论文标题
结构统计基础：统计流形
Foundations of Structural Statistics: Statistical Manifolds
论文作者
论文摘要
根据一致的拓扑统计理论，结构统计的应用需要量化模型空间的接近性结构。研究这些结构的一个重要工具是伪里曼尼亚式度量，在统计模型的类别中，统计差异引起了统计模型。本文通过差异结构将拓扑统计模型的符号扩展到统计流形，并引入差异几何基础，以通过其差分，riemannian和simbletical几何形状来研究分布家族。
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.
