Bayesian coherent analysis of in-spiral gravitational wave signals with a detector network

The present operation of the ground-based network of gravitational-wave laser interferometers in enhanced configuration and the beginning of the construction of second-generation (or advanced) interferometers with planned observation runs beginning by 2015 bring the search for gravitational waves into a regime where detection is highly plausible. The development of techniques that allow us to discriminate a signal of astrophysical origin from instrumental artefacts in the interferometer data and to extract the full range of information are therefore some of the primary goals of the current work. Here we report the details of a Bayesian approach to the problem of inference for gravitational wave observations using a network (containing an arbitrary number) of instruments, for the computation of the Bayes factor between two hypotheses and the evaluation of the marginalized posterior density functions of the unknown model parameters. The numerical algorithm to tackle the notoriously difficult problem of the evaluation of large multidimensional integrals is based on a technique known as nested sampling, which provides an attractive (and possibly superior) alternative to more traditional Markov-chain Monte Carlo methods. We discuss the details of the implementation of this algorithm and its performance against a Gaussian model of the background noise, considering the specific case of the signal produced by the in-spiral of binary systems of black holes and/or neutron stars, although the method is completely general and can be applied to other classes of sources. We also demonstrate the utility of this approach by introducing a new coherence test to distinguish between the presence of a coherent signal of astrophysical origin in the data of multiple instruments and the presence of incoherent accidental artefacts, and the effects on the estimation of the source parameters as a function of the number of instruments in the network.