Issue |
A&A
Volume 368, Number 1, March II 2001
|
|
---|---|---|
Page(s) | 1 - 14 | |
Section | Astrophysical processes | |
DOI | https://doi.org/10.1051/0004-6361:20000573 | |
Published online | 15 March 2001 |
Concerning parameter estimation using the cosmic microwave background
1
Observatoire Midi-Pyrénées, 14 Av. E. Belin, 31400 Toulouse, France Unité associée au CNRS ()
2
Observatoire de Strasbourg, Université Louis Pasteur, 11 rue de l'Université, 67000 Strasbourg, France Unité associée au CNRS ()
Corresponding author: J. G. Bartlett, bartlett@ast.obs-mip.fr
Received:
27
March
2000
Accepted:
19
December
2000
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, Cl) 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
© ESO, 2001
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