TEASING: a fast and accurate approximation for the low multipole likelihood of the Cosmic Microwave Background temperature

We explore the low-` likelihood of the angular spectrum C` of masked CMB temperature maps using an adaptive importance sampler. We find that, in spite of a partial sky coverage, the likelihood distribution of each C` closely follows an inverse gamma distribution. Our exploration is accurate enough to measure the inverse gamma parameters along with the correlation between multipoles. Those quantities are used to build an approximation of the joint posterior distribution of the low-` likelihood. The accuracy of the proposed approximation is established using both statistical criteria and a mock cosmological parameter fit. When applied to the WMAP5 data set, this approximation yields cosmological parameter estimates at the same level of accuracy as the best current techniques but with very significant speed gains.