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.

Review

From the reviews:

“It is a companion second volume to the author’s undergraduate text Fundamentals of Probability: A First course … . The author seeks to provide readers with a comprehensive coverage of probability for students, instructors, and researchers in areas such as statistics and machine learning. … It has extensive references to other sources, a large number of examples, and … this is sufficient for an instructor to rotate them between semesters.” (David J. Hand, International Statistical Review, Vol. 81 (1), 2013)
 

“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)
 

“The author provides a comprehensive overview of probability theory with a focus on applications in statistics and machine learning. The material in the book ranges from classical results to modern topics … . the book is a very good choice as a first reading. … contains a large number of exercises that support the reader in getting a deeper understanding of the topics. This collection makes the volume even more valuable as a text book for students or for a course on basic probability theory.” (H. M. Mai, Zentralblatt MATH, Vol. 1233, 2012)