  The present operation of the ground-based network of gravitational-wave laser
interferometers in "enhanced" configuration brings 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 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 of instruments, for the
computation of the Bayes factor between two hypotheses and the evaluation of
the marginalised posterior density functions of the unknown model parameters.
The numerical algorithm to tackle the notoriously difficult problem of the
evaluation of large multi-dimensional integrals is based on a technique known
as Nested Sampling, which provides an attractive alternative to more
traditional Markov-chain Monte Carlo (MCMC) 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.
