Impact of sample variance and reweighting on the Ω_GW spectrum. Left: 95% confidence on the spectrum calculated using 10⁵ (10⁶) samples in yellow (green) drawn from a fixed hyperparameter distribution, compared to the 95% confidence on the spectrum including uncertainty on the local merger rate parameter in brown. Unsurprisingly, the sample variance varies significantly with number of samples and when using large sample numbers is subdominant compared to population parameter uncertainty. Right: sample variance from the left panel compared to reweighted estimates of the Ω_GW spectrum. The reweighted spectra lie neatly within the sample variance uncertainty bounds, implying that the reweighted spectrum is indistinguishable from a regularly sampled spectrum, with these sample numbers.