Probability for Statistics and Machine Learning: Fundamentals and Advanced Topics

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Springer Science & Business Media, May 17, 2011 - Mathematics - 784 pages

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.

 

Contents

Chapter 1 Review of Univariate Probability
1
Chapter 2 Multivariate Discrete Distributions
95
Chapter 3 Multidimensional Densities
122
Chapter 4 Advanced Distribution Theory
167
Chapter 5 Multivariate Normal and Related Distributions
198
Chapter 6 Finite Sample Theory of Order Statistics and Extremes
221
Chapter 7 Essential Asymptotics and Applications
249
Chapter 8 Characteristic Functions and Applications
293
Chapter 13 Poisson Processes and Applications
437
Chapter 14 Discrete Time Martingales and Concentration Inequalities
463
Chapter 15 Probability Metrics
505
Chapter 16 Empirical Processes and VC Theory
527
Chaapter 17 Large Deviations
559
Chapter 18 The Exponential Family and Statistical Applications
583
Chapter 19 Simulation and Markov Chain Monte Carlo
613
Chapter 20 Useful Tools for Statistics and Machine Learning
688

Chapter 9 Asymptotics of Extremes and Order Statistics
323
Chapter 10 Markov Chains and Applications
339
Chapter 11 Random Walks
375
Chapter 12 Brownian Motion and Gaussian Processes
401
Appendix A Symbols Useful Formulas and Normal Table
747
Author Index
757
Subject Index
763
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About the author (2011)

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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