TY - JOUR
T1 - Equiaffine structures on statistical manifolds and Bayesian statistics
AU - Matsuzoe, Hiroshi
AU - Takeuchi, Jun ichi
AU - Amari, Shun ichi
N1 - Funding Information:
The authors would like to express their sincere gratitude to Professor Takashi Kurose for helpful suggestions about equiaffine geometry on curved exponential families, to Professor Udo Simon for useful comments about Tchebychev geometry, and to the referee for useful advice for preparation of this paper. The first author was partially supported by the Inamori foundation, and Grant-in-Aid for Encouragement of Young Scientists No. 14720046, The Ministry of Education, Science, Sports and Culture, Japan.
PY - 2006/12
Y1 - 2006/12
N2 - 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.
AB - 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.
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U2 - 10.1016/j.difgeo.2006.02.003
DO - 10.1016/j.difgeo.2006.02.003
M3 - Article
AN - SCOPUS:33751099565
SN - 0926-2245
VL - 24
SP - 567
EP - 578
JO - Differential Geometry and its Applications
JF - Differential Geometry and its Applications
IS - 6
ER -