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Although it is clear that the dominant statistical culture is still frequentism in HEP (and everywhere else), I am myself rather optimist on the possibility that the situation will change, at least in HEP, and that Bayesian reasoning will emerge from an intuitive to a conscious level. This is not a dream (although clearly several academic generations are still needed) if the theory is presented in a way that it is acceptable to an ``experienced physicist''.

Finally, I would like to give a last recommendation. Don't try to convince a physicist that he already is Bayesian, or that you want to convert him to become Bayesian. A physicist feels offended if you call him ``X-ian'', be it Newtonian, Fermian, or Einsteinian. But, being human, he has a natural feel for probability, just like everybody else. I would like to generalize this idea and propose reducing the use of the adjective ``Bayesian''. I think that the important thing is to have a theory of uncertainty in which ``probability'' has the same meaning for everybody, precisely that meaning which the human mind has naturally developed and that frequentists have tried to kill. Therefore I would rather call these methods probabilistic methods. And I conclude saying that, obviously, ``I am not a Bayesian''.


It is a pleasure to thank the organizers of Maxent98 for the warm hospitality in Garching, which favoured friendly and fruitful discussions among the participants.

23 For example frequentists completely misunderstand this points, when they state, e.g., that ``Bayesian methods proceed by invoking an interpretation of Bayes' theorem, in which one deems it sensible to consider a p.d.f. for the unknown true value mt'', or that ``a pragmatist can consider the utility of equations generated by the two approaches while skirting the issue of buying a whole philosophy of science' [6].

I find that also the Zellner's paper [26] demonstrating that Bayes' theorem makes the best use of the available information can help a lot to convince people. Back.

24 Although it may seem absurd, the Bayesian approach is recognized by ``frequentists'' to be ``well adapted to decision-making situations'' [3] (see also [6, 18]). I wonder what then probability is for these authors. Back.

25 Dogmatism is never desirable. It can be easily turned against the theory. For example, one criticism of [18] says, more or less, that Bayesian theory supports Jeffreys' priors, and not uniform priors, but, since Jeffreys' priors give unreasonable results in their application, then one should mistrust Bayesian methods! (see also [28].) One may object that the meaning and the role of Jeffreys' priors was misunderstood, but it seems to me difficult to control the use of objective priors or of reference analysis once they have left the community of experts aware of the ``rather special nature and role of the concept of a `minimally informative' prior specification - appropriately defined!'' [29]. Back.

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