2009/01/28 by K. Benabed, J. -F. Cardoso, J.-F. Cardoso +2
Physics and Astronomy · #Cosmology and Gravitation Theories #Radio Astronomy Observations and Technology #Scientific Research and Discoveries #astro-ph.CO
paper · pdf · doi:10.1111/j.1365-2966.2009.15202.x
10 pages, 10 figures, submitted to MNRAS
arxiv created 2009/01/28 · openalex publication_date 2009/10/15 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a novel approximation to the low-ℓ joint likelihood of the angular spectrum Cℓ 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 Cℓ 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.