Probability for statistics and machine learning: fundamentals and advanced topics

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. Unification of probability, statistics, and machine learning toolsprovidesa complete background for teaching and future research inmultiple areasLucid and encyclopedic coverage allows the user to find andconceptually understand numerous topics by using a single source1225 worked out examples and exercises provide essential skillsin problem solving and help in self-study INDICE: 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 andApplications. Chapter 14. Discrete Time Martingales and Concentration Inequalities. Chapter 15. Probability Metrics. Chapter 16. Empirical Processes and VCTheory. 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.

• ISBN: 978-1-4614-2884-8
• Editorial: Springer New York
• Encuadernacion: Rústica
• Páginas: 800
• Fecha Publicación: 29/03/2011
• Nº Volúmenes: 1
• Idioma: Inglés