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We introduce a method based on the loudest event statistic to calculate anupper limit or interval on the astrophysical rate of binary coalescence. Thecalculation depends upon the sensitivity and noise background of the detectors,and a model for the astrophysical distribution of coalescing binaries. Thereare significant uncertainties in the calculation of the rate due to bothastrophysical and instrumental uncertainties as well as errors introduced byusing the post--Newtonian waveform to approximate the full signal. We catalogthese uncertainties in detail and describe a method for marginalizing overthem. Throughout, we provide an example based on the initial LIGO detectors.

Interpreting the results of searches for gravitational waves from coalescing binaries