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We provide computationally convenient expressions for all marginaldistributions of the polarization CMB power spectrum distributionP(C_l|sigma_l), where C_l = {C_l^TT, C_l^TE, C_l^EE, C_l^BB} denotes the set ofensemble averaged polarization CMB power spectra, and sigma_l = {sigma_l^TT,sigma_l^TE, sigma_l^EE, sigma_l^BB} the set of the realization specificpolarization CMB power spectra. This distribution describes the CMB powerspectrum posterior for cosmic variance limited data. The expressions derivedhere are general, and may be useful in a wide range of applications. Twospecific applications are described in this paper. First, we employ the deriveddistributions within the CMB Gibbs sampling framework, and demonstrate a newconditional CMB power spectrum sampling algorithm that allows for differentbinning schemes for each power spectrum. This is useful because most CMBexperiments have very different signal-to-noise ratios for temperature andpolarization. Second, we provide new Blackwell-Rao estimators for each of themarginal polarization distributions, which are relevant to power spectrum andlikelihood estimation. Because these estimators represent marginals, they arenot affected by the exponential behaviour of the corresponding jointexpression, but converge quickly.

Marginal distributions for cosmic variance limited CMB polarization data