2011年6月
SYMPLECTIC STRUCTURES ON STATISTICAL MANIFOLDS
Journal of the Australian Mathematical Society
- 巻
- 90
- 号
- 3
- 開始ページ
- 371
- 終了ページ
- 384
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1017/s1446788711001285
- 出版者・発行元
- Cambridge University Press (CUP)
<title>Abstract</title>A relationship between symplectic geometry and information geometry is studied. The square of a dually flat space admits a natural symplectic structure that is the pullback of the canonical symplectic structure on the cotangent bundle of the dually flat space via the canonical divergence. With respect to the symplectic structure, there exists a moment map whose image is the dually flat space. As an example, we obtain a duality relation between the Fubini–Study metric on a projective space and the Fisher metric on a statistical model on a finite set. Conversely, a dually flat space admitting a symplectic structure is locally symplectically isomorphic to the cotangent bundle with the canonical symplectic structure of some dually flat space. We also discuss nonparametric cases.
- リンク情報
- ID情報
-
- DOI : 10.1017/s1446788711001285
- ISSN : 1446-7887
- eISSN : 1446-8107