I didn’t really realize that in Feller’s classic probability book he had the following dismissal of Bayesian statistics:
Unfortunately Bayes’ rule has been somewhat discredited by metaphysical applications of the type described above. In routine practice, this kind of argument can be dangerous. A quality control engineer is concerned with one particular machine and not with an infinite population of machines from which one was chosen at random. He has been advised to use Bayes’ rule on the grounds that it is logically acceptable and corresponds to our way of thinking. Plato used this type of argument to prove the existence of Atlantis, and philosophers used it to prove the absurdity of Newton’s mechanics. In our case it overlooks the circumstance that the engineer desires success and that he will do better by estimating and minimizing the sources of various types of errors in predicting and guessing. The modern method of statistical tests and estimation is less intuitive but more realistic. It may be not only defended but also applied.” — W. Feller, 1950 (pp. 124-125 of the 1970 edition)
A few weeks ago, a little note on Feller’s anti-Bayesianism was posted to ArXiV. It’s a bit of an emotional read; a mathematical Op-Ed if you will. However, it does present an interesting perspective on historical “received wisdom” in light of more modern approaches to statistics and Bayesian data analysis. As an example, take the methods from Michael Jordan’s talk at ISIT (video and slides on the ITSOC website now!), using which you can do some cross-validation to see that they are indeed producing the correct results on real data.
What I am missing (as an outsider to the internecine battles of statistics) is an even-handed explanation of what all the hullabaloo is about. Such an article probably exists, but I haven’t seen it…