GWB significance and parameter estimation from the 100 DR2full + IPTA simulations. Panel (a): 2D distributions of the noise marginalised HD S/N and the degeneracy coefficient (weighted average JSD). Panel (b): distribution of the median of log₁₀A_GWB and γ_GWB marginalised posterior distributions.. Panel (c): summary of the noise parameters estimation from the 100 realisations of DR2full (orange) and DR2full + IPTA (red) simulated data. Top: Median of the marginalised posterior distribution of the noise component amplitude, the true values are shown for reference (black crosses). Bottom: Savage-Dickey ratio of the amplitude posterior distributions; BF < 1 means the posterior is unconstrained, BF ≫1 means the posterior is very well constrained.