Probability Models

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.

Dr. Zhidong Bai is currently a full professor at the Northeast Normal University, in China. He obtained his Ph. D. degree in Statistics and Probability from the Department of Mathematics, The University of Science and Technology of China, in 1982. After he obtained his Ph. D. degree, he was subsequently employed as a Lecturer and associate professor at The University of Science and Technology of China, as a research associate at the Center for Multivariate Analysis University of Pittsburgh, as a senior research associate at the Center for Multivariate Analysis, the Penn State University, as an Associate Professor at the Department of Statistics, the Temple University, as a full professor at the Department of Applied Mathematics, the National Sun Yat-sen University, Taiwan, China, as a full professor at the Department of Statistics and Applied Probability, the National University of Singapore, Finally, he moved to the School of Mathematics and Statistics, the Northeast Normal University, China as a full Professor, in October, 2002. During his career, he concentrated on limiting theorems in statistics and probability. His research interests include General Information Criterion, Signal Processing, Image Processing, Robust Estimation, Density, and nonparametric regression estimation, Polya Urn model and applications to adaptive clinical Designs and random matrix theory, After Year 2000, he concentrated his research interest the Spectral Analysis of Large Dimensional Random Matrix and its applications to High Dimensional Statistics. He published nearly 300 research papers and 6 monographs. His research contribution is highly recognized internationally, He was elected as a Fellow of the Third World Academy of Science in 1989 and a Fellow of the Institute of Mathematical Statistics in 1995.

On the basis of work done at CU during the two year period, 1946-1948, C.R. Rao earned a Ph.D. degree and a few years later Sc.D. degree of CU and the rare honor of life fellowship of Kings College, Cambridge. He retired from ISI in 1980 at the mandatory age of 60 after working for 40 years during which period he developed ISI as an international center for statistical education and research. He also took an active part in establishing state statistical bureaus to collect local statistics and transmitting them to Central Statistical Organization in New Delhi. Rao played a pivitol role in launching undergraduate and postgraduate courses at ISI. He is the author of 475 research publications and several breakthrough papers contributing to statistical theory and methodology for applications to problems in all areas of human endeavor. There are a number of classical statistical terms named after him, the most popular of which are Cramer-Rao inequality, Rao-Blackwellization, Rao’s Orthogonal arrays used in quality control, Rao’s score test, Rao’s Quadratic Entropy used in ecological work, Rao’s metric and distance which are incorporated in most statistical books. He is the author of 10 books, of which two important books are, Linear Statistical Inference which is translated into German, Russian, Czec, Polish and Japanese languages,and Statistics and Truth which is translated into, French, German, Japanese, Mainland Chinese, Taiwan Chinese, Turkish and Korean languages. He directed the research work of 50 students for the Ph.D. degrees who in turn produced 500 Ph.D.’s. Rao received 38 hon. Doctorate degree from universities in 19 countries spanning 6 continents. He received the highest awards in statistics in USA,UK and India: National Medal of Science awarded by the president of USA, Indian National Medal of Science awarded by the Prime Minister of India and the Guy Medal in Gold awarded by the Royal Statistical Society, UK. Rao was a recipient of the first batch of Bhatnagar awards in 1959 for mathematical sciences and and numerous medals in India and abroad from Science Academies. He is a Fellow of Royal Society (FRS),UK, and member of National Academy of Sciences, USA, Lithuania and Europe. In his honor a research Institute named as CRRAO ADVANCED INSTITUTE OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE was established in the campus of Hyderabad University.

Preface
Arni S.R. Srinivasa Rao, Zhidong Bai and C.R. Rao

1. Stein’s methods
Qi-Man Shao and Zhuosong Zhang

2. Probabilities and thermodynamics third law
Angelo Plastino

3. Random Matrix Theory
Jeff Yao

4. General tools for understanding fluctuations of random variables
Sourav Chatterjee

5. An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions
Frank Nielsen

6. Chapter title to be confirmed
Qihua Wang

7. Probability Models Applied to Reliability and Availability Engineering
Kishor Trivedi, Kishor Trivedi and Liudong Xing

8. Backward stochastic differential equation– Stochastic optimization theory and viscous solution of HJB equation
Shige Peng

9. Probability Models in Machine Learning
Qi Meng

10. Chapter title to be confirmed
Grzegorz A. Rempala

11. The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials
Lixin Zhang

12. Random matrix theory: local laws and applications
Fan Yang, Yukun He and Zhigang Bao

13. KOO methods and their high-dimensional consistencies in some multivariate models
Y. Fujikoshi

14. Fourteen Lectures on Inference for Stochastic Processes
B.L.S. PRAKASA RAO

15. A multivariate cumulative damage model and some applications
Raul Fierro