Radical Compression of Cosmic Microwave Background Data
Abstract
Powerful constraints on theories can already be inferred from existing CMB anisotropy data. But performing an exact analysis of available data is a complicated task and may become prohibitively so for upcoming experiments with >~10^{4} pixels. We present a method for approximating the likelihood that takes power spectrum constraints, e.g., ``bandpowers,'' as inputs. We identify a bias which results if one approximates the probability distribution of the bandpower errors as Gaussianas is the usual practice. This bias can be eliminated by using specific approximations to the nonGaussian form for the distribution specified by three parameters (the maximum likelihood or mode, curvature or variance, and a third quantity). We advocate the calculation of this third quantity by experimenters, to be presented along with the maximumlikelihood bandpower and variance. We use this nonGaussian form to estimate the power spectrum of the CMB in 11 bands from multipole moment l=2 (the quadrupole) to l=3000 from all published bandpower data. We investigate the robustness of our power spectrum estimate to changes in these approximations as well as to selective editing of the data.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 2000
 DOI:
 10.1086/308625
 arXiv:
 arXiv:astroph/9808264
 Bibcode:
 2000ApJ...533...19B
 Keywords:

 COSMOLOGY: COSMIC MICROWAVE BACKGROUND;
 COSMOLOGY: MISCELLANEOUS;
 METHODS: DATA ANALYSIS;
 METHODS: STATISTICAL;
 Astrophysics
 EPrint:
 27 Pages, 11 Figures, AASTeX