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Astron. Astrophys. Suppl. Ser. 146, 507517
An approximation to the likelihood function for bandpower estimates of CMB anisotropies
J.G. Bartlett^{1} 
M. Douspis^{1} 
A. Blanchard^{1,2}

M. Le Dour^{1}
Send offprint request: J.G. Bartlett, email: barlett@ast.obsmip.fr
1  Observatoire MidiPyrénées, Unité associée au CNRS, 14 avenue E. Belin, 31400 Toulouse, France
http://www.omp.obsmip.fr/omp
2 
Observatoire de Strasbourg, Université Louis Pasteur, Unité associée au CNRS, 11 rue de l'Université, 67000
Strasbourg, France
http://astro.ustrasbg.fr/Obs.html
Received March 5, 1999; accepted August 18, 2000
Abstract:
Bandpower estimates of cosmic microwave background
fluctuations are now routinely used to place constraints on
cosmological parameters. For this to be done in a
rigorous fashion, the full likelihood function of
bandpower estimates must be employed. Even for Gaussian
theories, this likelihood function is not
itself Gaussian, for the simple reason that bandpowers
measure the
variance of the random sky
fluctuations. In the context of Gaussian sky
fluctuations, we use an ideal situation to motivate
a general form for the full likelihood function from a given
experiment. This form contains only two free parameters, which
can be determined if the 68% and 95% confidence
intervals of the true likelihood function are known.
The ansatz works remarkably well when compared to the
complete likelihood function for a number of experiments.
For application of this kind of approach, we suggest
that in the future both 68% and 95%
(and perhaps also the 99.7%) confidence intervals be
given when reporting experimental results.
Key words: cosmic microwave background  Cosmology: observations  maths: data analysis  methods: statistical
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