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A 250-year argument: belief, behavior, and the bootstrap. (English) Zbl 1267.62007

Summary: The year 2013 marks the 250th anniversary of the Bayes rule, one of the two fundamental inferential principles of mathematical statistics. The rule has been influential over the entire period – and controversial over most of it. Its reliance on prior beliefs has been challenged by frequentism, which focuses instead on the behavior of specific estimates and tests under repeated use. Twentieth-century statistics was overwhelmingly behavioristic, especially in applications, but the twenty-first century has seen a resurgence of Bayesianism. Some simple examples are used to show what’s at stake in the argument. The bootstrap, a computer-intensive inference machine, helps connect Bayesian and frequentist practice, leading finally to an empirical Bayes example of collaboration between the two philosophies.

MSC:

62-03 History of statistics
01A50 History of mathematics in the 18th century
01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
01A65 Development of contemporary mathematics
62F40 Bootstrap, jackknife and other resampling methods
62G09 Nonparametric statistical resampling methods
62C12 Empirical decision procedures; empirical Bayes procedures
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