Statistical Einstein manifolds of exponential families with group-invariant potential functions

Linyu Peng, Zhenning Zhang

研究成果: Article査読

2 被引用数 (Scopus)

抄録

This paper mainly contributes to a classification of statistical Einstein manifolds, namely statistical manifolds at the same time are Einstein manifolds. A statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. With the Fisher information metric as a Riemannian metric, information geometry was developed to understand the intrinsic properties of statistical models, which play important roles in statistical inference, etc. Among all these models, exponential families is one of the most important kinds, whose geometric structures are fully determined by their potential functions. To classify statistical Einstein manifolds, we derive partial differential equations for potential functions of exponential families; special solutions of these equations are obtained through the ansatz method as well as group-invariant solutions via reductions using Lie point symmetries.

本文言語English
ページ(範囲)2104-2118
ページ数15
ジャーナルJournal of Mathematical Analysis and Applications
479
2
DOI
出版ステータスPublished - 2019 11 15

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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