Flux diagram of the process involving BGM Std, BGM FASt, and the CMD fitting technique. BGM Std is summarised in Sect. 2.1; we present BGM FASt in Sect. 2.2, where the meaning of the subscripts and superscripts i (indicating the i^th Galactic component, e.g. thin disc, thick disc, halo, and bar) and j (associated with the j^th interval of the reduced parameter space) are explained in detail; regarding the fitting process, see in Sect. 2.3 the different components of the process as well as an extended explanation of the subscripts and superscripts k (referred to k^th iteration within an ABC step), n (indicating the n^th bin of the CMD), and t (corresponding to the t^th ABC step). See Mor et al. (2018) for a detailed explanation of the equations in the central panel.