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Methods of Information Geometry (Translations of Mathematical Monographs) by Shun-ichi Amari, Hiroshi Nagaoka; [translated from the Japanese by Daishi Harada] is a nonfiction available to read on EtoBox.

What is Methods of Information Geometry (Translations of Mathematical Monographs) about?

Elementary differential geometry -- Differentiable manifolds -- Tangent vectors and tangent spaces -- Vector fields and tensor fields -- Submanifolds -- Riemannian metrics -- Affine connections and covariant derivatives -- Flatness -- Autoparallel submanifolds -- Projection of connections and embedding curvature -- Riemannian connection -- The geometric structure of statistical models -- Statistical models -- The Fisher metric -- The [alpha]-connection -- Chentsov's theorem and some historical remarks -- The geometry of P (X) -- [alpha]-affine manifolds and [alpha]-families -- Dual connections -- Duality of connections -- Divergences: general contrast functions -- Dually flat spaces -- Canonical divergence -- The dualistic structure of exponential families -- The dualistic structure of [alpha]-affine manifolds and [alpha]-families -- Mutually dual foliations -- A further look at the triangular relation -- Statistical inference and differential geometry -- Estimation based on independent observations -- Exponential families and observed points -- Curved exponential families -- Consistency and first-order efficiency -- Higher-order asymptotic theory of estimation -- Asymptotics of Fi

Who reads Methods of Information Geometry (Translations of Mathematical Monographs)?

Author

Shun-ichi Amari, Hiroshi Nagaoka; [translated from the Japanese by Daishi Harada]

Publisher

American Mathematical Society

Published

2001

Language

EN

ISBN

9780821805312

Category

nonfiction

Subjects

Mathematics, Stem