  We introduce a new statistical method to estimate the primordial helium
abundance, Y_p from observed abundances in a sample of galaxies which have
experienced stellar helium enrichment. Rather than using linear regression on
metal abundance we construct a likelihood function using a Bayesian prior,
where the key assumption is that the true helium abundance must always exceed
the primordial value. Using a sample of measurements compiled from the
literature we find estimates of Y_p between 0.221 and 0.236, depending on the
specific subsample and prior adopted, consistent with previous estimates either
from a linear extrapolation of the helium abundance with respect to
metallicity, or from the helium abundance of the lowest metallicity HII region,
I Zw 18. We also find an upper limit which is insensitive to the specific
subsample or prior, and estimate a model-independent bound Y_p < 0.243 at 95%
confidence, favoring a low cosmic baryon density and a high primordial
deuterium abundance. The main uncertainty is not the model of stellar
enrichment but possible common systematic biases in the estimate of Y in each
individual HII region.
