Methods of Information Geometry

The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability distributions, and the general theory of dual affine connections. The second half of the text provides an overview of wide areas of applications, such as statistics, linear systems, information theory, quantum mechanics, convex analysis, neural networks, and affine differential geometry. The book will serve as a suitable text for a topics course for advanced undergraduates and graduate students.

This volume is copublished by the AMS and Oxford University Press. The AMS has exclusive distribution rights in North America. AMS members in Europe may purchase the book from the AMS. Both the AMS and OUP have worldwide distribution rights.

Contents

• Elementary differential geometry
• The geometric structure of statistical models
• Dual connections
• Statistical inference and differential geometry
• The geometry of time series and linear systems
• Multiterminal information theory and statistical inference
• Information geometry for quantum systems
• Miscellaneous topics
• Guide to the bibliography
• Bibliography
• Index