In Preparation: Computer-Age Statistical Inference, a new book by Bradley Efron and Trevor Hastie
From the Authors:
We live in an era of breathtaking expansion of statistical methodology, both in scope and influence. The popular name Big Data might better be called ''Big Inference'', as enormous data sets are boiled down by exotic statistical algorithms for the extraction, hopefully, of a few insightful conclusions. Statisticians work on both sides of this story, the algorithms and the inferential methods. Our book traces the interplay between methodology and inference as it has developed since the 1950s, the beginning of the statistics discipline's computer age. Methodology has moved faster but statistical inference --- the theory of how to decide between competing methodologies --- has also expanded beyond its classical limits.
The text proceeds in three parts, with each succeeding era building on the successes of its predecessor: Part I of the book reviews classical inference, Bayesian, frequentist, and Fisherian. Part II concerns early computer-age developments, from the mid 1950s to the 1990s: empirical Bayes, generalized linear models, cross-validation and C_p, the jackknife and bootstrap, and many others.
Each chapter reviews the growth of methodology and its effects on inference. The survival analysis chapter, for example, traces the progress from life tables to Kaplan-Meier curves to the log-rank test, and finally to proportional hazards modeling, each step showing increased inferential sophistication.
Part III of this book (in progress) will discuss 21st Century topics, including false discovery rates, automatic model building (Lasso and LARS), objective Bayes inference, machine learning (random forests, boosting, support vector machines, neural nets), and inference after model selection. The ongoing succession of inferential ideas --- boosting following logistic regression, random forests following regression trees, false-discovery rates succeeding Bonferroni bounds --- will be emphasized.
This title is expected to appear in early 2016.