Geometry of statistical manifolds for integrable and non-integrable systems

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740047
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Nagoya Institute of Technology
• Principal Investigator: MATSUZOE Hiroshi 名古屋工業大学, 工学(系)研究科(研究院), 准教授 (90315177)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 統計多様体 / 捩れを許す統計多様体 / アファイン微分幾何学 / アファイン分布 / 情報幾何学 / プレコントラスト関数 / Tsallis統計 / 非可積分推定関数

Outline of Final Research Achievements

The notion of statistical manifold is a differential geometric formulation of a set of probability distributions. For statistical manifold structures for statistical models, geometric structures are studied from the viewpoints of integrable and non-integrable systems. In particular, natural statistical manifold structures of statistical models are elucidated using geometry of estimating functions. In addition, the notions of expectations and independences are generalized from the viewpoint of differential geometry, and relations between expectations of random variables and generalized conformal structures of statistical manifolds are elucidated.

Free Research Field

幾何学