Weighing the evidence for a gravitational-wave background in the first International Pulsar Timing Array data challenge

We describe an analysis of the First International Pulsar Timing Array Data Challenge, which was designed to test the ability of new and existing algorithms to constrain the properties of a stochastic gravitational-wave background influencing the arrival times of pulsar signals. We employ a robust, unbiased Bayesian framework developed by van Haasteren to study the three Open and Closed data sets of the International Pulsar Timing Array data challenge. We test various models for each data set and use MultiNest to recover the evidence for the purposes of Bayesian model selection. The parameter constraints of the favored model are confirmed using an adaptive Markov chain Monte Carlo technique. Our results for Closed1 favor a gravitational-wave background with strain amplitude at f=1 yr^-1, A, of (1. 10. 1) 10^-14, power spectral index =4. 300. 15 and no evidence for red-timing noise or single sources. The evidence for Closed2 favors a gravitational-wave background with A= (6. 10. 3) 10^-14, =4. 340. 09, with no red-timing noise or single sources. Finally, the evidence for Closed3 favors the presence of red-timing noise and a gravitational-wave background, with no single sources. The properties of the background are A= (51) 10^-15 and =4. 230. 35, while the properties of the red noise are Nₑ₄₃= (124) ns and ₑ₄₃=1. 50. 3. In all cases the redness of the recovered background is consistent with a source population of inspiraling supermassive black-hole binaries. We also investigate the effect that down-sampling of the data sets has on parameter constraints and run time. Finally, we provide a proof-of-principle study of the ability of the Bayesian framework used in this paper to reconstruct the angular correlation of gravitational-wave background induced timing residuals, comparing this to the Hellings and Downs curve.