4.9
Upper limits
Detection of a signal is signified by a large value of the
-statistic that is unlikely to arise from the noise-only
distribution. If instead the value of
is consistent with pure noise with high probability we can place
an upper limit on the strength of the signal. One way of doing
this is to take the loudest event obtained in the search and
solve the equation
for signal-to-noise ratio
, where
is the detection probability given by Equation (47),
is the value of the
-statistic corresponding to the loudest event, and
is a chosen confidence
[12, 1]
. Then
is the desired upper limit with confidence
.
When gravitational-wave data do not conform to
a Gaussian probability density assumed in Equation (47), a more accurate upper limit can be obtained by injecting the
signals into the detector’s data and thereby estimating the
probability of detection
[3]
.