Comparison of the GW residuals RMS induced by the HORIZON-AGN population, using different modeling and populations, with the spectrum measured by the EPTA collaboration, shown in red. The average GE spectra of both circular and eccentric ensembles are depicted as solid and dashed lines, respectively. The distribution of the maximum-a-posteriori samples for the GWB spectra of the 2000 Universe realizations obtained using the population (Pop) method and a realistic PTA-like inference with and without TMM, are shown in dashed contours and light blue color, respectively, for the circular population. The effect of spectral leakage on the GWB inference results in a shallower spectral shape, significantly biasing the inference when TMM is not included. For some Universe realizations, spectral leakage still has appreciable effects at high frequencies even when TMM is applied.