  The temporal evolution of the gravitational wave background signal resulting
from stellar-mass binary black hole (BBH) inspirals has a unique statistical
signature. We describe the application of a new filter, based on the
`probability event horizon' (PEH) concept, that utilizes both the temporal and
spatial source distribution to constrain the local rate density, $r_{0}$, of
BBH inspiral events in the nearby Universe. Assuming Advanced LIGO
sensitivities and an upper rate of Galactic BBH inspirals of $
30\hspace{1mm}\mathrm{Myr}^{-1}$, we simulate GW data and apply a fitting
procedure to the PEH filtered data. To determine the accuracy of the PEH filter
in constraining $r_{0}$, a comparison is made with a fit to the brightness
distribution of events. We apply both methods to a data stream containing a
background of Gaussian distributed false alarms. We find that the brightness
distribution yields lower standard errors, but is biased by the false alarms.
In comparison the PEH method is less prone to errors resulting from false
alarms but has a lower resolution as fewer events contribute to the data. Used
in combination, the PEH and brightness distribution methods provide an improved
estimate of the rate density.
