Abstract
Pulsar-timing-array experiments have reported evidence for a stochastic
background of nanohertz gravitational waves consistent with the signal expected
from a population of supermassive--black-hole binaries. Those analyses assume
power-law spectra for intrinsic pulsar noise and for the background, as well as
a Hellings--Downs cross-correlation pattern among the
gravitational-wave--induced residuals across pulsars. These assumptions are
idealizations that may not be realized in actuality. We test them in the
NANOGrav 15 yr data set using Bayesian posterior predictive checks: after
fitting our fiducial model to real data, we generate a population of simulated
data-set replications, and use them to assess whether the optimal-statistic
significance, inter-pulsar correlations, and spectral coefficients assume
extreme values for the real data when compared to the replications. We confirm
that the NANOGrav 15 yr data set is consistent with power-law and
Hellings--Downs assumptions. We also evaluate the evidence for the stochastic
background using posterior-predictive versions of the frequentist optimal
statistic and of Bayesian model comparison, and find comparable significance
(3.2\ $\sigma$ and 3\ $\sigma$ respectively) to what was previously reported
for the standard statistics. We conclude with novel visualizations of the
reconstructed gravitational waveforms that enter the residuals for each pulsar.
Our analysis strengthens confidence in the identification and characterization
of the gravitational-wave background as reported by NANOGrav.