We introduce a new CMB temperature likelihood approximation called the Gaussianized Blackwell-Rao ( GBR ) estimator .
This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians , and then approximate their joint transformed distribution by a multivariate Gaussian .
The method is exact for full-sky coverage and uniform noise , and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as WMAP and Planck .
The result is a stable , accurate and computationally very efficient CMB temperature likelihood representation that allows the user to exploit the unique error propagation capabilities of the Gibbs sampler to high \ell ’ s .
A single evaluation of this estimator between \ell = 2 and 200 takes \sim 0.2 CPU milliseconds , while for comparison , a singe pixel space likelihood evaluation between \ell = 2 and 30 for a map with \sim 2500 pixels requires \sim 20 seconds .
We apply this tool to the 5-year WMAP temperature data , and re-estimate the angular temperature power spectrum , C _ { \ell } , and likelihood , \mathcal { L } ( C _ { \ell } ) , for \ell \leq 200 , and derive new cosmological parameters for the standard six-parameter \Lambda CDM model .
Our spectrum is in excellent agreement with the official WMAP spectrum , but we find slight differences in the derived cosmological parameters .
Most importantly , the spectral index of scalar perturbations is n _ { \textrm { s } } = 0.973 \pm 0.014 , 1.9 \sigma away from unity and 0.6 \sigma higher than the official WMAP result , n _ { \textrm { s } } = 0.965 \pm 0.014 .
This suggests that an exact likelihood treatment is required to higher \ell ’ s than previously believed , reinforcing and extending our conclusions from the 3-year WMAP analysis .
In that case , we found that the sub-optimal likelihood approximation adopted between \ell = 12 and 30 by the WMAP team biased n _ { \textrm { s } } low by 0.4 \sigma , while here we find that the same approximation between \ell = 30 and 200 introduces a bias of 0.6 \sigma in n _ { \textrm { s } } .