Geometry of statistical manifolds for integrable and non-integrable systems
| Project/Area Number |
23740047
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
MATSUZOE Hiroshi 名古屋工業大学, 工学(系)研究科(研究院), 准教授 (90315177)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| 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 |
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| 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.
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Report
(5 results)
Research Products
(45 results)
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[Presentation] 統計多様体の共形構造2014
Author(s)
松添博
Organizer
統計多様体の諸分野への応用
Place of Presentation
京都大学
Year and Date
2014-11-19 – 2014-11-21
Related Report
Invited
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[Presentation] Information geometry of Bayesian statistics2014
Author(s)
Hiroshi Matsuzoe
Organizer
34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Place of Presentation
Chateau Clos Luce, Amboise, France
Year and Date
2014-09-21 – 2014-09-26
Related Report
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