deletions | additions       diff --git a/subsection_Luminosity_distance_label_sec__.tex b/subsection_Luminosity_distance_label_sec__.tex  index 3da155f..15262bb 100644  --- a/subsection_Luminosity_distance_label_sec__.tex  +++ b/subsection_Luminosity_distance_label_sec__.tex 
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The distance is degenerate with the inclination \citep{Cutler_1994,Aasi_2013}, and the inclination can be better constrained for precessing systems \citep{van_der_Sluys_2008,Vitale_2014}. Since we are considering a population with low spins, precession is minimal, and there should be little effect from including spin in the analysis.  We quantify distance measurement accuracy using symmetric credible intervals: the distance credible interval $\mathrm{CI}_p^{D}$ in the range that contains the central $p$ of the integrated posterior, with $(1-p)/2$ falling both above and below the limits \citep{Aasi_2013}. The absolute size of the credible interval approximately scales with the distance, hence we divide the credible interval by the true (injected) distance $D_\star$; this gives an approximate analogue of twice the fractional uncertainty \citep{Berry_2014}. The cumulative distribution of the scaled credible intervals is plotted in Figure \ref{fig:distance}. The mean (median) values of $\mathrm{CI}_{0.5}^{D}/D_\star$ for the spinning and non-spinning analyses are $0.435$ ($0.378$) and $0.426$ ($0.363$) respectively; the values of $\mathrm{CI}_{0.9}^{D}/D_\star$ are $0.978$ ($0.845$) and $0.951$ ($0.819$), and the fractional uncertainties $\sigma_D/\langle D\rangle$ are $0.262$ ($0.257$) and $0.245$ ($0.239$).  There is negligible difference between the spinning and non-spinning analyses as expected.