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Computer Age Statistical Inference


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Table of Contents

Part I. Classic Statistical Inference: 1. Algorithms and inference; 2. Frequentist inference; 3. Bayesian inference; 4. Fisherian inference and maximum likelihood estimation; 5. Parametric models and exponential families; Part II. Early Computer-Age Methods: 6. Empirical Bayes; 7. James-Stein estimation and ridge regression; 8. Generalized linear models and regression trees; 9. Survival analysis and the EM algorithm; 10. The jackknife and the bootstrap; 11. Bootstrap confidence intervals; 12. Cross-validation and Cp estimates of prediction error; 13. Objective Bayes inference and Markov chain Monte Carlo; 14. Statistical inference and methodology in the postwar era; Part III. Twenty-First Century Topics: 15. Large-scale hypothesis testing and false discovery rates; 16. Sparse modeling and the lasso; 17. Random forests and boosting; 18. Neural networks and deep learning; 19. Support-vector machines and kernel methods; 20. Inference after model selection; 21. Empirical Bayes estimation strategies; Epilogue; References; Index.

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Take an exhilarating journey through the modern revolution in statistics with two of the ringleaders.

About the Author

Bradley Efron is Max H. Stein Professor, Professor of Statistics, and Professor of Biomedical Data Science at Stanford University, California. He has held visiting faculty appointments at Harvard University, Massachusetts, the University of California, Berkeley, and Imperial College of Science, Technology and Medicine, London. Efron has worked extensively on theories of statistical inference, and is the inventor of the bootstrap sampling technique. He received the National Medal of Science in 2005 and the Guy Medal in Gold of the Royal Statistical Society in 2014. Trevor Hastie is John A. Overdeck Professor, Professor of Statistics, and Professor of Biomedical Data Science at Stanford University, California. He is coauthor of Elements of Statistical Learning, a key text in the field of modern data analysis. He is also known for his work on generalized additive models and principal curves, and for his contributions to the R computing environment. Hastie was awarded the Emmanuel and Carol Parzen prize for Statistical Innovation in 2014.


