Result of the MCMC analysis for the parametrisation described in Eq. (3) with f_esc added as a fitting parameter. Here, all three sets of observational data were used as constraints. The contours show the 1-, 2-, and 3-σ confidence levels for log(ρ_z=8), f_esc and the derived parameter τ. Colours correspond to the different values of the magnitude limit used in the analysis: purple for M_lim =−10, blue for M_lim = −13 and orange for M_lim = −17. These results can be compared to reionisation histories displayed in Fig. 8a and b.