  In studies of the connection between active galactic nuclei (AGN) and their
host galaxies there is widespread disagreement on some key aspects stemming
largely from a lack of understanding of the nature of the full underlying AGN
population. Recent attempts to probe this connection utilize both observations
and simulations to correct for a missed population, but presently are limited
by intrinsic biases and complicated models. We take a simple simulation for
galaxy evolution and add a new prescription for AGN activity to connect galaxy
growth to dark matter halo properties and AGN activity to star formation. We
explicitly model selection effects to produce an "observed" AGN population for
comparison with observations and empirically motivated models of the local
universe. This allows us to bypass the difficulties inherent in many models
which attempt to infer the AGN population by inverting selection effects. We
investigate the impact of selecting AGN based on thresholds in luminosity or
Eddington ratio on the "observed" AGN population. By limiting our model AGN
sample in luminosity, we are able to recreate the observed local AGN luminosity
function and specific star formation-stellar mass distribution, and show that
using an Eddington ratio threshold introduces less bias into the sample by
selecting the full range of growing black holes, despite the challenge of
selecting low mass black holes. We find that selecting AGN using these various
thresholds yield samples with different AGN host galaxy properties.
