Comparison between inferred absolute magnitudes and true periods for validation sets A and B. The black solid and red dashed lines represent the projections of the PM_KZ relation of Eq. (13) and the relation inferred by our HM (adopting the median value of the posterior distribution of each coefficient), respectively, for a value of the true metallicity equal to the median of the values generated according to the text. The colour encodes the metallicity according to the scale on the right.