Information Geometry

Section I<br>Foundations of information geometry<br>1. Revisiting the connection between Fisher information and entropy’s rate of change <br>A.R. Plastino, A. Plastino, and F. Pennini<br>2. Pythagoras theorem in information geometry and applications to generalized linear models <br>Shinto Eguchi<br>3. Rao distances and conformal mapping <br>Arni S.R. Srinivasa Rao and Steven G. Krantz<br>4. Cramer-Rao inequality for testing the suitability of divergent partition functions <br>Angelo Plastino, Mario Carlos Rocca, and Diana Monteoliva<br>5. Information geometry and classical Cram<ER–RAO-TYPE <br inequalities>Kumar Vijay Mishra and M. Ashok Kumar<br>Section II<br>Theoretical applications and physics<br>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 <br>B. Roy Frieden<br>7. Quantum metrology and quantum correlations <br>Diego G. Bussandri and Pedro W. Lamberti<br>8. Information, economics, and the Cramer-Rao bound <br>Raymond J. Hawkins and B. Roy Frieden<br>9. Zipf’s law results from the scaling invariance of the Cramer–Rao inequality <br>Alberto Hernando and Angelo Plastino<br>Section III<br>Advanced statistical theory<br>10. λ-Deformed probability families with subtractive and divisive normalizations <br>Jun Zhang and Ting-Kam Leonard Wong<br>11. Some remarks on Fisher information, the Cramer–Rao inequality, and their applications to physics <br>H.G. Miller, A. Plastino, and A.R. Plastino