Besides the intuitive use of Bayesian reasoning, there
are, in fact, some applications in which the Bayes' theorem
is explicitly applied. This happens when frequentist methods
``do not work'', i.e. they give
manifestly absurd results,
or in solving more complicated problems than just
inferring the value of a quantity, like, for example, the deconvolution
of a spectrum (``unfolding''). Nevertheless, these methods are
mostly used with a utilitarian spirit, without
having really understood the meaning of subjective probability, or even
remaining skeptical about it. They are used as one uses one of
the many frequentist ``ad hoc-eries''
^{(14)} ,
after it has been ``proved''
that they work by MC
simulation ^{(15)} .

Some of the cases in which the conventional methods do not work
have even induced the PDG
[3]
to present Bayesian methods. But, according to the PDG, a paper
published this year
[18]
finally gives a frequentist solution to the problems, and this
solution is recommended for publishing the results. Let us review
the situation citing directly
[18]:
``Classical confidence intervals
are the traditional way in which high energy physicists report errors
on results of experiments. ... In recent years, there has been
considerable dissatisfaction ...for upper confidence limits...
This dissatisfaction led the PDG to describe procedures for Bayesian
interval construction in the troublesome cases: Poisson processes
with background and Gaussian errors with a bounded physical region.
... In this paper, we...use (...) to
obtain a unified set of classical confidence
intervals for setting upper limits and quoting two-sided confidence
intervals. ...We then obtain confidence intervals which are
never unphysical or empty. Thus they remove an original motivation
for the description of Bayesian intervals by the PDG.''
In fact, the 1998 issue of the *Review
of Particle Physics* still exhibits
the Bayesian approach (with the typical misconceptions
that frequentists have about it), but then it suggests two papers by
frequentists
[6,
2]
(``a balanced discussion''
[3])
to help practitioners to form their own idea on the subject, and, finally,
it warmly recommends the new frequentist approach.
It is easy to imagine what the reaction
of the average HEP physicist will be when confronted by
the authority of the PDG, unaware
that ``the PDG'' which rules analysis methods is in reality constituted of
no more than one or two persons who recommend a paper written by
their friends (as is clear from the references and the cross
acknowledgements). One should also notice
that this paper claims important progress in statistics,
but was in fact published in a physics journal (I wonder what
the reaction of a referee of a
statistics journal would have been...).

In conclusion, there is still a large gap between good sense and the dominating statistical culture. For this reason we must still be very careful in interpreting published results and in evaluating whether or not the conventional methods used lead to correct scientific conclusions ``by chance''. Some cases of misleading results will be described in the next section.

^{14} For example,
this was exactly the attitude which I had some years ago, when I wrote a
*Bayesian unfolding* program
[17],
and that of the large majority my
colleagues who still use the program. Now, after having attended
the 1998 Valencia Meeting on Bayesian Statistics, I have realized
that this pragmatic frequentist-like use of Bayesian methods
is rather common.
Back.

^{15} I would like to point out that
sometimes the conclusions derived from
MC checks of Bayesian procedures may be
misleading, as discussed in detail in
[7].
Back.