结构统计学基础：统计流形
Foundations of Structural Statistics: Statistical Manifolds
摘要：
结构统计学的应用需要在一致的拓扑统计理论基础上对模型空间的邻近结构进行量化。研究这些结构的一个重要工具是伪黎曼度量，它在统计模型的范畴中由统计分歧引起。本文将拓扑统计模型的微分结构表示法推广到统计流形，并介绍了用微分几何、黎曼几何和辛几何研究分布族的微分几何基础。
英文摘要：
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices, which in the category of statistical models are induced by statistical divergences. The present article extends the notation of topological statistical models by a differential structure to statistical manifolds and introduces the differential geometric foundations to study distribution families by their differential-, Riemannian- and symplectic geometry.
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