An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix?
We investigate the statistics of the available Pantheon+ dataset. Noticing that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics&g...
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| author | Ryan E. Keeley Arman Shafieloo Benjamin L’Huillier |
| author_facet | Ryan E. Keeley Arman Shafieloo Benjamin L’Huillier |
| author_sort | Ryan E. Keeley |
| collection | DOAJ |
| description | We investigate the statistics of the available Pantheon+ dataset. Noticing that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> value for the best-fit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM model to the real data is small, we quantify how significant its smallness is by calculating the distribution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> values for the best-fit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>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 ∼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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM model achieves a normal value of 1580 and no deviation from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM is detected. We further quantify how consistent the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula>, 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 | Article |
| id | doaj-art-aee1cdf1844c4c0fbb2a65aa1c8c049b |
| institution | Kabale University |
| issn | 2218-1997 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj-art-aee1cdf1844c4c0fbb2a65aa1c8c049b2024-12-27T14:57:15ZengMDPI AGUniverse2218-19972024-11-01101243910.3390/universe10120439An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix?Ryan E. Keeley0Arman Shafieloo1Benjamin L’Huillier2Department of Physics, University of California Merced, 5200 North Lake Road, Merced, CA 95343, USAKorea Astronomy and Space Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon 34055, Republic of KoreaDepartment of Physics and Astronomy, Sejong University, Seoul 05006, Republic of KoreaWe investigate the statistics of the available Pantheon+ dataset. Noticing that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> value for the best-fit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM model to the real data is small, we quantify how significant its smallness is by calculating the distribution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> values for the best-fit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>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 ∼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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM model achieves a normal value of 1580 and no deviation from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM is detected. We further quantify how consistent the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula>, 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.https://www.mdpi.com/2218-1997/10/12/439cosmology: observationsdistance scalesupernovae methods: statistical |
| spellingShingle | Ryan E. Keeley Arman Shafieloo Benjamin L’Huillier An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix? Universe cosmology: observations distance scale supernovae methods: statistical |
| title | An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix? |
| title_full | An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix? |
| title_fullStr | An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix? |
| title_full_unstemmed | An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix? |
| title_short | An Analysis of Variance of the Pantheon+ Dataset: Systematics in the Covariance Matrix? |
| title_sort | analysis of variance of the pantheon dataset systematics in the covariance matrix |
| topic | cosmology: observations distance scale supernovae methods: statistical |
| url | https://www.mdpi.com/2218-1997/10/12/439 |
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