Equiaffine structures on statistical manifolds and Bayesian statistics

Hiroshi Matsuzoe, Jun ichi Takeuchi, Shun ichi Amari

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Relations between equiaffine geometry and Bayesian statistics are studied. A prior distribution in Bayesian statistics is regarded as a volume form on a statistical manifold. Applying equiaffine geometry to Bayesian statistics, the relation between alpha-parallel priors and the Jeffreys prior is given. As geometric results, conditions for a statistical submanifold to have an equiaffine structure are also given.

Original languageEnglish
Pages (from-to)567-578
Number of pages12
JournalDifferential Geometry and its Application
Volume24
Issue number6
DOIs
Publication statusPublished - Dec 1 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics

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