Probability for Statistics and Machine Learning: Fundamentals and Advanced Topics / Edition 1

by Anirban DasGupta

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.

Product Details

ISBN-13:	9781441996336
Publisher:	Springer New York
Publication date:	05/27/2011
Series:	Springer Texts in Statistics
Edition description:	2011
Pages:	784
Product dimensions:	6.54(w) x 9.30(h) x 1.90(d)

About the Author

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.

Table of Contents

Chapter 1. Review of Univariate Probability.- Chapter 2. Multivariate Discrete Distributions.- Chapter 3. Multidimensional Densities.- Chapter 4. Advance Distribution Theory.- Chapter 5. Multivariate Normal and Related Distributions.- Chapter 6. Finite Sample Theory of Order Statistics and Extremes.- Chapter 7. Essential Asymptotics and Applications.- Chapter 8. Characteristic Functions and Applications.- Chapter 9. Asymptotics of Extremes and Order Statistics.- Chapter 10. Markov Chains and Applications.- Chapter 11. Random Walks.- Chapter 12. Brownian Motion and Gaussian Processes.- Chapter 13. Posson Processes and Applications.- Chapter 14. Discrete Time Martingales and Concentration Inequalities.- Chapter 15. Probability Metrics.- Chapter 16. Empirical Processes and VC Theory.- Chapter 17. Large Deviations.- Chapter 18. The Exponential Family and Statistical Applications.- Chapter 19. Simulation and Markov Chain Monte Carlo.- Chapter 20. Useful Tools for Statistics and Machine Learning.- Appendix A. Symbols, Useful Formulas, and Normal Table.

Editorial Reviews

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)

From the Publisher