But Tukey publicly denied Bayesianism. When working on the NBC projects, he said he wasn’t using Bayes, instead he was “borrowing strength.” He didn’t allow anybody on his team to talk about their methods, either, saying it was proprietary information.
According to this paper, Tukey used the term “borrowing strength” to describe empirical Bayes techniques, which comprise an entirely different methodology than Bayesianism.
In what sense is empirical Bayes—using the frequencies in initial data to set the original priors—“entirely” different from “Bayesianism”, as opposed to be an interesting subset or variation?
Empirical Bayes procedures can be shown to be robust to the distribution of the data in a way that Bayesian procedures cannot. The difference between Empirical bayes and Bayesianism along this important dimension make them very distinct procedures from the perspective of many users.
This difference is most commonly seen in practice when some density must be estimated for inference. Use of kernel density estimation in empirical Bayes ensures an asymptotic convergence to the true density at some rate. In contrast, no Bayesian prior has yet been developed with consistency for density estimation.
According to this paper, Tukey used the term “borrowing strength” to describe empirical Bayes techniques, which comprise an entirely different methodology than Bayesianism.
Good-Turing estimation which was part of the Enigma project should also go under the empirical heading.
In what sense is empirical Bayes—using the frequencies in initial data to set the original priors—“entirely” different from “Bayesianism”, as opposed to be an interesting subset or variation?
Empirical Bayes procedures can be shown to be robust to the distribution of the data in a way that Bayesian procedures cannot. The difference between Empirical bayes and Bayesianism along this important dimension make them very distinct procedures from the perspective of many users.
This difference is most commonly seen in practice when some density must be estimated for inference. Use of kernel density estimation in empirical Bayes ensures an asymptotic convergence to the true density at some rate. In contrast, no Bayesian prior has yet been developed with consistency for density estimation.