Introduction

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.