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Context. Strong lensing mass measurements require the knowledge of theredshift of both the lens and the source galaxy. Traditionally, spectroscopicredshifts are used for this purpose. Upcoming surveys, however, will lead tothe discovery of $\sim10^5$ strong lenses, and it will be very difficult toobtain spectroscopic redshifts for most of them. Photometric redshiftmeasurements will also be very challenging, due to the blending between lensand source light.  Aims. The goal of this work is to demonstrate how to carry out an inferenceof the structural properties of the galaxy population from the analysis of aset of strong lenses with no individual source redshift measurements, and toassess the loss in precision compared to the case in which spectroscopicredshifts are available.  Methods. Building on the formalism introduced in Paper III, I developed amethod that allows to carry out a statistical strong lensing inference whilemarginalising over the source redshifts. This method, which relies on theknowledge of the properties of the unlensed background source population and ofthe selection function of the survey, generalises an approach known asphotogeometric redshift, originally introduced by the Strong Lensing LegacySurvey collaboration. I tested the method on simulated data consisting of asubset of 137 strong lenses that is complete above a cut in observationalspace.  Results. The method recovers the properties of the galaxy population, with aprecision that is comparable to that attainable in the case in which individualsource redshifts are known.  Conclusions. The photogeometric redshift method is a viable approach for theanalysis of large sets of strong lenses, provided that the background sourcepopulation properties and lens selection function are well-known.

Statistical strong lensing. IV. Inferences with no individual source redshifts