Astronomy and Astrophysics – Astrophysics
Scientific paper
1997-08-22
Phys.Rev. D57 (1998) 2117-2137
Astronomy and Astrophysics
Astrophysics
23 Pages, 16 Figures. Final published version
Scientific paper
10.1103/PhysRevD.57.2117
We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and the other is an estimator that is a minimum-variance weighted quadratic function of the data. Applied iteratively, the quadratic estimator is not distinct from likelihood analysis, but is rather a rapid means of finding the power spectrum that maximizes the likelihood function. Our results bear this out: direct evaluation and quadratic estimation converge to the same C_ls. The quadratic estimator can also be used to directly determine cosmological parameters and their uncertainties. While the two methods both require O(N^3) operations, the quadratic is much faster, and both are applicable to datasets with arbitrary chopping patterns and noise correlations. We also discuss approximations that may reduce it to O(N^2) thus making it practical for forthcoming megapixel datasets.
Bond Richard J.
Jaffe Andrew H.
Knox Lloyd
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