Bayesian inference on the Numerical INJection Analysis (NINJA) data set using a nested sampling algorithm

Abstract

We present the results of an analysis of the first data release of the Numerical INJection Analysis (NINJA) project to search for gravitational waves generated by the coalescence of black hole binaries. We adopt a Bayesian approach implemented through a nested sampling algorithm to explore how different waveform families affect the confidence of detection of signals generated by numerically evolving a two-body system in full general relativity. In particular we consider the standard second-order post-Newtoninan approximation to the inspiral phase (TaylorF2 approximant) and the inspiral-merger-rigdown phenomenological waveforms suggested by Ajith and collaborators (2008 Phys. Rev. D 77 104017) (IMRPhenomA approximant). We show that the latter family consistently out-performs TaylorF2 waveforms, and 112 of the 126 signals present in the data set are recovered with a log Bayes factor larger than 3. We also carry out a study of the recovered source parameters, and in particular we discuss the errors affecting the determination of the total mass and sky position.