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An empirical forward-modeling framework is developed to interpret themultiwavelength properties of Active Galactic Nuclei (AGN) and provide insightsinto the overlap and incompleteness of samples selected at different parts ofthe electromagnetic spectrum. The core of the model are observationally derivedprobabilites on the occupation of galaxies by X-ray selected AGN. These areused to seed mock galaxies drawn from stellar-mass functions with accretionevents and then associate them with spectral energy distributions that describeboth the stellar and AGN emission components. This approach is used to studythe 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. Wethen infer the level of contamination of the WISE selection and show that thisis dominated by non-AGN at redshifts z < 0.5. These are star-forming galaxiesthat scatter into the WISE AGN selection wedge because of photometricuncertainties affecting their colours. Our baseline model shows a sharp drop inthe number density of heavily obscured AGN above the Compton thick limit in theWISE bands. The model also overpredicts by a factor of 1.5 the fraction ofX-ray associations in the WISE AGN selection box compared to observations. Thissuggests a population of X-ray faint sources that is not reproduced by themodel. This discrepancy is discussed in the context of either heavily obscuredor intrinsically X-ray weak AGN. Evidence is found in favour of the latter.

Forward modeling the multiwavelength properties of Active Galactic Nuclei: application to X-ray and WISE mid-infrared samples