Overview

This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.

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9781441996336

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Reviews

From the reviews: This book provides extensive coverage of the numerous applications that probability theory has found in statistics over the past century and more recently in machine learning. ... All chapters are completed with numerous examples and exercises. Moreover, the book compiles an extensive bibliography that is conveniently appended to each relevant chapter. It is a valuable reference for both experienced researchers and students in statistics and machine learning. Several courses could be taught using this book as a reference ... . (Philippe Rigollet, Mathematical Reviews, Issue 2012 d)

Author Information

Anirban DasGupta has been professor of statistics at Purdue University since 1994. He is the author of Springer's Asymptotic Theory of Probability and Statistics, and Fundamentals of Probability, A First Course. He is an associate editor of the Annals of Statistics and has also served on the editorial boards of JASA, Journal of Statistical Planning and Inference, International Statistical Review, Statistics Surveys, Sankhya, and Metrika. He has edited four research monographs, and has recently edited the selected works of Debabrata Basu. He was elected a Fellow of the IMS in 1993, is a former member of the IMS Council, and has authored a total of 105 monographs and research articles.

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