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 $√- 2 2$ 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 $SNR → ∞$ .
4		Working with analytic signals $h (t) = a(t)eϕ(t)+iϕ0$ , where $a(t)$ and $ϕ(t)$ are the time-varying amplitude and phase of the signal, respectively, we see that the initial phase $ϕ 0$ 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 $D$ ), 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 $pα$ .
8		A Bayesian interpretation of $𝒫 (Δp α)$ is the probability of having the true signal parameters lie somewhere inside the ellipsoidal volume centered at the Maximum Likelihood point $- pα$ .
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 $M$ at a redshift of $z$ will appear as a black hole of mass $Mz = (1+ z)M$ . 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 $M < 1.2× 108M ⊙∕(1+ z)$ can be observed at a redshift $z$ .
11		By large spins we mean values that are close to the maximum value allowed by general relativity. If $J$ is the magnitude of the spin angular momentum then general relativity requires that $\|J\| ≤ M 2$
12		In Newton’s theory a two-body problem can be reduced to a one-body problem, in which a body of reduced mass $μ$ moves in an effective potential. The parameter $v$ is the velocity of the reduced mass, if the orbit is circular. In the extreme mass ratio limit $ν → 0$ , $v$ is the velocity of the smaller mass.
13		QUaD stands for QUEST (Q and U Extragalactic Survey Telescope) at DASI (Degree Angular Scale Interferometer).