A Bayesian estimate of the primordial helium abundance

We introduce a new statistical method to estimate the primordial helium abundance Y_p from observed abundances in a sample of galaxies that 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 by an amount that may be as large as some maximum enrichment w. We compute the likelihood as a function of the two parameters Y_p and w using samples 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 using different techniques. We detect evidence for stellar enrichment (w≠0) even in the lowest metallicity subsamples, but in all samples the most conservative upper bound on Y_p occurs for w = 0. This yields 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 in the Y_p bound is not the model of stellar enrichment but possible common systematic biases in the estimate of Y in each individual H II region.