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Ben Farr edited component_masses.tex
about 8 years ago
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Figure \ref{fig:comp_masses} compares cartoon $90\%$ credible regions in component-mass space of $5$ chosen simulated signals \cite[cf.]{Hannam_2013,Chatziioannou_2014}. As a consequence of the difficulty of estimating the narrow and nonlinearly correlated credible regions in $m_1$--$m_2$ space, we illustrate the credible regions in $m_1$--$m_2$ space as the projection of a rectangular region in $\mathcal{M}_\mathrm{c}$--$q$ space.
\textbf{To To define the rectangular region we use $90\%$ credible intervals of the one-dimensional posterior PDFs of $\mathcal{M}_\mathrm{c}$ and $q$; for $\mathcal{M}_\mathrm{c}$ we use the central $90\%$ credible interval ($5$th to $95$th percentile), and for $q$ the upper $90\%$ credible interval ($10$th to $100$th percentile). These differing credible intervals were chosen to better summarize the one-dimensional posterior PDFs, which are typically normal for $\mathcal{M}_\mathrm{c}$ and skewed toward high values for $q$ (see figure
\ref{fig:mass_pdfs}).} \ref{fig:mass_pdfs}).