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A recent analysis of data from the resonant g.w. detectors Explorer and
Nautilus [1] has shown some hints of a possible signal over
the background expected from random coincidences.
The indication appears only when the data are analyzed as a
function of the sidereal time.
Reference [1] does not contain
statements concerning the probability that some of the observed
coincidences could be due to g.w.'s rather than background.
Only bottom plots of Fig. 5 and Fig. 7 of that paper gives p-values
(the meaning of `p-value`, to which physicists are not accustomed, will
be clarified later) for each bin in sidereal
time, given the average observed background at that bin.
But p-values are not probabilities that the `only background'
hypothesis is true, though they are often erroneously taken as such, leading to
unpleasant consequences in the interpretation of the
data [2].
Indeed, in this case too, Fig. 5 and Fig. 7 of Ref. [1] might have
produced in some reader sentiments different from those of the
members of the ROG Collaboration,
who do not believe with high probability to have observed g.w.'s.
However, the fact remains that the data are somewhat intriguing,
and it is therefore important to quantify how much we can reasonably
believe the hypothesis that they might contain some g.w. events.
The aim of this paper is to show how to make a quantitative assessment
of how much the experimental data prefer the different models in hand.
The choice of the Bayesian approach is quite natural to
tackle these kind of problems, in which we are finally interested
in the comparison of the probabilities that different models
could explain the observed data. In fact, the concept of probability
of hypotheses, probability of `true values', probability of causes, etc.,
are only meaningful in this approach. The alternative
(`frequentistic') approach forbids to speak about
probability of hypotheses. Frequentistic `hypothesis test' results are given
in terms of `statistical significance', a concepts which notoriously
confuses most practitioners, since it is commonly (incorrectly!) interpreted
as it would be the probability of the `null hypothesis' [2].
Moreover, this approach provides
only `accepted/rejected' conclusions, and thus it is
not suited to extract evidence from noisy data
and to combine it with other evidence provided by other data.

In the next section we present shortly the experimental data, referring
to Ref. [1] and references therein for details.
Then we review how the problem is approached
in conventional statistics, explaining the reasons why we think
that is unsatisfactory.
Finally, we illustrate the Bayesian
alternative for parametric inference and model comparison, and apply it
to the ROG data.

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Giulio D'Agostini
2005-01-09