Inferred merger-rate density ﹩{ \mathcal R }({\chi }_{{\rm{eff}}};z)﹩ evaluated at redshifts z = 0.2 (blue) and z = 0.8 (orange) for three-dimensional PIXELPOP (left) and the HYBRID model (right), defined in Equations (6) and (7), respectively. The dashed line shows the true population, while the solid line and shaded region represent the posterior median and central 90% credible region.