On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays
Pulsar Timing Array (PTA) projects have reported various lines of evidence suggesting the presence of a stochastic gravitational wave (GW) background in their data. One key line of evidence involves a detection statistic sensitive to inter-pulsar correlations, such as those induced by GWs. A $p$-value is then calculated to assess how unlikely it is for the observed signal to arise under the null hypothesis $H_0$, purely by chance. However, PTAs cannot empirically draw samples from $H_0$. As a w…
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