Beta流形的α-几何结构  

The α-geometric Structures of Beta Manifold

作　　者：许皓 谢亭亭 王君琦 XU Hao;XIE Tingting;WANG Junqi(College of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China;College of Mathematic Science,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]电子科技大学数学科学学院,成都611731

出　　处：《西华师范大学学报（自然科学版）》2020年第3期249-255,共7页Journal of China West Normal University(Natural Sciences)

基　　金：四川省科技计划重点研发项目(2019YFG0299);西华师范大学博士科研启动专项项目(17E082)。

摘　　要：为了有效分析和利用Beta分布的性质,本文从信息几何方法的角度给出Beta流形的α-几何结构以及相关几何性质。通过推导计算,得出Beta流形上的Fisher信息矩阵、α-联络和α-曲率等几何结构以及与指数族相关的几何性质。同时,本文还给出Beta流形上的α-散度和几类不同的特殊散度函数,并通过具体图例进行分析比较。利用计算结果和相关结论,可以进一步了解和掌握Beta分布的性质和应用,并将之有效应用于相关问题处理中。To effectively analyze and utilize the properties of Beta distribution,geometric structures of Beta manifold and its relevant geometric properties are presented by information geometry method in this paper.Some geometric structures including Fisher information matrix,α-connection and α-curvature as well as geometric properties related to exponential family are obtained through deduction and calculation.In addition,the α-divergence and some special divergence functions are given and comparatively analyzed by specific examples.The nature and application of Beta distribution are further understood and grasped through calculating results and relevant conclusions,which can be effectively applied to the treatment of related problems.

关 键 词：信息几何 Beta流形 几何结构 曲率 散度 

分 类 号：O186[理学—数学]