Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. II. Hypothesis Testing of Nested Model Components for Poisson Data
A novel model of systematic errors for the regression of Poisson data is applied to hypothesis testing of nested model components with the introduction of a generalization of the Δ C statistic that applies in the presence of systematic errors. This paper shows that the null-hypothesis parent distrib...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2025-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/ad9b1f |
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| author | Massimiliano Bonamente Dale Zimmerman Yang Chen |
| author_facet | Massimiliano Bonamente Dale Zimmerman Yang Chen |
| author_sort | Massimiliano Bonamente |
| collection | DOAJ |
| description | A novel model of systematic errors for the regression of Poisson data is applied to hypothesis testing of nested model components with the introduction of a generalization of the Δ C statistic that applies in the presence of systematic errors. This paper shows that the null-hypothesis parent distribution of this Δ C _sys statistic can be obtained either through a simple numerical procedure, or in a closed form by making certain simplifying assumptions. It is found that the effects of systematic errors on the test statistic can be significant, and therefore the inclusion of sources of systematic errors is crucial for the assessment of the significance of the nested model component in practical applications. The methods proposed in this paper provide a simple and accurate means of including systematic errors for hypothesis testing of nested model components in a variety of applications. |
| format | Article |
| id | doaj-art-b2a543fc746d4707a25f4c97c59ea00f |
| institution | Kabale University |
| issn | 1538-4357 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal |
| spelling | doaj-art-b2a543fc746d4707a25f4c97c59ea00f2025-02-10T08:56:43ZengIOP PublishingThe Astrophysical Journal1538-43572025-01-01980114010.3847/1538-4357/ad9b1fMaximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. II. Hypothesis Testing of Nested Model Components for Poisson DataMassimiliano Bonamente0https://orcid.org/0000-0002-8597-9742Dale Zimmerman1https://orcid.org/0000-0003-1212-4089Yang Chen2https://orcid.org/0000-0002-9516-8134Department of Physics and Astronomy, University of Alabama in Huntsville , Huntsville, AL 35899, USADepartment of Statistics and Actuarial Science, University of Iowa , Iowa City, IA 52242, USADepartment of Statistics, University of Michigan , Ann Arbor, MI 48109, USAA novel model of systematic errors for the regression of Poisson data is applied to hypothesis testing of nested model components with the introduction of a generalization of the Δ C statistic that applies in the presence of systematic errors. This paper shows that the null-hypothesis parent distribution of this Δ C _sys statistic can be obtained either through a simple numerical procedure, or in a closed form by making certain simplifying assumptions. It is found that the effects of systematic errors on the test statistic can be significant, and therefore the inclusion of sources of systematic errors is crucial for the assessment of the significance of the nested model component in practical applications. The methods proposed in this paper provide a simple and accurate means of including systematic errors for hypothesis testing of nested model components in a variety of applications.https://doi.org/10.3847/1538-4357/ad9b1fAstrostatistics |
| spellingShingle | Massimiliano Bonamente Dale Zimmerman Yang Chen Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. II. Hypothesis Testing of Nested Model Components for Poisson Data The Astrophysical Journal Astrostatistics |
| title | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. II. Hypothesis Testing of Nested Model Components for Poisson Data |
| title_full | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. II. Hypothesis Testing of Nested Model Components for Poisson Data |
| title_fullStr | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. II. Hypothesis Testing of Nested Model Components for Poisson Data |
| title_full_unstemmed | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. II. Hypothesis Testing of Nested Model Components for Poisson Data |
| title_short | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. II. Hypothesis Testing of Nested Model Components for Poisson Data |
| title_sort | maximum likelihood regression with systematic errors for astronomy and the physical sciences ii hypothesis testing of nested model components for poisson data |
| topic | Astrostatistics |
| url | https://doi.org/10.3847/1538-4357/ad9b1f |
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