  Second generation interferometric gravitational wave detectors, such as
Advanced LIGO and Advanced Virgo, are expected to begin operation by 2015. Such
instruments plan to reach sensitivities that will offer the unique possibility
to test General Relativity in the dynamical, strong field regime and
investigate departures from its predictions, in particular using the signal
from coalescing binary systems. We introduce a statistical framework based on
Bayesian model selection in which the Bayes factor between two competing
hypotheses measures which theory is favored by the data. Probability density
functions of the model parameters are then used to quantify the inference on
individual parameters. We also develop a method to combine the information
coming from multiple independent observations of gravitational waves, and show
how much stronger inference could be. As an introduction and illustration of
this framework - and a practical numerical implementation through the Monte
Carlo integration technique of nested sampling - we apply it to gravitational
waves from the inspiral phase of coalescing binary systems as predicted by
General Relativity and a very simple alternative theory in which the graviton
has a non-zero mass. This method can trivially (and should) be extended to more
realistic and physically motivated theories.
