An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix?
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913881959432192 |
|---|---|
| author | Keeley, Ryan Shafieloo, Arman L'Huillier, Benjamin |
| author_facet | Keeley, Ryan Shafieloo, Arman L'Huillier, Benjamin |
| contents | We investigate the statistics of the available Pantheon+ dataset. Noticing that the $χ^2$ value for the best-fit $Λ$CDM model to the real data is small, we quantify how significant its smallness is by calculating the distribution of $χ^2$ values for the best-fit $Λ$CDM model fit to mock Pantheon+-like datasets, using the provided covariance matrix. We further investigate the distribution of the residuals of the Pantheon+ dataset with respect to the best-fit $Λ$CDM model, and notice that they scatter less than would be expected from the covariance matrix but find no significant kurtosis. These results point to the conclusion that the Pantheon+ covariance matrix is over-estimated. One simple interpretation of these results is a $\sim$7\% overestimation of errors on SN distance moduli in Pantheon+ data. When the covariance matrix is reduced by subtracting an intrinsic scatter term from the diagonal terms of the covariance matrix, the best-fit $χ^2$ for the $Λ$CDM model achieves a normal value of 1580 and no deviation from $Λ$CDM is detected. We further quantify how consistent the $Λ$CDM model is with respect to the modified data with the subtracted covariance matrix using model-independent reconstruction techniques such as the iterative smoothing method. We find that the standard model is consistent with the data. There are a number of potential explanations for this smallness of the $χ^2$, such as a Malmquist bias at high redshift, or accounting for systematic uncertainties by adding them to the covariance matrix, thus approximating systematic uncertainties as statistical ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07917 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix? Keeley, Ryan Shafieloo, Arman L'Huillier, Benjamin Cosmology and Nongalactic Astrophysics We investigate the statistics of the available Pantheon+ dataset. Noticing that the $χ^2$ value for the best-fit $Λ$CDM model to the real data is small, we quantify how significant its smallness is by calculating the distribution of $χ^2$ values for the best-fit $Λ$CDM model fit to mock Pantheon+-like datasets, using the provided covariance matrix. We further investigate the distribution of the residuals of the Pantheon+ dataset with respect to the best-fit $Λ$CDM model, and notice that they scatter less than would be expected from the covariance matrix but find no significant kurtosis. These results point to the conclusion that the Pantheon+ covariance matrix is over-estimated. One simple interpretation of these results is a $\sim$7\% overestimation of errors on SN distance moduli in Pantheon+ data. When the covariance matrix is reduced by subtracting an intrinsic scatter term from the diagonal terms of the covariance matrix, the best-fit $χ^2$ for the $Λ$CDM model achieves a normal value of 1580 and no deviation from $Λ$CDM is detected. We further quantify how consistent the $Λ$CDM model is with respect to the modified data with the subtracted covariance matrix using model-independent reconstruction techniques such as the iterative smoothing method. We find that the standard model is consistent with the data. There are a number of potential explanations for this smallness of the $χ^2$, such as a Malmquist bias at high redshift, or accounting for systematic uncertainties by adding them to the covariance matrix, thus approximating systematic uncertainties as statistical ones. |
| title | An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix? |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2212.07917 |