'How and why is computational statistics taking over the world? In this serious work of synthesis that is also fun to read, Efron and Hastie, two pioneers in the integration of parametric and nonparametric statistical ideas, give their take on the unreasonable effectiveness of statistics and machine learning in the context of a series of clear, historically informed examples.' Andrew Gelman, Columbia University, New York
'This unusual book describes the nature of statistics by displaying multiple examples of the way the field has evolved over the past sixty years, as it has adapted to the rapid increase in available computing power. The authors' perspective is summarized nicely when they say, 'very roughly speaking, algorithms are what statisticians do, while inference says why they do them'. The book explains this 'why'; that is, it explains the purpose and progress of statistical research through a close look at many major methods, methods the authors themselves have advanced and studied at great length. Both enjoyable and enlightening, Computer Age Statistical Inference is written especially for those who want to hear the big ideas, and see them instantiated through the essential mathematics that defines statistical analysis. It makes a great supplement to the traditional curricula for beginning graduate students.' Rob Kass, Carnegie Mellon University, Pennsylvania
'This is a terrific book. It gives a clear, accessible, and entertaining account of the interplay between theory and methodological development that has driven statistics in the computer age. The authors succeed brilliantly in locating contemporary algorithmic methodologies for analysis of 'big data' within the framework of established statistical theory.' Alastair Young, Imperial College London
'This is a guided tour of modern statistics that emphasizes the conceptual and computational advances of the last century. Authored by two masters of the field, it offers just the right mix of mathematical analysis and insightful commentary.' Hal Varian, Google
'Efron and Hastie guide us through the maze of breakthrough statistical methodologies following the computing evolution: why they were developed, their properties, and how they are used. Highlighting their origins, the book helps us understand each method's roles in inference and/or prediction. The inference-prediction distinction maintained throughout the book is a welcome and important novelty in the landscape of statistics books.' Galit Shmueli, National Tsing Hua University
'A masterful guide to how the inferential bases of classical statistics can provide a principled disciplinary frame for the data science of the twenty-first century.' Stephen Stigler, University of Chicago, and author of Seven Pillars of Statistical Wisdom
'Computer Age Statistical Inference offers a refreshing view of modern statistics. Algorithmics are put on equal footing with intuition, properties, and the abstract arguments behind them. The methods covered are indispensable to practicing statistical analysts in today's big data and big computing landscape.' Robert Gramacy, University of Chicago Booth School of Business
'Every aspiring data scientist should carefully study this book, use it as a reference, and carry it with them everywhere. The presentation through the two-and-a-half-century history of statistical inference provides insight into the development of the discipline, putting data science in its historical place.' Mark Girolami, Imperial College London
'Efron and Hastie are two immensely talented and accomplished scholars who have managed to brilliantly weave the fiber of 250 years of statistical inference into the more recent historical mechanization of computing. This book provides the reader with a mid-level overview of the last 60-some years by detailing the nuances of a statistical community that, historically, has been self-segregated into camps of Bayes, frequentist, and Fisher yet in more recent years has been unified by advances in computing. What is left to be explored is the emergence of, and role that, big data theory will have in bridging the gap between data science and statistical methodology. Whatever the outcome, the authors provide a vision of high-speed computing having tremendous potential to enable the contributions of statistical inference toward methodologies that address both global and societal issues.' Rebecca Doerge, Carnegie Mellon University, Pennsylvania
'In this book, two masters of modern statistics give an insightful tour of the intertwined worlds of statistics and computation. Through a series of important topics, Efron and Hastie illuminate how modern methods for predicting and understanding data are rooted in both statistical and computational thinking. They show how the rise of computational power has transformed traditional methods and questions, and how it has pointed us to new ways of thinking about statistics.' David Blei, Columbia University, New York
'Absolutely brilliant. This beautifully written compendium reviews many big statistical ideas, including the authors' own. A must for anyone engaged creatively in statistics and the data sciences, for repeated use. Efron and Hastie demonstrate the ever-growing power of statistical reasoning, past, present, and future.' Carl Morris, Harvard University, Massachusetts
'Computer Age Statistical Inference gives a lucid guide to modern statistical inference for estimation, hypothesis testing, and prediction. The book seamlessly integrates statistical thinking with computational thinking, while covering a broad range of powerful algorithms for learning from data. It is extraordinarily rare and valuable to have such a unified treatment of classical (and classic) statistical ideas and recent 'big data' and machine learning ideas. Accessible real-world examples and insightful remarks can be found throughout the book.' Joseph K. Blitzstein, Harvard University, Massachusetts
'Among other things, it is an attempt to characterize the current state of statistics by identifying important tools in the context of their historical development. It also offers an enlightening series of illustrations of the interplay between computation and inference ... This is an attractive book that invites browsing by anyone interested in statistics and its future directions.' Bill Satzer, Mathematical Association of America Reviews
'My take on Computer Age Statistical Inference is that experienced statisticians will find it helpful to have such a compact summary of twentieth-century statistics, even if they occasionally disagree with the book's emphasis; students beginning the study of statistics will value the book as a guide to statistical inference that may offset the dangerously mind-numbing experience offered by most introductory statistics textbooks; and the rest of us non-experts interested in the details will enjoy hundreds of hours of pleasurable reading.' Joseph Rickert, RStudio (www.rstudio.com)
'Efron and Hastie (both, Stanford Univ.) have superbly crafted a central text/reference book that presents a broad overview of modern statistics. The work examines major developments in computation from the late-20th and early-21st centuries, ranging from electronic computations to 'big data' analysis. Focusing primarily on the last six decades, the text thoroughly documents the progression within the discipline of statistics ... This text is highly recommended for graduate libraries.' D. J. Gougeon, Choice

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