Statistical strong lensing. IV. Inferences with no individual source
  redshifts
  Context. Strong lensing mass measurements require the knowledge of the
redshift of both the lens and the source galaxy. Traditionally, spectroscopic
redshifts are used for this purpose. Upcoming surveys, however, will lead to
the discovery of $\sim10^5$ strong lenses, and it will be very difficult to
obtain spectroscopic redshifts for most of them. Photometric redshift
measurements will also be very challenging, due to the blending between lens
and source light.
  Aims. The goal of this work is to demonstrate how to carry out an inference
of the structural properties of the galaxy population from the analysis of a
set of strong lenses with no individual source redshift measurements, and to
assess the loss in precision compared to the case in which spectroscopic
redshifts are available.
  Methods. Building on the formalism introduced in Paper III, I developed a
method that allows to carry out a statistical strong lensing inference while
marginalising over the source redshifts. This method, which relies on the
knowledge of the properties of the unlensed background source population and of
the selection function of the survey, generalises an approach known as
photogeometric redshift, originally introduced by the Strong Lensing Legacy
Survey collaboration. I tested the method on simulated data consisting of a
subset of 137 strong lenses that is complete above a cut in observational
space.
  Results. The method recovers the properties of the galaxy population, with a
precision that is comparable to that attainable in the case in which individual
source redshifts are known.
  Conclusions. The photogeometric redshift method is a viable approach for the
analysis of large sets of strong lenses, provided that the background source
population properties and lens selection function are well-known.
