  Here I examine how to determine the sensitivity of the LIGO, VIRGO, and LAGOS
gravitational wave detectors to sources of gravitational radiation by
considering the process by which data are analyzed in a noisy detector. By
constructing the probability that the detector output is consistent with the
presence of a signal, I show how to (1) quantify the uncertainty that the
output contains a signal and is not simply noise, and (2) construct the
probability distribution that the signal parameterization has a certain value.
  From the distribution and its mode I determine volumes $V(P)$ in parameter
space such that actual signal parameters are in $V(P)$ with probability $P$. If
we are {\em designing} a detector, or determining the suitability of an
existing detector for observing a new source, then we don't have detector
output to analyze but are interested in the ``most likely'' response of the
detector to a signal. I exploit the techniques just described to determine the
``most likely'' volumes $V(P)$ for detector output corresponding to the source.
Finally, as an example, I apply these techniques to anticipate the sensitivity
of the LIGO and LAGOS detectors to the gravitational radiation from a perturbed
Kerr black hole.
