  The connection between galaxies and dark matter halos is often inferred from
data using probabilistic models, such as the Halo Occupation Distribution
(HOD). Conventional HOD formulations assume that only halo mass governs the
galaxy-halo connection. Violations of this assumption, known as galaxy assembly
bias, threaten the HOD program. We introduce decorated HODs, a new, flexible
class of models designed to account for assembly bias. Decorated HODs minimally
expand the parameter space and maximize the independence between traditional
and novel HOD parameters. We use decorated HODs to quantify the influence of
assembly bias on clustering and lensing statistics. For SDSS-like samples, the
impact of assembly bias on galaxy clustering can be as large as a factor of two
on r ~ 200 kpc scales and ~15% in the linear regime. Assembly bias can either
enhance or diminish clustering on large scales, but generally increases
clustering on scales r <~ 1 Mpc. We performed our calculations with Halotools,
an open-source, community-driven python package for studying the galaxy-halo
connection (http://halotools.readthedocs.org). We conclude by describing the
use of decorated HODs to treat assembly bias in otherwise conventional
likelihood analyses.
