## List of Footnotes

 1 In the case of an inspiraling binary, the root mean square of the two polarization amplitudes in a direction orthogonal to the orbital plane will be a factor larger than in the plane. 2 In Sections 5.1 we will use parameters called chirp times, instead of the masses, to characterize a binary. The timescale defined here is closely related to the chirp times. 3 How large the SNR should be to presume that there is no bias in the estimation of parameters depends on the number of parameter-space dimensions and strictly speaking the statement is true only in the limit as . 4 Working with analytic signals , where and are the time-varying amplitude and phase of the signal, respectively, we see that the initial phase of the signal simply factors out as a constant phase in the Fourier domain and we can maximize over this initial phase by simply taking the absolute value of the scalar product of a template with a signal. 5 Even though we deal with normed signals (which amounts to fixing ), astrophysical gravitational wave signals are characterized by this additional parameter. 6 We have followed the definition of the metric as is conventional in parameter estimation theory (see, e.g., [159, 161, 115, 67]), which differs from that used in template placement algorithms (see, e.g., [278]) by a factor of two. This difference will impact the relationship between the metric and the match, as will be apparent in what follows. 7 In what follows we shall use an over-line to distinguish the measured parameters from the true parameters . 8 A Bayesian interpretation of is the probability of having the true signal parameters lie somewhere inside the ellipsoidal volume centered at the Maximum Likelihood point . 9 A black hole can, in principle, carry an electric charge in addition to mass and spin angular momentum. However, astrophysical black holes are believed to be electrically neutral 10 Note that a black hole of physical mass at a redshift of will appear as a black hole of mass . This shifts the frequency of the QNM to the lower end of the spectrum. Assuming a frequency cutoff of 10–4 Hz for LISA, this means that only black holes of intrinsic mass can be observed at a redshift . 11 By large spins we mean values that are close to the maximum value allowed by general relativity. If is the magnitude of the spin angular momentum then general relativity requires that 12 In Newton’s theory a two-body problem can be reduced to a one-body problem, in which a body of reduced mass moves in an effective potential. The parameter is the velocity of the reduced mass, if the orbit is circular. In the extreme mass ratio limit , is the velocity of the smaller mass. 13 QUaD stands for QUEST (Q and U Extragalactic Survey Telescope) at DASI (Degree Angular Scale Interferometer).