Estimation of polarized power spectra by Gibbs sampling

Earlier papers introduced a method of accurately estimating the angular cosmic microwave background temperature power spectrum based on Gibbs sampling. Here we extend this framework to polarized data. All advantages of the Gibbs sampler still apply, and exact analysis of megapixel polarized data sets is thus feasible. These advantages may be even more important for polarization measurements than for temperature measurements. While approximate methods can alias power from the larger E-mode spectrum into the weaker B-mode spectrum, the Gibbs sampler ( or equivalently, exact likelihood evaluations) allows for a statistically optimal separation of these modes in terms of power spectra. To demonstrate the method, we analyze two simulated data sets: ( 1) a hypothetical future CMBPol mission, with the focus on B-mode estimation; and ( 2) a Planck-like mission, to highlight the computational feasibility of the method.