Performance comparison of multidetector detection statistics in targeted compact binary coalescence gravitational wave searches

A global network of advanced interferometric gravitational wave detectors is expected to be on-line soon. Coherent observation of gravitational waves from a distant compact binary coalescence with a network of interferometers located in different continents gives crucial information about the source, such as its location and polarization. In this paper we compare different multidetector network detection statistics for compact binary coalescence searches. In maximum likelihood ratio based detection approaches, the likelihood ratio is optimized to obtain the best model parameters, and the best likelihood ratio value is used as a statistic to make decisions regarding the presence of signals. However, an alternative Bayesian approach involves the marginalization of the likelihood ratio over the parameters and obtains the average likelihood ratio test. We obtain an analytical expression for the Bayesian statistic using the two effective synthetic data streams for targeted searches of nonspinning compact binary systems with an uninformative prior on the parameters. Simulations are carried out to test the validity of the approximation and compare the detection performance with the maximum likelihood ratio and the "hybrid" statistic. We observe that the hybrid statistic gives comparable or better performance with respect to the Bayesian statistic.