Upper panel: differential (solid blue) distribution of the number of spurious detections and differential (solid red) distribution of catalogue sources. The integral distributions of spurious detections (thin blue, dashed) and catalogue sources (thin red, dashed) are shown in addition with the labelling given on the right y-axis. The solid black thin line gives the theoretical differential relation between the detection likelihood and the probability that a source is spurious. Lower panel: fraction of spurious detections as a function of the existence likelihood. Details of the simulations are described in Sect. 4.4.1.