We aim to constrain the evolution of AGN as a function of obscuration using an X-ray selected sample of $sim2000$ AGN from a multi-tiered survey including the CDFS, AEGIS-XD, COSMOS and XMM-XXL fields. The spectra of individual X-ray sources are anal
ysed using a Bayesian methodology with a physically realistic model to infer the posterior distribution of the hydrogen column density and intrinsic X-ray luminosity. We develop a novel non-parametric method which allows us to robustly infer the distribution of the AGN population in X-ray luminosity, redshift and obscuring column density, relying only on minimal smoothness assumptions. Our analysis properly incorporates uncertainties from low count spectra, photometric redshift measurements, association incompleteness and the limited sample size. We find that obscured AGN with $N_{H}>{rm 10^{22}, cm^{-2}}$ account for ${77}^{+4}_{-5}%$ of the number density and luminosity density of the accretion SMBH population with $L_{{rm X}}>10^{43}text{ erg/s}$, averaged over cosmic time. Compton-thick AGN account for approximately half the number and luminosity density of the obscured population, and ${38}^{+8}_{-7}%$ of the total. We also find evidence that the evolution is obscuration-dependent, with the strongest evolution around $N_{H}thickapprox10^{23}text{ cm}^{-2}$. We highlight this by measuring the obscured fraction in Compton-thin AGN, which increases towards $zsim3$, where it is $25%$ higher than the local value. In contrast the fraction of Compton-thick AGN is consistent with being constant at $approx35%$, independent of redshift and accretion luminosity. We discuss our findings in the context of existing models and conclude that the observed evolution is to first order a side-effect of anti-hierarchical growth.
