Interpreting the results of searches for gravitational waves from coalescing binaries

TL;DR

This paper presents a statistical method to estimate upper limits on the rate of binary coalescences from gravitational wave searches, accounting for detector sensitivity, noise, and astrophysical uncertainties.

Contribution

It introduces a loudest event statistic approach for rate estimation, including a detailed treatment of uncertainties and marginalization techniques, with an example based on initial LIGO data.

Findings

Method effectively incorporates detector noise and astrophysical uncertainties.

Provides a framework for upper limit calculation on binary coalescence rates.

Demonstrates application with initial LIGO detector data.

Abstract

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.