The effect on cosmological parameter estimation of a parameter dependent covariance matrix
Cosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the parameter dependence of this covariance matrix, focusing on the pa...
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| Format: | Article |
| Language: | English |
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Maynooth Academic Publishing
2019-03-01
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| Series: | The Open Journal of Astrophysics |
| Subjects: | |
| Online Access: | https://astro.theoj.org/article/7716-the-effect-on-cosmological-parameter-estimation-of-a-parameter-dependent-covariance-matrix |
| _version_ | 1819044347066187776 |
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| author | Darsh Kodwani Pedro G. Ferreira David Alonso |
| author_facet | Darsh Kodwani Pedro G. Ferreira David Alonso |
| author_sort | Darsh Kodwani |
| collection | DOAJ |
| description | Cosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the parameter dependence of this covariance matrix, focusing on the particular case of joint weak-lensing and galaxy clustering analyses. Using a Fisher matrix formalism (calibrated against exact likelihood evaluation in particular simple cases), we quantify the effect of using a parameter dependent covariance matrix on both the bias and variance of the parameters. We confirm that the approximation of a parameter-independent covariance matrix is exceptionally good in all realistic scenarios. The information content in the covariance matrix (in comparison with the two point functions themselves) does not change with the fractional sky coverage. Therefore the increase in information due to the parameter dependent covariance matrix becomes negligible as the number of modes increases. Even for surveys covering less than 1% of the sky, this effect only causes a bias of up to of order 10% of the statistical uncertainties, with a misestimation of the parameter uncertainties at the same level or lower. The effect will only be smaller with future large-area surveys. Thus for most analyses the effect of a parameter-dependent covariance matrix can be ignored both in terms of the accuracy and precision of the recovered cosmological constraints. |
| first_indexed | 2024-12-21T10:11:14Z |
| format | Article |
| id | doaj.art-297990436ffe44f48300a45a28116f9f |
| institution | Directory Open Access Journal |
| issn | 2565-6120 |
| language | English |
| last_indexed | 2024-12-21T10:11:14Z |
| publishDate | 2019-03-01 |
| publisher | Maynooth Academic Publishing |
| record_format | Article |
| series | The Open Journal of Astrophysics |
| spelling | doaj.art-297990436ffe44f48300a45a28116f9f2022-12-21T19:07:42ZengMaynooth Academic PublishingThe Open Journal of Astrophysics2565-61202019-03-01210.21105/astro.1811.11584The effect on cosmological parameter estimation of a parameter dependent covariance matrixDarsh Kodwani0Pedro G. Ferreira1David Alonso2University of OxfordUniversity of OxfordUniversity of OxfordCosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the parameter dependence of this covariance matrix, focusing on the particular case of joint weak-lensing and galaxy clustering analyses. Using a Fisher matrix formalism (calibrated against exact likelihood evaluation in particular simple cases), we quantify the effect of using a parameter dependent covariance matrix on both the bias and variance of the parameters. We confirm that the approximation of a parameter-independent covariance matrix is exceptionally good in all realistic scenarios. The information content in the covariance matrix (in comparison with the two point functions themselves) does not change with the fractional sky coverage. Therefore the increase in information due to the parameter dependent covariance matrix becomes negligible as the number of modes increases. Even for surveys covering less than 1% of the sky, this effect only causes a bias of up to of order 10% of the statistical uncertainties, with a misestimation of the parameter uncertainties at the same level or lower. The effect will only be smaller with future large-area surveys. Thus for most analyses the effect of a parameter-dependent covariance matrix can be ignored both in terms of the accuracy and precision of the recovered cosmological constraints.https://astro.theoj.org/article/7716-the-effect-on-cosmological-parameter-estimation-of-a-parameter-dependent-covariance-matrixgalaxy redshift surveyslarge-scale structure of the universecosmologystatisticscosmological parameters |
| spellingShingle | Darsh Kodwani Pedro G. Ferreira David Alonso The effect on cosmological parameter estimation of a parameter dependent covariance matrix The Open Journal of Astrophysics galaxy redshift surveys large-scale structure of the universe cosmology statistics cosmological parameters |
| title | The effect on cosmological parameter estimation of a parameter dependent covariance matrix |
| title_full | The effect on cosmological parameter estimation of a parameter dependent covariance matrix |
| title_fullStr | The effect on cosmological parameter estimation of a parameter dependent covariance matrix |
| title_full_unstemmed | The effect on cosmological parameter estimation of a parameter dependent covariance matrix |
| title_short | The effect on cosmological parameter estimation of a parameter dependent covariance matrix |
| title_sort | effect on cosmological parameter estimation of a parameter dependent covariance matrix |
| topic | galaxy redshift surveys large-scale structure of the universe cosmology statistics cosmological parameters |
| url | https://astro.theoj.org/article/7716-the-effect-on-cosmological-parameter-estimation-of-a-parameter-dependent-covariance-matrix |
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