Cumulative number of sources as a function of their flux. Solid blue lines represent associated 3FGL and 4FGL-DR2 sources; green bands show the envelope of sums of class probabilities for associated sources for the eight ML methods corrected for the presence of OTHER sources; solid orange lines (bands) show the sum of class probabilities for the LR model (the envelope of the eight ML methods), corrected for the presence of OTHER sources and added to the source count of associated sources; purple dashed (dotted) lines show the sum of class probabilities for associated sources for the LR method without oversampling and corrected (uncorrected) for the presence of OTHER sources; gray dash-dotted (dotted) lines show the sums of class probabilities from Saz Parkinson et al. (2016) using LR corrected (uncorrected) for the presence of OTHER sources; and gray bands show the envelope of sums of class probabilities for associated sources for LR and RF methods from Saz Parkinson et al. (2016) corrected for the presence of OTHER sources (for details, see Sect. 6.1).