In June we have finally learned[4]
that another `one *and a half'* gravitational waves from
Binary Black Hole mergers were also observed in 2015, where
by the `half' I refer to the October 12 event, highly *believed* by
the collaboration to be a gravitational wave, although having
only 1.7 *significance*
and therefore classified just
as LVT (LIGO-Virgo Trigger) instead of GW.
However, another figure of merit
has been provided by the collaboration for each event, a number
based on probability theory and that tells how much we
must modify the relative beliefs
of two alternative hypotheses in the light of the
experimental information. This number, at my knowledge
never even mentioned in press releases or seminars to large audiences,
is the Bayes factor (BF), whose meaning is
easily explained: if you considered *à priori*
two alternative hypotheses equally likely,
a BF of 100 changes your odds to 100 to 1;
if instead you considered one hypothesis rather unlikely,
let us say your odds were 1 to 100, a BF of turns
them the other way around, that is 100 to 1.
You will be amazed to learn that even the ``1.7 sigma''
LVT151012 has a BF of the order of
,
considered a very strong evidence in favor of the
hypothesis ``Binary Black Hole merger'' against the alternative
hypothesis ``Noise''. (Alan Turing
would have called the evidence provided by such
an huge `Bayes factor,' or what I. J. Good would have preferred to call
``Bayes-Turing factor''[5],^{2}100 *deciban*, well above the 17 deciban
threshold considered by the team
at Bletchley Park during World War II
to be reasonably confident of having cracked the
daily Enigma key[7].)

In the past I have been writing quite a bit on how `statistical' considerations based on p-values tend to create wrong expectations in frontier physics (see e.g. [8] and [9]). The main purpose of this paper is the opposite, i.e. to show how p-values might relegate to the role of a possible fluke what is most likely a genuine finding. In particular, the solution of the apparent paradox of how a marginal `1.7 sigma effect' could have a huge BF such as (and virtually even much more!) is explained in a didactic way.

Giulio D'Agostini 2016-09-06