Bayesian comparison of post-Newtonian approximations of gravitational wave chirp signals

We estimate the probability of detecting a gravitational wave signal from coalescing compact binaries in simulated data from a ground-based interferometer detector of gravitational radiation using Bayesian model selection. The simulated wave form of the chirp signal is assumed to be a spinless post-Newtonian (PN) wave form of a given expansion order, while the searching template is assumed to be either of the same post-Newtonian family as the simulated signal or one level below its post-Newtonian expansion order. Within the Bayesian framework, and by applying a reversible jump Markov Chain Monte Carlo simulation algorithm, we compare PN1.5 vs PN2.0 and PN3.0 vs PN3.5 wave forms by deriving the detection probabilities, the statistical uncertainties due to noise as a function of the signal-to-noise ratio, and the posterior distributions of the parameters. Our analysis indicates that the detection probabilities are not compromised when simplified models are used for the comparison, while the accuracies in the determination of the parameters characterizing these signals can be significantly worsened, no matter what the considered post-Newtonian order expansion comparison is.