtain posterior rates that are minimax optimal and adaptive to the regularity of the density, to the intrinsic dimension of the manifold, and to the size of the offset, provided that the latter is not too small—while still allowed to go to zero. Our Bayesian…