A 250-year Argument: Belief, Behavior, and the Bootstrap

The year 2013 marks the 250th anniversary of 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.