(ed.). Gravitational waves (IOP, 2001)(422s).

Achievable sensitivities to the SGWB 199Figure 12.5. The minimum (SNR = 1) detectable value of h 2 0 gw by a single detector.at f = 1 kHz. These values for ˜h f are very far from the sensitivity offirst generation interferometers, and are in fact even well below the limitationdue to quantum noise. A very interesting sensitivity, possibly even of orderh 2 0 gw ∼ 10 −13 , could instead be reached with a single detector, with the plannedspace interferometer LISA [17], at f ∼ 10 −3 Hz.Note also that, while correlating two detectors the SNR improves withintegration time (see equation (12.12)) this is not so with a single detector. So,independently of the low sensitivity, with a single detector it is conceptuallyimpossible to tell whether an excess noise is due to a physical signal or is a noiseof the apparatus that has not been properly accounted for. This might not be agreat problem if the SNR is very large, but certainly with a single detector wecannot make a reliable detection at SNR of order one, so that the above estimates(which have been obtained setting SNR = 1) are really overestimates.12.4.2 Two detectorsThe statistical treatment of the problem of the extraction of information from thecorrelation between two detectors has been extensively discussed in [7] in theframe of the so-called ‘decision theory’ [18]. According to the results of [7],fixed a false alarm rate α (1 − α is the fraction of experimental outcomes that thedecision rule correctly identifies the absence of a signal) and a minimum detectionrate δ (the fraction of experimental outcomes that the decision rule correctlyidentifies the presence of a signal with fixed mean value > 0), the theoretical