Conclusions

Fake claims of discoveries are mainly caused by statistical prescriptions that do not follow probabilistic reasoning, meant as mathematics of beliefs, as it was conceived as a whole by Laplace and that nowadays is known under the appellative `Bayesian'. As a consequence

• 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.

Unfortunately, this wobbly construction faces against the human predisposition to think naturally in terms of degrees of belief about anything we are in condition of uncertainty, including the several causes that might have produced the observed effects. The result of this mismatch is that

• 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.

In addition, the pretension that `priors are not scientific and should not enter the game' (``the data should speak by themselves'') avoids that sound scientific priors mitigate the deleterious effects of misunderstood p-values.

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.

I am pretty sure most people can make a good use of these pieces of information. Moreover, my recommendation to journalist and opinion makers (including bloggers and similar) is that, in the case of doubt:

• 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!)

To end, I would like to congratulate all people working at LHC on the amazing high quality work done in these years and on having been able to report these convincing hints on the Higgs boson in a record time (I had never betted in favor of this possibility in 2011 even six months ago! But now the real exciting bet is what next?).