A Bayesian Hierarchical Approach to Galaxy-Galaxy Lensing
  We present a Bayesian hierarchical inference formalism to study the relation
between the properties of dark matter halos and those of their central galaxies
using weak gravitational lensing. Unlike traditional methods, this technique
does not resort to stacking the weak lensing signal in bins, and thus allows
for a more efficient use of the information content in the data. Our method is
particularly useful for constraining scaling relations between two or more
galaxy properties and dark matter halo mass, and can also be used to constrain
the intrinsic scatter in these scaling relations. We show that, if
observational scatter is not properly accounted for, the traditional stacking
method can produce biased results when exploring correlations between multiple
galaxy properties and halo mass. For example, this bias can affect studies of
the joint correlation between galaxy mass, halo mass, and galaxy size, or
galaxy color. In contrast, our method easily and efficiently handles the
intrinsic and observational scatter in multiple galaxy properties and halo
mass. We test our method on mocks with varying degrees of complexity. We find
that we can recover the mean halo mass and concentration, each with a $0.1$ dex
accuracy, and the intrinsic scatter in halo mass with a $0.05$ dex accuracy. In
its current version, our method will be most useful for studying the weak
lensing signal around central galaxies in groups and clusters, as well as
massive galaxies samples with $\log{M_*} > 11$, which have low satellite
fractions.
