  The statistical distributions of active galactic nuclei (AGN), i.e. accreting
supermassive black holes (BHs), in mass, space and time, are controlled by a
series of key properties, namely the BH-galaxy scaling relations, Eddington
ratio distributions and fraction of active BHs (duty cycle). Shedding light on
these properties yields strong constraints on the AGN triggering mechanisms
whilst providing a clear baseline to create useful mock catalogues for the
planning of large galaxy surveys. We here delineate a robust methodology to
create mock AGN catalogs built on top of large N-body dark matter simulations
via state-of-the-art semi-empirical models. We show that by using as
independent tests the AGN clustering at fixed X-ray luminosity, galaxy stellar
mass and BH mass, along with the fraction of AGN in groups and clusters, it is
possible to significantly narrow down the choice in the relation between black
hole mass and host galaxy stellar mass, the duty cycle, and the average
Eddington ratio distribution, delivering well-suited constraints to guide
cosmological models for the co-evolution of BHs and galaxies. Avoiding such a
step-by-step methodology inevitably leads to strong degeneracies in the final
mock catalogs, severely limiting their usefulness in understanding AGN
evolution and in survey planning and testing.
