  The population analysis and estimation of merger rates of compact binaries is
one of the important topics in gravitational wave (GW) astronomy. The primary
ingredient in these analyses is the population-averaged sensitive volume.
Typically, sensitive volume, of a given search to a given simulated source
population, is estimated by drawing signals from the population model and
adding them to the detector data as injections. Subsequently injections, which
are simulated gravitational waveforms, are searched for by the search pipelines
and their signal-to-noise ratio (SNR) is determined. Sensitive volume is
estimated, by using Monte-Carlo (MC) integration, from the total number of
injections added to the data, the number of injections that cross a chosen
threshold on SNR and the astrophysical volume in which the injections are
placed. So far, only fixed population models have been used in the estimation
of the merger rates. However, as the scope of population analysis broaden in
terms of the methodologies and source properties considered, due to an increase
in the number of observed GW signals, the procedure will need to be repeated
multiple times at a large computational cost. In this letter we address the
problem by performing a weighted MC integration. We show how a single set of
generic injections can be weighted to estimate the sensitive volume for
multiple population models; thereby greatly reducing the computational cost.
The weights in this MC integral are the ratios of the output probabilities,
determined by the population model and standard cosmology, and the injection
probability, determined by the distribution function of the generic injections.
Unlike analytical/semi-analytical methods, which usually estimate sensitive
volume using single detector sensitivity, the method is accurate within
statistical errors, comes at no added cost and requires minimal computational
resources.
