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We present a statistical method based on a maximum likelihood approach toconstrain the number counts of extragalactic sources below the nominalflux-density limit of continuum imaging surveys. We extract flux densities froma radio map using positional information from an auxiliary catalogue and showthat we can model the number counts of this undetected population down to fluxdensity levels well below the detection threshold of the radio survey. Wedemonstrate the capabilities that our method will have with future generationwide-area radio surveys by performing simulations over various sky areas. Weshow that it is possible to accurately constrain the number counts of thesimulated distribution down to one tenth of the flux noise rms with just a skyarea of 100 deg$^2$. We then test the application of our method using data fromthe Faint Images of the Radio Sky at Twenty-Centimeters survey (FIRST). Weextract flux densities from the FIRST map, sensitive to 150 $\mu$Jy/beam (1$\sigma$), using the positional information from a catalogue in the same field,also acquired at the same frequency, sensitive to 12 $\mu$Jy/beam (1 $\sigma$).Implementing our method, with known source positions, we are able to recoverthe right differential number counts of the noise-dominated FIRST map fluxesdown to a flux density level which is one-tenth the FIRST detection threshold.

Beyond Stacking: A Maximum-Likelihood Method to Constrain Radio Source Counts Below the Detection Threshold