  The direct detection of gravitational waves with upcoming second-generation
gravitational wave detectors such as Advanced LIGO and Virgo will allow us to
probe the genuinely strong-field dynamics of general relativity (GR) for the
first time. We present a data analysis pipeline called TIGER (Test
Infrastructure for GEneral Relativity), which is designed to utilize detections
of compact binary coalescences to test GR in this regime. TIGER is a
model-independent test of GR itself, in that it is not necessary to compare
with any specific alternative theory. It performs Bayesian inference on two
hypotheses: the GR hypothesis $\mathcal{H}_{\rm GR}$, and $\mathcal{H}_{\rm
modGR}$, which states that one or more of the post-Newtonian coefficients in
the waveform are not as predicted by GR. By the use of multiple sub-hypotheses
of $\mathcal{H}_{\rm modGR}$, in each of which a different number of
parameterized deformations of the GR phase are allowed, an arbitrarily large
number of 'testing parameters' can be used without having to worry about a
model being insufficiently parsimonious if the true number of extra parameters
is in fact small. TIGER is well-suited to the regime where most sources have
low signal-to-noise ratios, again through the use of these sub-hypotheses.
Information from multiple sources can trivially be combined, leading to a
stronger test. We focus on binary neutron star coalescences, for which
sufficiently accurate waveform models are available that can be generated fast
enough on a computer to be fit for use in Bayesian inference. We show that the
pipeline is robust against a number of fundamental, astrophysical, and
instrumental effects, such as differences between waveform approximants, a
limited number of post-Newtonian phase contributions being known, the effects
of neutron star spins and tidal deformability on the orbital motion, and
instrumental calibration errors.
