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Equiaffine structures on statistical manifolds and Bayesian statistics |
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| Authors: | Hiroshi Matsuzoe Jun-ichi Takeuchi |
| Affiliation: | a Department of Computer Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, 466-8555, Japan b Internet Systems Research Laboratories, NEC Corporation, 1753 Shimonumabe, Nakahara-ku, Kawasaki, Kanagawa, 211-8666, Japan c RIKEN, Brain Science Institute, Mathematical Neuroscience Laboratory, Hirosawa 2-1, Wako-shi, Saitama 351-0198, Japan |
| 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. |
| Keywords: | 53A15 62F15 |
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