TEASING: a fast and accurate approximation for the low multipole likelihood of the cosmic microwave background temperature

We propose a novel approximation to the low-l joint likelihood of the angular spectrum C(l) of masked cosmic microwave background temperature maps which is both very accurate and very fast to evaluate. We show that, for a flat prior, the posterior distribution of each C(l) closely follows an inverse gamma distribution even with partial sky coverage and that the posterior correlation is weak enough that a copula approximation to the joint likelihood is quite accurate. In this paper, the quantities needed to build such a copula approximation (inverse gamma parameters at each angular frequency and a correlation matrix) are computed from an exploration of the posterior using adaptive importance sampling. The accuracy of the proposed approximation is assessed using statistical criteria as well as a mock cosmological parameter fit. When applied to the Wilkinson Microwave Anisotropy Probe 5 data set, the copula approximation yields cosmological parameter estimates at the same level of accuracy as the best current techniques.