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We consider the shape of the likelihood and posterior surfaces to be used when fitting cosmological models to cosmic microwave background (CMB) temperature and polarization power spectra measured from experiments. In the limit of an all-sky survey with Gaussian-distributed pixel noise we show that the true combined likelihood of the four CMB power spectra (TT, TE, EE and BB) has a Wishart distribution and we discuss the properties of this function. We compare various fits to the posterior surface of the Cl values, both in the case of a single auto-power spectrum and for a combination of temperature and polarization data. In the latter case, it is important that the fits can accurately match the Wishart distribution in the limit of near full-sky coverage. Simple extensions of auto-power spectrum fits to include polarization data generally fail to match correlations between the different power spectra in this limit. Directly fitting pixel values on large scales, as undertaken by the Wilkinson Microwave Anisotropy Probe team in their analysis of the 3-yr data, avoids the complications of characterizing the shape of the posterior for the power spectra. Finally, we demonstrate the importance of the likelihood distribution on analytic marginalization, and provide a formula for analytic marginalization over a calibration error given an all-sky survey. [ABSTRACT FROM AUTHOR]

We develop the pseudo- Cℓ method for reconstructing the cosmic microwave background (CMB) temperature and polarization auto- and cross-power spectra, and estimate the pseudo- Cℓ covariance matrix for a realistic experiment on the cut sky. We calculate the full coupling equations for all six possible CMB power spectra, relating the observed pseudo- Cℓ values to the underlying all-sky Cℓ values, and test the reconstruction on both full-sky and cut-sky simulated CMB data sets. In particular we consider the reconstruction of the Cℓ from upcoming ground-based polarization experiments covering areas of a few hundred deg2 and find that the method is fast, unbiased and performs well over a wide range of multipoles from to . We then calculate the full covariance matrix between the modes of the pseudo-temperature and polarization power spectra, assuming that the underlying CMB fields are Gaussian randomly distributed. The complexity of the covariance matrix prohibits its rapid calculation, required for parameter estimation. Hence we present an approximation for the covariance matrix in terms of convolutions of the underlying power spectra. The coupling matrices in these expressions can be estimated by fitting to numerical simulations, circumventing direct and slow calculation, and further, inaccurate analytic approximations. We show that these coupling matrices are mostly independent of cosmology, and that the full covariance matrix for all six pseudo- Cℓ power spectra can be quickly and accurately calculated for any given cosmological model using this method. We compare these semi-analytic covariance matrices against simulations and find good agreement, the accuracy of which depends mainly on survey area and the range of cosmological parameters considered. [ABSTRACT FROM AUTHOR]

Destriping methods for constructing maps of the cosmic microwave background (CMB) anisotropies have been investigated extensively in the literature. However, their error properties have been studied in less detail. Here we present an analysis of the effects of destriping errors on CMB power spectrum estimates forPlanck-like scanning strategies. Analytic formulae are derived for certain simple scanning geometries that can be rescaled to account for different detector noise. AssumingPlanck-like low-frequency noise, the noise power spectrum is accurately white at high multipoles. Destriping errors, though dominant at lower multipoles, are small in comparison to the cosmic variance. These results show that simple destriping map-making methods should be perfectly adequate for the analysis ofPlanckdata and support the arguments given in an earlier paper in favour of applying a fast hybrid power spectrum estimator to CMB data with realistic‘1/ f’ noise. [ABSTRACT FROM AUTHOR]