Information Geometry

This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo.

The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.

Table of Contents
Chapter 1: Introduction
Chapter 2: Finite Information Geometry
Chapter 3: Parametrized Measure Models
Chapter 4: The Intrinsic Geometry of Statistical Models
Chapter 5: Information Geometry and Statistics
Chapter 6: Fields of Application of Information Geometry
Appendix A: Measure Theory
Appendix B: Riemannian Geometry
Appendix C: Banach Manifolds

预览－Springer Information Geometry 3319564773.pdf