Multiparameter estimation with the Pseudo-Cl method

Within the standard model of cosmology there are about 10 parameters which characterise the properties of our Universe. It is one of the key goals of future CMB experiments such as MAP and Planck to determine these cosmological parameters to high precision. This undertaking faces the challenge that realistic CMB data is necessarily incomplete and noisy. The Galaxy obscures roughly a third of the sky and because of the smallness of the anisotropy signal, detector noise is not negligible in the analysis. This leads to the computational challenge which was expertly described at this meeting in the contribution by Borrill. In this talk we apply the pseudo-Cl formalism 2 to this problem and show that it can be used to develop an approximate form of the likelihood which has several useful properties: it is Gaussian and hence easy to apply; it does not suffer from the usual disadvantages of Gaussian approximations such as obtaining negative estimates of positive definite quantities; it is computationally efficient with memory usage of Npix and number of operations scaling as