PPDs on the marginal density of sources as a function of spin magnitude χ under both models. Top: results obtained with SUBPOPULATIONS model, for BHs in the low-mass + Gaussian tilts (blue), low-mass + isotropic tilts (orange, dashed), and high-mass + isotropic tilts (green) subpopulations. Bottom: results obtained under the CORRELATION model, in each bin of BH mass. Lines or shading enclose the 90% credible region.