论文标题
改善riemannian歧管上Stein方法表征范围的框架
A Framework for Improving the Characterization Scope of Stein's Method on Riemannian Manifolds
论文作者
论文摘要
Stein的方法已被广泛用于实现欧几里得空间中定义的概率分布的分布近似值。最近，已经报道了将Stein方法扩展到具有各个歧管上定义的分布的流动随机变量的技术。但是，其中几种方法对分布以及歧管和/或考虑非常特殊的案例施加了强大的规律条件。在本文中，我们使用弗里德里奇的扩展技术应用于自动辅助无界操作员的弗里德里奇扩展技术，介绍了斯坦因歧管上的斯坦因歧管方法的新颖框架。该框架适用于各种常规和非规定的情况，包括但不限于固有定义的非平滑分布，对riemannian歧管上的截断分布，关于不完整的Riemannian歧管分布的分布。不完整的Riemannian歧管等等。更重要的是，在歧视或目标分布上施加了强大的构图，即较强的适用性，我们的特征越来越强大，我们的特征是，我们的特征是，我们的表现能力，我们的表现能力，我们的表现能力，我们的表现能力，我们的表现能力均具有特征化的特征。斯坦因迄今未知的问题域的方法。我们提出了几个（非数字）示例，说明了所提出的理论的适用性。
Stein's method has been widely used to achieve distributional approximations for probability distributions defined in Euclidean spaces. Recently, techniques to extend Stein's method to manifold-valued random variables with distributions defined on the respective manifolds have been reported. However, several of these methods impose strong regularity conditions on the distributions as well as the manifolds and/or consider very special cases. In this paper, we present a novel framework for Stein's method on Riemannian manifolds using the Friedrichs extension technique applied to self-adjoint unbounded operators. This framework is applicable to a variety of conventional and unconventional situations, including but not limited to, intrinsically defined non-smooth distributions, truncated distributions on Riemannian manifolds, distributions on incomplete Riemannian manifolds, etc. Moreover, the stronger the regularity conditions imposed on the manifolds or target distributions, the stronger will be the characterization ability of our novel Stein pair, which facilitates the application of Stein's method to problem domains hitherto uncharted. We present several (non-numeric) examples illustrating the applicability of the presented theory.
