So, it is true that ``Fisherian and Neyman-Pearson-Wald ideas have shouldered Bayesian theory aside in statistical practice'', but ``The answer is simply that statisticians do not know what the statistical paradigm says. Why should they? There are very few universities in the world with statistics departments that provides a good course on the subject.'' Essentially, the main point of the Efron paper is to maintain traditional methods, despite the ``disturbing catalog of inconsistencies'', and the ``powerful theoretical reasons for preferring Bayesian inference''. Moreover, perhaps not everybody who cites the Efron paper is aware of further discussions about it, like the letter in which Zellner points out that one of the problems posed by Efron already had a Bayesian solution (in the Jeffreys' book), that Efron admitted to knowing and even to having used . As a kind of final comment on this debated paper, I would like to cite Efron's last published reply I am aware of :
``First of all let me thank the writers for taking my article in its intended spirit: not as an attack on the Bayesian enterprise, but rather as a critique of its preoccupation with philosophical questions, to the detriment of statistical practice. Meanwhile I have received some papers, in particular one from A.F.M. Smith, which show a healthy Bayesian interest in applications, so my worries were overstated if not completely groundless.''
There are some other references which I would like to suggest if you are interested in forming your own opinion on the subject. They have also appeared in The American Statistician, where in 1997 an entire Teaching Corner section of the journal was devoted to three papers presented in a round table on `Bayesian possibilities for introductory statistics' at the 156th Annual Meeting of the American Statistical Association, held in Chicago, in August 1996. For me these articles are particularly important because I was by chance in the audience of the round table (really `by chance'!). At the end of the presentations I was finally convinced that frequentism was dead, at least as a philosophical idea. I must say, I was persuaded by the non-arguments of the defender of frequentism even more than by the arguments of the defenders of the Bayesian approach. I report here the abstract8.18of Moore, who presented the `reason to hesitate' to teach Bayesian statistics:
``The thesis of this paper is that Bayesian inference, important though it is for statisticians, is among the mainly important statistical topics that it is wise to avoid in most introductory instruction. The first reason is pragmatic (and empirical): Bayesian methods are as yet relatively little used in practice. We have an obligation to prepare students to understand the statistics they will meet in their further studies and work, not the statistics we may hope will someday replace now-standard methods. A second argument also reflects current conditions: Bayesians do not agree on standard approaches to standard problem settings. Finally, the reasoning of Bayesian inference, depending as it does on ideas of conditional probability, is quite difficult for beginners to appreciate. There is of course no easy path to a conceptual grasp of inference, but standard inference at least rests on repetition of one straightforward question, What would happen if I did this many times? ''Even if some arguments might be valid, thinking about statisticians who make surveys in a standardized form (in fields that they rarely understand, such as medicine and agriculture), surely they do not hold in physics, even less in frontier physics. As I commented to Moore after his talk, what is important for a physicist is not ``what would happen if I did this many times?'', but ``what am I learning by the experiment?''.8.19