Information geometry and its applications / Shun-ichi Amari.

Includes bibliographical references and index.

1 Manifold, Divergence and Dually Flat Structure.-
2 Exponential Families and Mixture Families of Probability Distributions.-
3 Invariant Geometry of Manifold of Probability Distributions.-
4 Alpha-Geometry, Tsallis q-Entropy and Positive-Definite Matrices.-
5 Elements of Differential Geometry.-
6 Dual Affine Connections and Dually Flat Manifold.-
7 Asymptotic Theory of Statistical Inference.-
8 Estimation in the Presence of Hidden Variables.-
9 Neyman-Scott Problem.-
10 Linear Systems and Time Series.-
11 Machine Learning.-
12 Natural Gradient Learning and its Dynamics in Singular regions.-
13 Signal Processing and Optimization.

This is the first comprehensive book on information geometry, written by the founder of the field. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry.