Methods of Information Geometry (Softcover)

Condition

VERY GOOD: This book is in excellent condition. It shows only slight signs of use and wear and was printed on acid-free paper.

Product Details

This book is Volume 191 in theTranslations of Mathematical Monographs from the American Mathematical Society and Oxford University Press. This monograph was translated from the Japanese by Daishi Harada.

Also from the back cover: "Information geometry proves the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the α-connections. The duality between the α-connection and the (-α)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective."

Chapters

1. Elementary differential geometry
2. The geometric structure of statistical models
3. Dual connections
4. Statistical inference and differential geometry
5. The geometry of time series and linear systems
6. Multiterminal information theory and statistical inference
7. Information geometry for quantum systems
8. Miscellaneous topics

The book concludes with Guide to the Bibliography, Bibliography, and Index.