Free access article

A&A 368, 1-14 (2001)
DOI: 10.1051/0004-6361:20000573

Concerning parameter estimation using the cosmic microwave background

M. Douspis¹, J. G. Bartlett¹, A. Blanchard^{1, 2} and M. Le Dour<sup>1

1</sup>  Observatoire Midi-Pyrénées, 14 Av. E. Belin, 31400 Toulouse, France Unité associée au CNRS (http://www.omp.obs-mip.fr/omp)
²  Observatoire de Strasbourg, Université Louis Pasteur, 11 rue de l'Université, 67000 Strasbourg, France Unité associée au CNRS (http://astro.u-strasbg.fr/Obs.html)

(Received 27 March 2000 / Accepted 19 December 2000)

Abstract
Most parameter constraints obtained from cosmic microwave background (CMB) anisotropy data are based on power estimates and rely on approximate likelihood functions; computational difficulties generally preclude an exact analysis based on pixel values. With the specific goal of testing this kind of approach, we have performed a complete (un-approximated) likelihood analysis combining the COBE, Saskatoon and MAX data sets. We examine in detail the ability of certain approximate techniques based on band-power estimates to recover the full likelihood constraints. The traditional -method does not always find the same best-fit model as the likelihood analysis (a bias), due mainly to the false assumption of Gaussian likelihoods that makes the method overly sensitive to data outliers. Although an improvement, other approaches employing non-Gaussian flat-band likelihoods do not always faithfully reproduce the complete likelihood constraints either; not even when using the exact flat-band likelihood curves. We trace this to the neglect of spectral information by simple flat band-power estimates. A straightforward extension incorporating a local effective slope (of the power spectrum, C_l) provides a faithful representation of the likelihood surfaces without significantly increasing computing cost. Finally, we also demonstrate that the best-fit model to this particular data set is a good fit, or that the observations are consistent with Gaussian sky fluctuations, according to our statistics.

Key words: cosmic microwave background -- cosmology: observations -- cosmology: theory

Offprint request: J. G. Bartlett, bartlett@ast.obs-mip.fr

© ESO 2001

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