Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • SYMPLECTIC STRUCTURES ON STATISTICAL MANIFOLDS

  • Part of
  • TOMONORI NODA
  • Journal:
    Journal of the Australian Mathematical Society / Volume 90 / Issue 3 / June 2011
    Published online by Cambridge University Press:
    15 June 2011, pp. 371-384
    Print publication:
    June 2011
    • Article
      • You have access
    • PDF
    • Export citation

  • 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.