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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 perform a blind multicomponent analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP) 1-yr foreground-cleaned maps using Spectral Matching Independent Component Analysis ( smica). We provide a new estimate of the cosmic microwave background (CMB) power spectrum as well as the amplitude of the CMB anisotropies across frequency channels. We show that the CMB anisotropies are compatible with temperature fluctuations as expected from the standard paradigm. The analysis also allows us to identify and separate a weak residual Galactic emission, present significantly in the Q band outside of the Kp2 1 mask limits, and mainly concentrated at low Galactic latitudes. We produce a map of this residual component by Wiener filtering using estimated parameters. The level of contamination of CMB data by this component is compatible with the WMAP-team estimation of foreground residual contamination. In addition, the multicomponent analysis allows us to estimate jointly the power spectrum of unresolved point-source emission. [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]

We presentXspect, a method to obtain estimates of the angular power spectrum of the cosmic microwave background (CMB) temperature anisotropies including analytical error bars developed for theArcheopsexperiment. Cross-power spectra are computed from a set of maps and each of them is in itself an unbiased estimate of the power spectrum as long as the detector noises are uncorrelated. Then, the cross-power spectra are combined into a final temperature power spectrum with error bars analytically derived from the cross-correlation matrix.This method presents three main useful properties: (1) no estimation of the noise power spectrum is needed; (2) complex weighting schemes including sky covering and map noise properties can be easily taken into account, and corrected for, for each input map; and (3) error bars are quickly computed analytically from the data themselves with no Monte Carlo simulations involved.Xspectalso permits the study of common fluctuations between maps from different sky surveys such as CMB, Sunyaev–Zel'dovich effect or mass fluctuations from weak lensing observations. [ABSTRACT FROM AUTHOR]