Distribution of L′_CO/M_* (observational proxy of the gas fraction f_gas) for AGN host galaxies (red) and non-active galaxies of the control sample (blue). Upper panel: filled histograms show the total distributions, obtained by joining the sampled posterior distribution of each target for both samples. The blue squares indicate the measure of each non-active galaxy (98 targets), red circles that of each AGN (40 targets). The blue and red triangles indicate upper limits if pointing leftward and lower limits if pointing rightward for the gas fraction of non-active galaxies and AGN, respectively. Lower panel: violin plots show the sampled posterior distribution of the mean of the hierarchical Gaussian prior used in our Bayesian analysis. The diamonds show the measured mean value μ_fgas of AGN (red) and non-active galaxies (blue). The top axis is derived by assuming α_CO = 3.6 M_⊙/(K km s⁻¹ pc²) and serves for illustration purposes only since we only consider L′_CO in our quantitative analysis (see Sect. 5.2).