Accounting for population-level systematic effects using a hierarchical strategy

One of the largest sources of systematics in time-delay cosmography arises from Mass Sheet Transformation (MST). The degeneracy associated with this transformation is often broken by an assumed profile shape, such as a power-law. A hierarchical strategy has been developed which constrains the global profile shape on a population level, constrained collectively by the kinematics measurements of the lenses. This framework allows one to include non-time-delay lenses to provide constraints to the global profile, improving the H₀ constraints. This work tests the hierarchical framework using analytical profiles, and additionally tests the capacity to combine two populations which come from the same profiles but probe different radii due to a change in source redshift. We find that the hierarchical framework is able to compensate for this effect, and the addition of non-time-delay lenses improves the H₀ constraint, even though these lenses have different Einstein radii than their time-delay counterparts.