Astronomy and Astrophysics – Astrophysics
Scientific paper
1999-03-02
Astron.Astrophys.Suppl.Ser.146:507-517,2000
Astronomy and Astrophysics
Astrophysics
Published version
Scientific paper
10.1051/aas:2000284
Band-power 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 band-power estimates must be employed. Even for Gaussian theories, this likelihood function is not itself Gaussian, for the simple reason that band-powers measure the {\em 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.
Bartlett James G.
Blanchard Alain
Dour M. Le
Douspis Marian
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