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 H\"older 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 procedure, based on location-scale mixtures of Gaussians, appears to be convenient to implement and yields good practical results, even for quite singular data.

翻译：我们研究了在欧几里德空间一个未知的子元值抵消下生活的巴伊西亚密度估计数据。 从这个角度讲,我们引入了一种新的“厌食性H”老化者概念,用于潜在的密度,并获得最优和适应密度的正常性、多元的内在维度和抵消的大小的后继率,只要后者不是太小 -- -- 但仍被允许为零。我们的巴伊西亚程序以高斯人的位置级混合物为基础,似乎便于实施并产生良好的实际结果,即使是非常单一的数据也是如此。