Statistical strong lensing. III. Inferences with complete samples of lenses
Context. Existing samples of strong lenses have been assembled by giving priority to sample size, but this is often at the cost of a complex selection function. However, with the advent of the next generation of wide-field photometric surveys, it might become possible to identify subsets of the lens population with well-defined selection criteria, trading sample size for completeness. Aims: There are two main advantages of working with a complete sample of lenses. First, such completeness makes possible to recover the properties of the general population of galaxies, of which strong lenses are a biased subset. Second, the relative number of lenses and non-detections can be used to further constrain models of galaxy structure. The present work illustrates how to carry out a statistical strong lensing analysis that takes advantage of these features. Methods: I introduce a general formalism for the statistical analysis of a sample of strong lenses with known selection function, and then test it on simulated data. The simulation consists of a population of 105 galaxies with an axisymmetric power-law density profile, a population of background point sources, and a subset of ∼103 strong lenses, which form a complete sample above an observational cut. Results: The method allows the user to recover the distribution of the galaxy population in Einstein radius and mass density slope in an unbiased way. The number of non-lenses helps to constrain the model when magnification data are not available. Conclusions: Complete samples of lenses are a powerful asset with which to turn precise strong lensing measurements into accurate statements on the properties of the general galaxy population.