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This work presents a Bayesian algorithm to fit the recombination andcollisionally excited line spectra of gas photoionized by clusters of youngstars. The current model consists in fourteen dimensions: two electrontemperatures, one electron density, the extinction coefficient, the opticaldepth on the $HeI$ recombination lines and nine ionic species. The results arein very good agreement with those previously published using the traditionalmethodology. The probabilistic programming library PyMC3 was chosen to explorethe parameter space via a NUTs sampler. These machine learning tools providedexcellent convergence quality and speed. The primordial helium abundancemeasured from a multivariable regression using oxygen, nitrogen and sulfur was$Y_{P,\,O-N-S}=0.243\pm0.005$ in agreement with a standard Big Bang scenario.

A Bayesian direct method implementation to fit emission line spectra: Application to the primordial He abundance determination