INFORMATION GEOMETRY
9,685.00₹ 11,099.00₹
- Author: NIHAT AY
- ISBN: 9783319564777
- Availability: In Stock
Buy INFORMATION GEOMETRY | Technical Books, New Arrivals
ABOUT THE BOOK
The book provides a comprehensive introduction and a
novel mathematical foundation of the field of information geometry with
complete proofs and detailed background material on measure theory, Riemannian
geometry and Banach space theory. Parametrised measure models are defined
as fundamental geometric objects, which can be both finite or infinite
dimensional. Based on these models, canonical tensor fields are introduced and
further studied, including the Fisher metric and the Amari-Chentsov tensor, and
embeddings of statistical manifolds are investigated.
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
Back Matter