Probability Models

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· Handbook of Statistics 第 51 冊 · Elsevier
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Probability Models, Volume 51 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on Stein's methods, Probabilities and thermodynamics third law, Random Matrix Theory, General tools for understanding fluctuations of random variables, An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions, Probability Models Applied to Reliability and Availability Engineering, Backward stochastic differential equation– Stochastic optimization theory and viscous solution of HJB equation, and much more.Additional chapters cover Probability Models in Machine Learning, The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials, Random matrix theory: local laws and applications, KOO methods and their high-dimensional consistencies in some multivariate models, Fourteen Lectures on Inference for Stochastic Processes, and A multivariate cumulative damage model and some applications. - Provides the latest information on probability models - Offers outstanding and original reviews on a range of probability models research topics - Serves as an indispensable reference for researchers and students alike

關於作者

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.

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