The subject of information geometry blends several areas of statistics, computer science, physics, and mathematics. The subject evolved from the groundbreaking article published by legendary statistician C.R. Rao in 1945. His works led to the creation of Cramer-Rao bounds, Rao distance, and Rao-Blackawellization. Fisher-Rao metrics and Rao distances play a very important role in geodesics, econometric analysis to modern-day business analytics. The chapters of the book are written by experts in the field who have been promoting the field of information geometry and its applications.
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Table of Contents
Section IFoundations of information geometry
1. Revisiting the connection between Fisher information and entropy's rate of change
A.R. Plastino, A. Plastino, and F. Pennini
2. Pythagoras theorem in information geometry and applications to generalized linear models
Shinto Eguchi
3. Rao distances and conformal mapping
Arni S.R. Srinivasa Rao and Steven G. Krantz
4. Cramer-Rao inequality for testing the suitability of divergent partition functions
Angelo Plastino, Mario Carlos Rocca, and Diana Monteoliva
5. Information geometry and classical Cram
Kumar Vijay Mishra and M. Ashok Kumar
Section II
Theoretical applications and physics
6. Principle of minimum loss of Fisher information, arising from the Cramer-Rao inequality: Its role in evolution of bio-physical laws, complex systems and universes
B. Roy Frieden
7. Quantum metrology and quantum correlations
Diego G. Bussandri and Pedro W. Lamberti
8. Information, economics, and the Cramer-Rao bound
Raymond J. Hawkins and B. Roy Frieden
9. Zipf's law results from the scaling invariance of the Cramer-Rao inequality
Alberto Hernando and Angelo Plastino
Section III
Advanced statistical theory
10. ?-Deformed probability families with subtractive and divisive normalizations
Jun Zhang and Ting-Kam Leonard Wong
11. Some remarks on Fisher information, the Cramer-Rao inequality, and their applications to physics
H.G. Miller, A. Plastino, and A.R. Plastino
