  An empirical forward-modeling framework is developed to interpret the
multiwavelength properties of Active Galactic Nuclei (AGN) and provide insights
into the overlap and incompleteness of samples selected at different parts of
the electromagnetic spectrum. The core of the model are observationally derived
probabilites on the occupation of galaxies by X-ray selected AGN. These are
used to seed mock galaxies drawn from stellar-mass functions with accretion
events and then associate them with spectral energy distributions that describe
both the stellar and AGN emission components. This approach is used to study
the complementarity between X-ray and WISE mid-infrared AGN selection methods.
We first show that the basic observational properties of the X-ray and WISE AGN
(magnitude, redshift distributions) are adequately reproduced by the model. We
then infer the level of contamination of the WISE selection and show that this
is dominated by non-AGN at redshifts z < 0.5. These are star-forming galaxies
that scatter into the WISE AGN selection wedge because of photometric
uncertainties affecting their colours. Our baseline model shows a sharp drop in
the number density of heavily obscured AGN above the Compton thick limit in the
WISE bands. The model also overpredicts by a factor of 1.5 the fraction of
X-ray associations in the WISE AGN selection box compared to observations. This
suggests a population of X-ray faint sources that is not reproduced by the
model. This discrepancy is discussed in the context of either heavily obscured
or intrinsically X-ray weak AGN. Evidence is found in favour of the latter.
