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统计流形在切丛上提升的等积仿射结构

Complete Lifts Equiaffine Structure on Tangent Bundle over Statistical Manifolds
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摘要 具有等积仿射结构的统计流形在贝叶斯统计理论中有着重要应用,主要讨论统计流形及其切丛上的等积仿射结构,得到了统计流形的无挠仿射联络和其在切丛上提升的仿射联络的等积仿射性是一致的. The statistical manifolds with equiaffine structures have important applications to Bayesian statistics.This paper proves that the torsion-free affine connection on statistical manifolds is equiaffine if and only if its complete lifts connection is an equiaffine connection.
作者 秦华军 舒级
机构地区 四川师范大学数学与软件科学学院
出处 《四川师范大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第1期10-12,共3页 Journal of Sichuan Normal University（Natural Science）
基金 国家自然科学基金(10926034和10771151)资助项目
关键词 统计流形 对偶联络 等积仿射结构 完全提升 切丛 dual connection equiaffine structure statistical manifolds complete lifts tangent bundle
分类号 O186.12 [理学—基础数学]
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参考文献15

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二级参考文献7

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四川师范大学学报（自然科学版）
2011年 第1期

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