Simulated light curves of constant sources with Poisson noise. Black circles show the total counts without background subtraction, and red points show the expected background count rates in the source region (Eq. (4)). Top panel: source with a high count rate with a constant 3 cts/s, where the source counts are always above the expected background counts. Bottom panel: source with a low count rate with a constant 0.03 cts/s, where source region counts and background counts are comparable and show substantial Poisson scatter. Grey error bars show classical net source count-rate estimates (Eqs. (3) and 5). Black error bars show Bayesian net source count-rate posterior distributions (Eq. (7)).