Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: I. The optimal statistic

Understand

A gravitational-wave background can be detected in pulsar-timing-array data as Hellings--Downs correlations among the timing residuals measured for different pulsars.

• The optimal statistic implements this concept as a classical null-hypothesis statistical test: a null model with no correlations can be rejected if the observed value of the statistic is very unlikely under that model.
• To address the dependence of the statistic on the uncertain pulsar noise parameters, the pulsar-timing-array community has adopted a hybrid classical--Bayesian scheme (Vigeland et al.
• 2018) in which the posterior distribution of the noise parameters induces a posterior distribution for the statistic.