snarles comments on A History of Bayes' Theorem - Less Wrong

53 Post author: lukeprog 29 August 2011 07:04AM

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Comment author: snarles 03 September 2011 01:04:41AM *  3 points [-]

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.

Comment author: fool 03 September 2011 04:05:28PM 4 points [-]

Good-Turing estimation which was part of the Enigma project should also go under the empirical heading.

Comment author: gwern 13 June 2012 09:02:39PM 1 point [-]

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?

Comment author: snarles 02 July 2012 07:20:35PM *  0 points [-]

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.