Ben Farr edited results.tex  almost 9 years ago

Commit id: c86d2d52f150618b6bc080b15fb8e0bb9fcd31ab

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To trace individual parameter uncertainties across the population we use the fractional uncertainties $\sigma_{\{\mathcal{M}_\mathrm{c},~q}\}/\{\overline{\mathcal{M}_\mathrm{c}},~\overline{q}\}$, where $\sigma_x$ and $\overline{x}$ are the standard deviation and mean of the distributions, respectively. Figure \ref{fig:mass_std_snr} shows the distribution of chirp-mass and mass-ratio fractional uncertainties, with colors corresponding to the S/N recovered by the detection pipeline. The average fractional uncertainties in chirp mass and mass ratio for the simulated population are $0.0675\%$ and $28.7\%$, respectively, with both generally increasing as S/N decreases.    Projecting the very 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 very narrow bananas that lie along lines of constant chirp mass, bounded by the constraints on mass ratio (see Figure \ref{fig:component_mass} \ref{fig:comp_masses}  for some examples posteriors).