An MCMC determination of the primordial helium abundance

Spectroscopic observations of the chemical abundances in metal-poor H II regions provide an independent method for estimating the primordial helium abundance. H II regions are described by several physical parameters such as electron density, electron temperature, and reddening, in addition to y, the ratio of helium to hydrogen. It had been customary to estimate or determine self-consistently these parameters to calculate y. Frequentist analyses of the parameter space have been sown to be successful in these parameter determinations, and Markov Chain Monte Carlo (MCMC) techniques have proven to be very efficiency in sampling this parameters space. Nevertheless, accurate determination of the primordial helium abundance from observations of H II regions is constrained by both systematic and statistical uncertainties. In an attempt to better reduce the latter, and continue to better characterize the former, we apply MCMC methods to the large dataset recently compiled by Izotov, Thuan, & Stasinska (2007). To improve the reliability of the determination, a high quality dataset is needed. In pursuit of this, a variety of cuts are explored. The efficacy of the He I lambda 4026 emission line as a constraint on the solutions is first examined, revealing the introduction of systematic bias through its absence. As a clear measure of the quality of the physical solution, a chi(2) analysis proves instrumental in the selection of data compatible with the theoretical model. Nearly two-thirds of the observations fall outside a standard 95% confidence level cut, which highlights the care necessary in selecting systems and warrants further investigation into potential deficiencies of the model or data. In addition, the method also allows us to exclude systems for which parameter estimations are statistical outliers. As a result, the final selected dataset gains in reliability and exhibits improved consistency. Regression to zero metallicity yields Y-p = 0.2534 +/- 0.0083, in broad agreement with the WMAP result. The inclusion of more observations shows promise for further reducing the uncertainty, but more high quality spectra are required.