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We study different variants of the Gibbs sampler algorithm from theperspective of their applicability to the estimation of power spectra of thecosmic microwave background (CMB) anisotropies. These include approachesstudied earlier in the CMB literature as well as new ones which are proposed inthis work. We demonstrate all these variants on full and cut sky simulationsand compare their performance, assessing both their computational andstatistical efficiency. For this we employ a consistent comparison metric, aneffective sample size (ESS) per second, commonly used in this context in thestatistical literature. We show that one of the proposed approaches, referredto as Centered overrelax, which capitalizes on additional, auxiliary variablesto minimize computational time needed per sample, and uses overrelaxation todecorrelate subsequent samples, performs better than the standard Gibbs samplerby a factor between one and two orders of magnitude in the nearly full-sky,satellite-like cases. It therefore potentially provides an interestingalternative to the currently favored approaches.

Improved Gibbs samplers for Cosmic Microwave Background power spectrum estimation