Reconciling frequentist and Bayesian detection statistics in pulsar-timing-array searches for gravitational waves

The pulsar-timing-array community has converged on the detection of "Hellings-Downs" correlations among the timing residuals of multiple pulsars as definitive evidence for the presence of a stochastic gravitational-wave signals. I describe how correlations emerge in frequentist (optimal statistic) and Bayesian (model comparison) tests; I outline how frequentist and Bayesian detection statements can be reconciled within a Bayesian model-checking outlook; and I discuss the appropriate level of significance for the first detection claim.