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Title: LIKELIHOOD OF THE POWER SPECTRUM IN COSMOLOGICAL PARAMETER ESTIMATION

Abstract

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 any survey, where the central limit theorem does not apply. We show that various forms of Gaussian likelihoods can have a significant impact on the estimation of the primordial non-Gaussianity parameter f{sub NL} 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 of the power spectrum is used, the estimated parameters may be still biased. As such, the likelihoods and estimators need to be thoroughly examined for potential systematic errors.

Authors:
; ;  [1]
  1. Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012 (China)
Publication Date:
OSTI Identifier:
22270644
Resource Type:
Journal Article
Journal Name:
Astrophysical Journal
Additional Journal Information:
Journal Volume: 777; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; ASTRONOMY; ASTROPHYSICS; COSMOLOGY; ENERGY SPECTRA; GALAXIES; GAUSS FUNCTION; POTENTIALS; RELICT RADIATION; SHEAR

Citation Formats

Sun, Lei, Wang, Qiao, and Zhan, Hu. LIKELIHOOD OF THE POWER SPECTRUM IN COSMOLOGICAL PARAMETER ESTIMATION. United States: N. p., 2013. Web. doi:10.1088/0004-637X/777/1/75.
Sun, Lei, Wang, Qiao, & Zhan, Hu. LIKELIHOOD OF THE POWER SPECTRUM IN COSMOLOGICAL PARAMETER ESTIMATION. United States. https://doi.org/10.1088/0004-637X/777/1/75
Sun, Lei, Wang, Qiao, and Zhan, Hu. 2013. "LIKELIHOOD OF THE POWER SPECTRUM IN COSMOLOGICAL PARAMETER ESTIMATION". United States. https://doi.org/10.1088/0004-637X/777/1/75.
@article{osti_22270644,
title = {LIKELIHOOD OF THE POWER SPECTRUM IN COSMOLOGICAL PARAMETER ESTIMATION},
author = {Sun, Lei and Wang, Qiao and Zhan, Hu},
abstractNote = {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 any survey, where the central limit theorem does not apply. We show that various forms of Gaussian likelihoods can have a significant impact on the estimation of the primordial non-Gaussianity parameter f{sub NL} 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 of the power spectrum is used, the estimated parameters may be still biased. As such, the likelihoods and estimators need to be thoroughly examined for potential systematic errors.},
doi = {10.1088/0004-637X/777/1/75},
url = {https://www.osti.gov/biblio/22270644}, journal = {Astrophysical Journal},
issn = {0004-637X},
number = 1,
volume = 777,
place = {United States},
year = {Fri Nov 01 00:00:00 EDT 2013},
month = {Fri Nov 01 00:00:00 EDT 2013}
}