2009/02/28 by Samira Hamimeche, Antony Lewis · 34 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Cosmic microwave background #Cosmology and Gravitation Theories #Covariance #Estimator #Mathematics #Physics #Quantum mechanics #Radio Astronomy Observations and Technology #Spectral density #Statistical physics #Statistics #astro-ph.CO
paper · pdf · doi:10.1103/physrevd.79.083012
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 79(8) (American Physical Society) · 15 pages, 11 figures; updated to match version accepted by PRD
arxiv created 2009/04/08 · openalex publication_date 2009/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Fast robust methods for calculating likelihoods from cosmic microwave background observations on small scales generally rely on approximations based on a set of power spectrum estimators and their covariances. We investigate the optimality of these approximations, how accurate the covariance needs to be, and how to estimate the covariance from simulations. For a simple case with azimuthal symmetry we compare optimality of hybrid pseudo-Cl cosmic microwave background power spectrum estimators with the exact result, indicating that the loss of information is not negligible, but neither is it enough to have a large effect on standard parameter constraints. We then discuss the number of samples required to estimate the covariance from simulations, with and without a good analytic approximation, and assess the use of shrinkage estimators. Finally we discuss how to combine an approximate high-l likelihood with a more exact low-l harmonic-space likelihood as a practical method for accurate likelihood calculation on all scales.