Supplement: The Rate of Binary Black Hole Mergers Inferred from Advanced   LIGO Observations Surrounding GW150914
  Supplemental information for a Letter reporting the rate of binary black hole (BBH) coalescences inferred from 16 days of coincident Advanced LIGO observations surrounding the transient gravitational wave signal GW150914. In that work we reported various rate estimates whose 90\% credible intervals fell in the range $2$--$600 \, \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$. Here we give details of our method and computations, including information about our search pipelines, a derivation of our likelihood function for the analysis, a description of the astrophysical search trigger distribution expected from merging BBHs, details on our computational methods, a description of the effects and our model for calibration uncertainty, and an analytic method of estimating our detector sensitivity that is calibrated to our measurements. 
The LIGO Scientific Collaboration and the Virgo Collaboration: B. P.   Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. ...
astro-ph.HE astro-ph.IM