BASILISK: Bayesian Hierarchical Inference of the Galaxy-Halo Connection
  using Satellite Kinematics--I. Method and Validation
  We present a Bayesian hierarchical inference formalism (Basilisk) to
constrain the galaxy-halo connection using satellite kinematics. Unlike
traditional methods, Basilisk does not resort to stacking the kinematics of
satellite galaxies in bins of central luminosity, and does not make use of
summary statistics, such as satellite velocity dispersion. Rather, Basilisk
leaves the data in its raw form and computes the corresponding likelihood. In
addition, Basilisk can be applied to flux-limited, rather than volume-limited
samples, greatly enhancing the quantity and dynamic range of the data. And
finally, Basilisk is the only available method that simultaneously solves for
halo mass and orbital anisotropy of the satellite galaxies, while properly
accounting for scatter in the galaxy-halo connection. Basilisk uses the
conditional luminosity function to model halo occupation statistics, and
assumes that satellite galaxies are a relaxed tracer population of the host
halo's potential with kinematics that obey the spherical Jeans equation. We
test and validate Basilisk using mocks of varying complexity, and demonstrate
that it yields unbiased constraints on the galaxy-halo connection and at a
precision that rivals galaxy-galaxy lensing. In particular, Basilisk accurately
recovers the full PDF of the relation between halo mass and central galaxy
luminosity, and simultaneously constrains the orbital anisotropy of the
satellite galaxies. Basilisk's inference is not affected by potential velocity
bias of the central galaxies, or by slight errors in the inferred, radial
profile of satellite galaxies that arise as a consequence of interlopers and
sample impurity.
