Parent distributions of N_H, Γ, and L_X (from left to right). Top row: parent distributions of the main parameters (dashed blue) compared to those after selection (black). The parent distribution of L_X is not shown because it was computed based on other spectral parameters and then selected by the XLF (see Sect. 4.1). Middle and bottom rows: average bias and dispersion with 1σ uncertainties (blue area) of the Bayesian method with respect to the true values. In each bin we randomly drew one value from each PDF and then computed the bias and dispersion, and this procedure was repeated for 1000 times to obtain the average bias and dispersion, together with their uncertainties.