Information Geometry

Information Geometry

1st Edition - September 20, 2021

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  • Editors: Arni S.R. Srinivasa Rao, C.R. Rao, Angelo Plastino
  • Hardcover ISBN: 9780323855679
  • eBook ISBN: 9780323855686

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Description

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.

Key Features

  • Written by experts for users of information geometry
  • Basics to advanced readers are equally taken care
  • Origins and Clarity on Foundations

Readership

Statisticians, computer scientists, physicists, econometricians and mathematicians

Table of Contents

  • 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. λ-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

Product details

  • No. of pages: 248
  • Language: English
  • Copyright: © North Holland 2021
  • Published: September 20, 2021
  • Imprint: North Holland
  • Hardcover ISBN: 9780323855679
  • eBook ISBN: 9780323855686

About the Series Volume Editors

Arni S.R. Srinivasa Rao

Arni S.R. Srinivasa Rao
Arni S.R. Srinivasa Rao works in pure mathematics, applied mathematics, probability, and artificial intelligence and applications in medicine. He is a Professor at the Medical College of Georgia, Augusta University, U.S.A, and the Director of the Laboratory for Theory and Mathematical Modeling housed within the Division of Infectious Diseases, Medical College of Georgia, Augusta, U.S.A. Previously, Dr. Rao conducted research and/or taught at Mathematical Institute, University of Oxford (2003, 2005-07), Indian Statistical Institute (1998-2002, 2006-2012), Indian Institute of Science (2002-04), University of Guelph (2004-06). Until 2012, Dr. Rao held a permanent faculty position at the Indian Statistical Institute. He has won the Heiwa-Nakajima Award (Japan) and Fast Track Young Scientists Fellowship in Mathematical Sciences (DST, New Delhi). Dr. Rao also proved a major theorem in stationary population models, such as, Rao's Partition Theorem in Populations, Rao-Carey Theorem in stationary populations, and developed mathematical modeling-based policies for the spread of diseases like HIV, H5N1, COVID-19, etc. He developed a new set of network models for understanding avian pathogen biology on grid graphs (these were called chicken walk models), AI Models for COVID-19 and received wide coverage in the science media. Recently, he developed concepts such as “Exact Deep Learning Machines”, and “Multilevel Contours” within a bundle of Complex Number Planes.

Affiliations and Expertise

Professor, Medical College of Georgia, USA

C.R. Rao

C.R. Rao
Professor C. R. Rao, born in India, is one of this century's foremost statisticians, and received his education in statistics at the Indian Statistical Institute (ISI), Calcutta. He is Emeritus Holder of the Eberly Family Chair in Statistics at Penn State and Director of the Center for Multivariate Analysis. He has long been recognized as one of the world's top statisticians, and has been awarded 34 honorary doctorates from universities in 19 countries spanning 6 continents. His research has influenced not only statistics, but also the physical, social and natural sciences and engineering.

In 2011 he was recipient of the Royal Statistical Society's Guy Medal in Gold which is awarded triennially to those "who are judged to have merited a signal mark of distinction by reason of their innovative contributions to the theory or application of statistics". It can be awarded both to fellows (members) of the Society and to non-fellows. Since its inception 120 years ago the Gold Medal has been awarded to 34 distinguished statisticians. The first medal was awarded to Charles Booth in 1892. Only two statisticians, H. Cramer (Norwegian) and J. Neyman (Polish), outside Great Britain were awarded the Gold medal and C. R. Rao is the first non-European and non-American to receive the award.

Other awards he has received are the Gold Medal of Calcutta University, Wilks Medal of the American Statistical Association, Wilks Army Medal, Guy Medal in Silver of the Royal Statistical Society (UK), Megnadh Saha Medal and Srinivasa Ramanujan Medal of the Indian National Science Academy, J.C.Bose Gold Medal of Bose Institute and Mahalanobis Centenary Gold Medal of the Indian Science Congress, the Bhatnagar award of the Council of Scientific and Industrial Research, India and the Government of India honored him with the second highest civilian award, Padma Vibhushan, for “outstanding contributions to Science and Engineering / Statistics”, and also instituted a cash award in honor of C R Rao, “to be given once in two years to a young statistician for work done during the preceding 3 years in any field of statistics”.

For his outstanding achievements Rao has been honored with the establishment of an institute named after him, C.R.Rao Advanced Institute for Mathematics, Statistics and Computer Science, in the campus of the University of Hyderabad, India.

Affiliations and Expertise

The Pennsylvania State University, University Park, PA, USA

Angelo Plastino

Angelo Plastino, PhD is Emeritus Professor of Physics, La Plata National University, Honorary Professor, University of Buenos Aires, Doctor Honoris Causa, University of Pretoria, Member of the Brazilian Academy of Sciences, Member of the Mexican Academy of Sciences, received the Scopus Elsevier Award to the most cited Argentine physicist in the period 1998-2008 and is the author of 680 refereed papers published in scientific journals (up to December 2020).

Affiliations and Expertise

National University La Plata, La Plata, Argentina

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