1306.5064 (L. Sun et al.)
L. Sun, Q. Wang, H. Zhan
The likelihood function is a crucial element of parameter estimation. In analyses of galaxy overdensities and weak lensing shear, one often approximates the likelihood of the power spectrum with a Gaussian distribution. The posterior probability derived from such a likelihood deviates considerably from the exact posterior on the largest scales probed by the sample. We show that various forms of Gaussian likelihoods can have a significant impact on the estimation of the primordial non-Gaussianity parameter $\fnl$ from the galaxy angular power spectrum. The Gaussian plus log-normal likelihood, which has been applied successfully in analyses of the cosmic microwave background, outperforms the Gaussian likelihoods. Nevertheless, even if the exact likelihood is used, the estimated parameters may be still biased. As such, the likelihoods and estimators need to be thoroughly examined for potential systematic errors.
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http://arxiv.org/abs/1306.5064
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