Results of the MCMC run for He abundance derivation (y⁺). Top panel: Corner plots and marginalized PDF for the parameters in our model. Compared to the framework adopted in Sect. 4.2, here we included corrections for the optical depth τ and for the collisional excitation of hydrogen and helium lines (expressed as a function of temperature and the residual fraction of neutral hydrogen ξ) as additional terms, as discussed in the text of Appendix B. Bottom panel: Comparison between modeled and observed He-to-Hβ line ratios included in our fit.