http://arxiv.org/abs/2305.01116
We show via both analytical calculation and numerical simulation that the optimal cross-correlation statistic (OS) for stochastic gravitational-wave-background (GWB) searches using data from pulsar timing arrays follows a generalized chi-squared (GX2) distribution-i.e., a linear combination of chi-squared distributions with coefficients given by the eigenvalues of the quadratic form defining the statistic. This observation is particularly important for calculating the frequentist statistical significance of a possible GWB detection, which depends on the exact form of the distribution of the OS signal-to-noise ratio (S/N) $\hat\rho \equiv \hat A_{\rm gw}^2/\sigma_0$ in the absence of GW-induced cross correlations (i.e., the null distribution). Previous discussions of the OS have incorrectly assumed that the analytic null distribution of $\hat\rho$ is well-approximated by a zero-mean unit-variance Gaussian distribution. Empirical calculations show that the null distribution of $\hat\rho$ has “tails” which differ significantly from those for a Gaussian distribution, but which follow (exactly) a GX2 distribution. So, a correct analytical assessment of the statistical significance of a potential detection requires the use of a GX2 distribution.
J. Hazboun, P. Meyers, J. Romano, et. al.
Wed, 3 May 23
26/67
Comments: 13 pages, 3 Figures