Posterior predictive tests and Bayesian cross-validation for nano-Hz gravitational-wave background analyses

The most recent results from NANOGrav, the Parkes Pulsar Timing Array, and the European Pulsar Timing Array report evidence of a common red noise process across the arrays that is consistent with a gravitational-wave background from a superposition of signals from supermassive black hole binaries. However, no evidence of Hellings-Downs spatial correlation between pulsars, which is required for a detection claim, has been reported. In this talk we explore what to do in the event that we think we have made a detection. We cover Bayesian cross-validation methods, for example leaving one pulsar out of the array and using the array from the remaining pulsars to predict its data. We also discuss alternative detection statistics which offer a different perspective on our results, and can make slightly different statements than classical p-values and Bayes factors.