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Collett et al are attempting to use all the information in the galaxy catalog for the field around a strong lens (well, the stellar masses and photometric redshifts, at least) in order to reconstruct, using a halo model, the external convergence at the lens (like Wong, Keeton et al have been doing). In fact, their code (Pangloss) returns the PDF Pr(kappa|data), which can then be propagated into a time delay distance measurement. The model is pretty simple right now, and so everything has to be calibrated to N-body simulations (not dissimilarly from how the Suyu/COSMOGRAIL "H0LiCoW" group have been treating this problem in B1608 and RXJ1131). The goal for the future is to break free of this calibration by increasing the flexibility and physical realism of the mass model.

This is a very interesting paper indeed - Karpenka et al are trying to detect the weak lensing effect on SNe Ia, using a halo model for the line of sight structure. The interesting part is that they infer the parameters of the halo model simultaneously with the cosmological parameters, with the individual convergences playing a fleeting role before being quickly marginalised out. This is the Right Thing To Do - very computationally intensive, but feasible, as they show!

Although, to qualify that comment about computational intensity: they do not include scatter in their assumed scaling relation between halo mass and galaxy luminosity. To do that properly needs a whole slew of additional parameters, one for the true mass of every galaxy in sight...

It is similar to what I wrote a paper about in 2001. It is good to see this idea is being pursued. It has always seemed to me that you would do better with galaxy-galaxy lensing because of the much larger numbers.