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

This work presents a Bayesian algorithm to fit the recombination and collisionally excited line spectra of gas photoionized by clusters of young stars. The current model consists in fourteen dimensions: two electron temperatures, one electron density, the extinction coefficient, the optical depth on the $HeI$ recombination lines and nine ionic species. The results are in very good agreement with those previously published using the traditional methodology. The probabilistic programming library PyMC3 was chosen to explore the parameter space via a NUTs sampler. These machine learning tools provided excellent convergence quality and speed. The primordial helium abundance measured 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.