Accurate delimitation of the geographic range of a species is important for control of biological invasions, conservation of threatened species, and understanding species range dynamics under environmental change. However, estimating range boundaries is challenging because monitoring methods are imperfect, the area that might contain individuals is often incompletely surveyed, and species may have patchy distributions. In these circumstances, large areas can be surveyed without finding individuals despite occupancy extending beyond surveyed areas, resulting in underestimation of range limits. We developed a delimitation method that can be applied with imperfect survey data and patchy distributions. The approach is to construct polygons indicative of the geographic range of a species. Each polygon is associated with a specific probability such that each interior point of the polygon has at least that posterior probability of being interior to the true boundary according to a Bayesian model. The method uses the posterior distribution of latent quantities derived from an agent-based Bayesian model and calculates the posterior distribution of the range as a derived quantity from Markov chain Monte Carlo samples. An application of this method described here informed the Australian campaign to eradicate red imported fire ants (Solenopsis invicta).