Differential-Geometrical Methods in Statistics

Volume 28 of the series Lecture Notes in Statistics pp 11-65

Differential Geometry of Statistical Models

  • Shun-ichi AmariAffiliated withFaculty of Engineering Department of Mathematical Engineering and Information Physics, University of Tokyo

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The present chapter is devoted to the introduction of fundamental differential-geometrical structures of statistical models. The tangent space, the Riemannian metric and the α-connections are introduced in a statistical manifold. No differential-geometrical background is required for reading this monograph, because the present chapter provides a readable introduction to differential geometry.