Dynamical Systems and Geometric Structures:Symmetry,Singularity,and Quantization
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1.Geodesic Flow fortheStatistical Transformation Model ofMultivariate Normal Distributions
- 关键词：
- Digital arithmetic;Higher order statistics;Linear algebra;Mathematical transformations;Statistics;% reductions;Fisher-Rao metric;Geodesic flow;Information geometry;Lie-groups;Marsden-weinstein reduction;Statistical transformation;Sub-riemannian;Subriemannian structure;Transformation modeling
- Tarama, Daisuke
- 《16th APCA International Conference on Automatic Control and Soft Computing, CONTROLO 2024》
- 2025年
- July 17, 2024 - July 19, 2024
- Porto, Portugal
- 会议
The statistical transformation models are a class of mathematical models in statistics with Lie group symmetries. Their information geometry is of much interest. This work deals with the geodesic flow arising from the statistical transformation model for the family of multivariate normal distributions on Euclidean spaces with the symmetry by the semi-direct product Lie group GL+(n,R)⋉Rn. The Fisher-Rao metric and the equation of the geodesic flow are explicitly deduced and their geometric properties are discussed. Particularly, a subriemannian structure is related with the geodesic flow. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
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