Marginalised probability distribution of the disfavoured models’ source parameters at z ∼ 8, 9, and 10 for allUL case. The results are for the A_r = 0 scenario. The black, red, and green curves refer to the Single-z case at z = 8.3, 9.1 and 10.1, respectively, while the blue curves are for the Joint-z analysis case. The solid curves represent results derived from the LOFAR upper limits only, while the dotted curves refer to cases where we have used all available upper limits.