Assessing Colour-dependent Occupation Statistics Inferred from Galaxy
  Group Catalogues
  We investigate the ability of current implementations of galaxy group finders
to recover colour-dependent halo occupation statistics. To test the fidelity of
group catalogue inferred statistics, we run three different group finders used
in the literature over a mock that includes galaxy colours in a realistic
manner. Overall, the resulting mock group catalogues are remarkably similar,
and most colour-dependent statistics are recovered with reasonable accuracy.
However, it is also clear that certain systematic errors arise as a consequence
of correlated errors in group membership determination, central/satellite
designation, and halo mass assignment. We introduce a new statistic, the halo
transition probability (HTP), which captures the combined impact of all these
errors. As a rule of thumb, errors tend to equalize the properties of distinct
galaxy populations (i.e. red vs. blue galaxies or centrals vs. satellites), and
to result in inferred occupation statistics that are more accurate for red
galaxies than for blue galaxies. A statistic that is particularly poorly
recovered from the group catalogues is the red fraction of central galaxies as
function of halo mass. Group finders do a good job in recovering galactic
conformity, but also have a tendency to introduce weak conformity when none is
present. We conclude that proper inference of colour-dependent statistics from
group catalogues is best achieved using forward modelling (i.e., running group
finders over mock data), or by implementing a correction scheme based on the
HTP, as long as the latter is not too strongly model-dependent.
