Estimation of Polarized Power Spectra by Gibbs Sampling

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