• bayesian statistics
• general relativity
• gravitational waves

To date, ground-based detectors such as LIGO and Virgo detected almost 100 gravitational wave signals coming from the coalescence of compact binary systems. Such a number of signals allows, for the first time, population-based investigations on the dynamics of space-time, hence to test the predictions of general relativity (GR). Tests of GR, in general, rely on investigations on the so-called post-Newtonian series, the expansion of Einstein’s equations used to build models for the coalesce of compact binaries.
In this thesis, we investigate the presence of systematic effects in current tests of GR by looking for correlations between the intrinsic parameters of a coalescing binary (e.g. total mass and mass ratio) and the resulting testing coefficients, both for generic parametrised tests and to the specific propagation tests aimed at constraining any departure from the expected non-dispersive propagation of gravitational waves.
Our investigation is based on an application of Bayesian probability theory, whence probability is a measure of the level of confidence of a proposition and it represents a state of knowledge rather then a physical entity. Starting from publicly available posterior distributions of parameters derived from observed O1, O2 and O3 binary BH events, we search for a functional relation between the phase deviation coefficients and the binary total mass M and (inverse) mass ratio q. For propagation tests, we look instead at the strength of the dispersion modification and the mass posteriors. We investigate linear and quadratic relations among the relevant parameters, obtain posterior distributions for their defining parameters and compare their "goodness of fit" by means of the Bayesian evidence.
Our findings reveal that the purely uncorrelated model tends to be disfavoured compared to the linear or the quadratic relation, hence suggesting the presence of non-trivial relationships among the binary parameters and the testing coefficients. We interpret these findings as evidence for the presence of unaccounted for systematic effects in the waveform models. The most interesting case is the leading order (0PN case), for which we find an hyperbolic trend, strongly suggesting the presence of systematics.
Looking at the results from tests of gravitational wave propagation, we note an established preference for the linear regression at all orders, showing once again the presence of a systematic which reports the data as correlated from each other.
Finally, we note that the events driving the systematics are low-mass. We thus conclude by briefly reviewing some of the suggestions present in the literature that could explain our findings.