Principal bundles over statistical manifolds
  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 $\alpha$-structure of frame bundles over statistical manifolds with respect to $\alpha$-connections, by giving geometric structures. The manifold of one-dimensional normal distributions appears in the end as an application and a concrete example. 
Didong Li, Huafei Sun, Chen Tao and Lin Jiu
math.DG stat.OT