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Computer age statistical inference : algorithms, evidence, and data science
Efron B., Hastie T., Cambridge University Press, New York, NY, 2016. 476 pp. Type: Book (978-1-107149-89-2)
Date Reviewed: Jan 18 2017

No healthy scientific discipline stands still, and active practitioners recognize the flux of ideas and frequently contribute to it. But the exigencies of pedagogy make it difficult for a student to understand the trajectory of a field. Textbooks tend to concentrate on presenting the array of tools and theorems that represent the current state of the discipline, while historical treatises are often pitched toward readers with limited technical sophistication and maintain a high level of generality. In this volume, two recognized leaders of modern statistics provide a technically rigorous overview of how the field got to where it is now, and what opportunities lie ahead.

The discussion situates statistical ideas in three dimensions: theoretical orientation, purpose, and mechanism.

The theoretical dimension involves the contrast between the frequentist, Bayesian, and Fisherian views of statistics. After presenting an exceptionally clear analysis of the characteristics of the three approaches, the authors show how modern techniques draw their power sometimes from one, sometimes from another of these viewpoints. Some books are openly biased toward one or another orientation. This volume is much more ecumenical. Figure 14.1, a revision of a figure from Efron’s 1996 Fisher lecture, situates 15 major ideas that characterize the period between 1950 and 1990, in the space spanned by these three approaches, showing how the modern statistician inevitably draws on all three traditions.

The dimension of purpose distinguishes algorithms developed for specific purposes from inferential arguments that justify those arguments and establish certainty bounds. While the book documents both algorithms and inference, the focus is more on inference, as the title suggests.

The dimension of mechanism describes the degree to which various techniques depend on the availability of digital computation. This dependency naturally increases as one moves through time, and forms the major organizational axis of the book.

The first five chapters deal with classic statistical inference, as developed in the centuries before computers. They present and compare the frequentist, Bayesian, and Fisherian approaches and describe the low-dimensional parametric models whose mathematical tractability made them essential to the progress of all three approaches without access to computation.

Chapters 6 through 14 review 15 early computer-based methods, starting in the 1950s and extending through the 1990s. They begin with a discussion of empirical Bayes, whose ability to replace a subjective prior with information drawn from a large collection of similar cases exemplifies two ways that computation contributes to inference. The computer not only performs computations too numerous to envision doing by hand, but also facilitates the collection of the massive data on which these mechanisms depend. Other methods include James-Stein estimation, ridge regression, generalized linear models, regression trees, survival analysis and expectation maximization, the jackknife, the bootstrap, cross-validation, objective Bayes, Gibbs sampling, and MCMD, culminating in the summary of chapter 14.

The last seven chapters explore more recent ideas that exploit not only advances in computational power, but also the increasing availability of big data and wide data (with more variables than instances). The topics here include false discovery rates in large-scale hypothesis testing, the lasso for dealing with sparse data, random forests, boosting, neural networks and recent advances in deep learning, support vector machines, and dealing with the interference of the model selection process with inference. The section ends with a return to empirical Bayes, discussing more recent techniques for exploiting indirect evidence.

This volume is not a textbook to introduce new concepts to students, but rather a framework to organize concepts with which readers are presumed to be acquainted already. There are no exercises, but extensive notes in each chapter outline the proofs of key theorems and point the reader to other literature, documented in an extensive bibliography whose entries come down to 2016. The volume is beautifully produced, with attractive use of color in the many illustrative plots, and it points the reader to packages in the R statistical analysis system that implement many of the techniques discussed. It would form an excellent supplement to courses in advanced statistics, and will be an invaluable handbook for the practicing data analyst.

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Reviewer:  H. Van Dyke Parunak Review #: CR145005 (1704-0221)
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