  We have developed a new Bayesian method to correct the flux densities of
astronomical sources. The hybrid method combines a simulated likelihood to
model survey selection together with an analytic source-count-based prior. The
simulated likelihood captures the effect of complicated selection methods, such
as multi-frequency filtering or imposed restrictions on recovered sample
properties (e.g., color cuts). Simulations are also able to capture
unanticipated sources of uncertainty. In this way, the method enables a broader
application of Bayesian techniques. Use of an analytic prior allows variation
of assumed source count models without re-simulating the likelihood. We present
the method along with a detailed description of an application to real survey
data from the Atacama Cosmology Telescope.
