统计流形上的等仿射结构(英文)

Equiaffine structures on statistical manifolds

作者首先研究了等仿射几何与贝叶斯统计学之间的关系,这里贝叶斯统计学的先验分布被看作统计流形上的体积形式,然后利用统计流形上α平行先验估计和体积形式的关系,结合子流形上的基本方程和基本公式给出了一个统计子流形上具有等仿射结构的条件.

In this paper, information geometric theories are generalized, relations between equiaffine geometry and Bayesian statistics are studied, where a prior distribution in Bayesian statistics is regarded as a volume form on a statistical manifold. Then by applying the relation between α-parallel priors and the volume forms on statistical manifolds, the sufficient conditions for a statistical submanifolds to have an equiaffine structure are given.