Probability for Statistics and Machine Learning Fundamentals and Adv
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,
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Anirban DasGupta
Probability for Statistics and Machine Learning Fundamentals and Advanced Topics
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Anirban DasGupta Department of Statistics Purdue University 150 N. University Street West Lafayette, IN 47907, USA [email protected]
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ISBN 978-1-4419-9633-6 e-ISBN 978-1-4419-9634-3 DOI 10.1007/978-1-4419-9634-3 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011924777 c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Persi Diaconis, Peter Hall, Ashok Maitra, and my mother, with affection
Preface
This is the companion second volume to my undergraduate text Fundamentals of Probability: A First Course. The purpose of my writing this book is to give graduate students, instructors, and researchers in statistics, mathematics, and computer science a lucidly written unique text at the confluence of probability, advanced stochastic processes, statistics, and key tools for machine learning. Numerous topics in probability and stochastic processes of current importance in statistics and machine learning that are widely scattered in the literature in many different specialized books are all brought together under one fold in this book. This is done with an extensive bibliography for each topic, and numerous worked-out examples and exercises. Probability, with all its models, techniques, and its poignant beauty, is an incredibly powerful tool for anyone who deals with data or randomness. The content and the style of this book reflect that philosophy; I emphasize lucidity, a wide background, and the far-reaching applicability of probability in science. The book starts with a self-contained and fairly complete review of basic probability, and then traverses its way through the classics, to advanced modern topics and tools, including a substantial amount of statistics itself. Because of its nearly encyclopaedic coverage, it can serve as a graduate text for a year-long probability sequence, or for focused short courses on selected topics, for self-study, and as a nearly unique reference for research in statistics, probability, and computer science.
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