We introduce a method based on the loudest event statistic to calculate an upper limit or interval on the astrophysical rate of binary coalescence. The calculation depends upon the sensitivity and noise background of the detectors, and a model for the astrophysical distribution of coalescing binaries. There are significant uncertainties in the calculation of the rate due to both astrophysical and instrumental uncertainties as well as errors introduced by using the post--Newtonian waveform to approximate the full signal. We catalog these uncertainties in detail and describe a method for marginalizing over them. Throughout, we provide an example based on the initial LIGO detectors.
