Principal bundles over statistical manifolds

2014/03/18 by Li, Didong, Sun, Huafei, Tao, Chen +1
#Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Other Statistics (stat.OT)

paper · doi:10.48550/arxiv.1403.4471

Abstract

In this paper, we introduce the concept of principal bundles on statistical manifolds. After necessary preliminaries on information geometry and principal bundles on manifolds, we study the α-structure of frame bundles over statistical manifolds with respect to α-connections, by giving geometric structures. The manifold of one-dimensional normal distributions appears in the end as an application and a concrete example.

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