  In this paper we elaborate on earlier work by the same authors in which a
novel Bayesian inference framework for testing the strong-field dynamics of
General Relativity using coalescing compact binaries was proposed. Unlike
methods that were used previously, our technique addresses the question whether
one or more 'testing coefficients' (e.g. in the phase) parameterizing
deviations from GR are non-zero, rather than all of them differing from zero at
the same time. The framework is well-adapted to a scenario where most sources
have low signal-to-noise ratio, and information from multiple sources as seen
in multiple detectors can readily be combined. In our previous work, we
conjectured that this framework can detect generic deviations from GR that can
in principle not be accomodated by our model waveforms, on condition that the
change in phase near frequencies where the detectors are the most sensitive is
comparable to that induced by simple shifts in the lower-order phase
coefficients of more than a few percent ($\sim 5$ radians at 150 Hz). To
further support this claim, we perform additional numerical experiments in
Gaussian and stationary noise according to the expected Advanced LIGO/Virgo
noise curves, and coherently injecting signals into the network whose phasing
differs structurally from the predictions of GR, but with the magnitude of the
deviation still being small. We find that even then, a violation of GR can be
established with good confidence.
