emission from stellar X-ray binaries). In addition, hard X-rays ($\gtrsim2$ keV) are able to penetrate moderate column densities of obscuring material at these redshifts (equivalent hydrogen column densities $\mathrm{N_H}\lesssim10^{23}$ cm$^{-2}$). Thus, hard X-ray selection provides a reasonably accurate probe of the AGN luminosity and should track the bulk of the AGN population. The effect of the (highly variable) flux limits of the X-ray observations over the three PRIMUS fields was fully accounted for by the @Aird12 work. We note that hard X-ray selection will fail to identify the most heavily obscured, Compton-thick sources. It remains unclear how large a fraction of the population is hidden by such high levels of obscuration. However, our measurements of the overall X-ray luminosity function (which we compare with our model predictions, see Section \[sec:xlf\] below) also use hard X-ray selection to identify AGN and thus are subject to the same incompleteness.

@Aird12 showed that the probability of a galaxy with a given stellar mass and redshift hosting an AGN could be described by a single power law distribution of specific accretion rates. This distribution is independent of stellar mass and evolves strongly with redshift, $$p(\lambda {\;|\;}{\mathcal{M}_*},z) {\;\mathrm{d}}\log\lambda = A \lambda^\gamma \left(\frac{1+z}{1+z_0}\right)^\beta {\;\mathrm{d}}\log\lambda
\label{eq:pldist}$$ where 