  The dark ages of the Universe end with the formation of the first generation
of stars residing in primeval galaxies. These objects were the first to produce
ultraviolet ionizing photons in a period when the cosmic gas changed from a
neutral state to an ionized one, known as Epoch of Reionization (EoR). A
pivotal aspect to comprehend the EoR is to probe the intertwined relationship
between the fraction of ionizing photons capable to escape dark haloes, also
known as the escape fraction ($f_{esc}$), and the physical properties of the
galaxy. This work develops a sound statistical model suitable to account for
such non-linear relationships and the non-Gaussian nature of $f_{esc}$. This
model simultaneously estimates the probability that a given primordial galaxy
starts the ionizing photon production and estimates the mean level of the
$f_{esc}$ once it is triggered. The model was employed in the First Billion
Years simulation suite, from which we show that the baryonic fraction and the
rate of ionizing photons appear to have a larger impact on $f_{esc}$ than
previously thought. A naive univariate analysis of the same problem would
suggest smaller effects for these properties and a much larger impact for the
specific star formation rate, which is lessened after accounting for other
galaxy properties and non-linearities in the statistical model.
