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Large-scale inference. Empirical Bayes methods for estimation, testing, and prediction. (English) Zbl 1277.62016
Institute of Mathematical Statistics Monographs 1. Cambridge: Cambridge University Press (ISBN 978-0-521-19249-1/hbk). xii, 263 p. (2010).
Publisher’s description: We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods.
Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing, and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.

MSC:
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62C12 Empirical decision procedures; empirical Bayes procedures
62J15 Paired and multiple comparisons; multiple testing
62F12 Asymptotic properties of parametric estimators
62F05 Asymptotic properties of parametric tests
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