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.
General
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