Information Geometry

Information Geometry explained in detail by experts

Arni S.R. Srinivasa Rao (Volume editor), C.R. Rao (Volume editor), Angelo Plastino (Volume editor)

9780323855679, Elsevier Science

Hardback, published 28 September 2021

248 pages
22.9 x 15.2 x 2.1 cm, 0.6 kg

"From the cover of the book: “Introduction to probability and statistics for engineers and scientists, now in its trusted Sixth Edition, provides a valuable overview of the subject written in the engaging style of Best-Selling Probability expert and author, Sheldon Ross. The book uniquely emphasizes how probability informs statistical problems to develop an intuitive understanding of the statistical procedures most commonly used by practicing engineers and scientists. Utilizing real data from actual studies across life science, engineering, computing and business, this useful introduction supports reader comprehension through a wide variety of exercises and examples throughout the text. These examples and exercises are combined with updated problem sets and applications to connect probability theory to everyday statistical problems and situations....The book can be very recommended to all readers, students and instructors, who are interested in this field." --zbMath/European Mathematical Society and the Heidelberg Academy of Sciences and Humanities

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.

Section I Foundations 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 CramKumar 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

Subject Areas: Stochastics [PBWL]