deletions | additions       diff --git a/results.tex b/results.tex  index b1298ea..d5cc9f5 100644  --- a/results.tex  +++ b/results.tex 
...
To trace individual parameter uncertainties across the population we use the fractional uncertainties $\sigma_{\{\mathcal{M}_\mathrm{c},~q\}}/\{\langle\mathcal{M}_\mathrm{c}\rangle,~\langle q\rangle\}$, where $\sigma_x$ and $\langle x\rangle$ are the standard deviation and mean of the distributions respectively. The average fractional uncertainties in chirp mass and mass ratio for the simulated population are $0.0675\%$ and $28.7\%$.  The fractional uncertainties for both the chirp mass and the mass ratio both decrease as S/N increases as shown in Figure  \ref{fig:Mc_q_std_snr}, which also shows results from the non-spinning analysis. As expected from Fisher Matrix studies \citep[e.g.,]{FinnChernoff}, all except the $\sigma_q/\langle q\rangle$ from the spinning analysis appear to be inversely proportional to the S/N: the exception is better fit as $\propto \rho^{-1/2}$. The mass-ratio uncertainty from the spinning analysis does not improve as rapidly with increasing S/N as a consequence of the mass--spin degeneracy.   Projecting the tightly constrained chirp mass and poorly constrained mass ratio $90\%$ credible region from $\mathcal{M}_\mathrm{c}$--$q$ space into component-mass space makes it obvious how important mass-ratio uncertainties are for extracting astrophyical information. The credible regions in component-mass space are narrow bananas that lie along lines of constant chirp mass, bounded by the constraints on mass ratio (see Figure \ref{fig:comp_masses} for some examples posteriors).