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''.
- First, it is not difficult to get a consensus
on the observation that
subjective probability is the natural concept developed by
the human mind to quantify the plausibility of events in
conditions of uncertainty.
- Second, one should insist on the fact
that Bayes' theorem is in fact
a natural way of reasoning in updating probability,
and not a philosophical point of view
that somebody tries to apply to data analysis
- Bayes' theorem is not ``all''. It only works in situations
where the nice scheme of prior and likelihood is applicable.
In many circumstances one can assess a subjective probability
(try asking a carpenter how much he believes the result of his measurement!).
- The coherent bet (à la de Finetti
forces people to be honest and to make the best (i.e. ``most objective'')
assessments of probability.
- It is preferable not to mix up probability evaluation with
In other words, the coherent bet
should be considered hypothetical. This makes a clear distinction
between our beliefs and our wishes (the example in
should teach something in this respect).
- One may think, naïvely,
that the ``objective Bayesian theory'' is more
suited for science than the
``subjective one''. Instead, it seems to me easier to convince
experienced physicists that ``there is nothing really that is
objective'', than it is to accept an objective theory containing
ingredients which appear
from the physicist point of view
Any experienced physicist knows already that the only ``objective'' thing
in science is the reading of digital scales. When we want to
transform this information into scientific knowledge we have to make
use of many implicit and explicit beliefs
(see section 3.2). Nevertheless,
the ``honest'' (but naïve) ideal of objectivity can be recovered if
scientific knowledge is considered
as a kind of very solid networks of beliefs,
based on centuries of experimentation, with fuzzy borders
which correspond to the areas of present research.
My preferred motto is that ``no one should be allowed to talk about
objectivity, unless he has 10 or 20 years of experience in frontier
science, economics, or any other real world application''. In
particular, mathematicians should refrain from using the word
objectivity when talking about the physical world.
- It is very important to work on applications:
the simplicity and the naturalness of the Bayesian reasoning
will certainly attract people.
- Many conventional methods can be easily recovered as limit cases
of the Bayesian ones, if some well defined
restricting conditions are valid, as already
discussed in section 3.4. For example,
when I make
a 2 fit
I consider myself to be using a Bayesian method,
although in a simplified form. This attitude contrasts
to that of practitioners who use methods in which the Bayes' theorem
is explicitly applied, but as if it were one of the many
frequentist cooking recipes.
- It is important to make efforts to introduce Bayesian thinking
in teaching, starting from the basic
courses. I am not the first to have realized that the Bayesian approach
is simple for students. The resistance comes from our colleagues,
who are unwilling to renew the contents of their lectures, and who have
developed a distorted way of thinking.
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
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'
I find that also the Zellner's paper
demonstrating that Bayes' theorem makes the best use of the
available information can
help a lot to convince people.
24 Although it may seem absurd,
the Bayesian approach is recognized by ``frequentists''
to be ``well adapted to decision-making situations''
I wonder what then probability is for these authors.
25 Dogmatism is never desirable. It can
be easily turned against the theory. For example, one criticism of
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
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!''