Analysis of LIGO data for gravitational waves from binary neutron stars

We report on a search for gravitational waves from coalescing compact binary systems in the Milky Way and the Magellanic Clouds. The analysis uses data taken by two of the three LIGO interferometers during the first LIGO science run and illustrates a method of setting upper limits on inspiral event rates using interferometer data. The analysis pipeline is described with particular attention to data selection and coincidence between the two interferometers. We establish an observational upper limit of $\mathcal{R}<1.7\ifmmode\times\else\texttimes\fi{}{10}^{2}$ per year per Milky Way Equivalent Galaxy (MWEG), with 90% confidence, on the coalescence rate of binary systems in which each component has a mass in the range $1--3{M}_{\ensuremath{\bigodot}}.$