- the concept of probability of causes is refused;
- the role of Bayes' theorem to update beliefs
is rejected, and hence
- the role of prior knowledge is not explicitly recognized;
- the myth has been created that a single hypothesis can be `tested' without taking explicitly into account alternative(s);

- the intuitive concept of `probabilities of causes'
has been surrogated by
*ad hoc*hypothesis test prescriptions,- whose choice and use are rather arbitrary;
- whose results are routinely misinterpreted.

- probabilities of the effects given the causes are confused with the probabilities of the causes given the effects;
- even worse, p-values are used as if they were the probability that the hypothesis under test is true.

But, fortunately, being the natural intuition of physicists
rather `Bayesian'[20], after all it is more
a question of *rough scientific communication*
than of *rough science*.
In fact, even the initial
excitement of someone who takes a bit too seriously
claims that the rest of the physics community
classifies immediately as `fake' - priors! -
is harmless, if the discussions remain in the community.
And the debates are often even profitable, because they
offer an opportunity to check how new possible phenomena
and new explanations could fit into the present
*network of beliefs*
based on all previous experimental observations. This
is for example what has recently happened with the exchange
of ideas that has followed
the Opera result on neutrino speed, from which
most of us have learned something.

As far as the communication of claims to non experts, that include also physicists of other branches, or even of a close sub-branch, my recommendation is of making use, at least qualitatively, of the Bayesian odd update, i.e.

- state how much the experimental
*data push*towards either possibility (that is the Bayes factor, which*has nothing to do with p-values*); - state also how
*believable*are the two hypotheses*independently of the data in object*.

- don't accept answers in terms of p-values, unless you are sure you understand them well and you feel capable to explain their correct meaning to the general public without they become somehow probabilities of the hypotheses to be compared (good luck!);
- refuse as well `confidence levels', `95% confidence exclusion curves' and similar;
*ask straight the direct questions*:- How probable it is? (Possibly informing - threatening! -
him/her in advance that his/her answer will be
reported as ``Dr X.Y. considers
it such and such percent
*probable*''.) - How much do you believe? (Same as the previous one.)
- How much would you believe in either hypothesis if you did not have this data? (The answer allows you to estimate the priors odds.)
- How much would you believe in either hypothesis given these data, if you considered the two hypotheses initially equally probable? (The answer allows you to evaluate the Bayes factor.)
- How much would you bet in favor of your claim?
(And if you realize there are the conditions described
in section 5.3 and figure
2,
*don't miss the opportunity to gain some money!*)

- How probable it is? (Possibly informing - threatening! -
him/her in advance that his/her answer will be
reported as ``Dr X.Y. considers
it such and such percent

Giulio D'Agostini 2012-01-02