Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data
This paper presents a new statistical method that enables the use of systematic errors in the maximum-likelihood regression of integer-count Poisson data to a parametric model. The method is primarily aimed at the characterization of the goodness-of-fit statistic in the presence of the over-dispersi...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2025-01-01
|
| Series: | The Astrophysical Journal |
| Subjects: | |
| Online Access: | https://doi.org/10.3847/1538-4357/ad9b1e |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823860920909037568 |
|---|---|
| author | Massimiliano Bonamente Yang Chen Dale Zimmerman |
| author_facet | Massimiliano Bonamente Yang Chen Dale Zimmerman |
| author_sort | Massimiliano Bonamente |
| collection | DOAJ |
| description | This paper presents a new statistical method that enables the use of systematic errors in the maximum-likelihood regression of integer-count Poisson data to a parametric model. The method is primarily aimed at the characterization of the goodness-of-fit statistic in the presence of the over-dispersion that is induced by sources of systematic error, and is based on a quasi-maximum-likelihood method that retains the Poisson distribution of the data. We show that the Poisson deviance, which is the usual goodness-of-fit statistic and that is commonly referred to in astronomy as the Cash statistics, can be easily generalized in the presence of systematic errors, under rather general conditions. The method and the associated statistics are first developed theoretically, and then they are tested with the aid of numerical simulations and further illustrated with real-life data from astronomical observations. The statistical methods presented in this paper are intended as a simple general-purpose framework to include additional sources of uncertainty for the analysis of integer-count data in a variety of practical data analysis situations. |
| format | Article |
| id | doaj-art-c03884cc18c049af8fd60770c247c968 |
| 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-c03884cc18c049af8fd60770c247c9682025-02-10T08:55:47ZengIOP PublishingThe Astrophysical Journal1538-43572025-01-01980113910.3847/1538-4357/ad9b1eMaximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson DataMassimiliano Bonamente0https://orcid.org/0000-0002-8597-9742Yang Chen1https://orcid.org/0000-0002-9516-8134Dale Zimmerman2https://orcid.org/0000-0003-1212-4089Department of Physics and Astronomy, University of Alabama in Huntsville , Huntsville, AL 35899, USADepartment of Statistics, University of Michigan , Ann Arbor, MI 48109, USADepartment of Statistics and Actuarial Science, University of Iowa , Iowa City, IA 52242, USAThis paper presents a new statistical method that enables the use of systematic errors in the maximum-likelihood regression of integer-count Poisson data to a parametric model. The method is primarily aimed at the characterization of the goodness-of-fit statistic in the presence of the over-dispersion that is induced by sources of systematic error, and is based on a quasi-maximum-likelihood method that retains the Poisson distribution of the data. We show that the Poisson deviance, which is the usual goodness-of-fit statistic and that is commonly referred to in astronomy as the Cash statistics, can be easily generalized in the presence of systematic errors, under rather general conditions. The method and the associated statistics are first developed theoretically, and then they are tested with the aid of numerical simulations and further illustrated with real-life data from astronomical observations. The statistical methods presented in this paper are intended as a simple general-purpose framework to include additional sources of uncertainty for the analysis of integer-count data in a variety of practical data analysis situations.https://doi.org/10.3847/1538-4357/ad9b1eAstrostatisticsRegressionMaximum likelihood estimationPoisson distributionParametric hypothesis testsMeasurement error model |
| spellingShingle | Massimiliano Bonamente Yang Chen Dale Zimmerman Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data The Astrophysical Journal Astrostatistics Regression Maximum likelihood estimation Poisson distribution Parametric hypothesis tests Measurement error model |
| title | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data |
| title_full | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data |
| title_fullStr | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data |
| title_full_unstemmed | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data |
| title_short | Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data |
| title_sort | maximum likelihood regression with systematic errors for astronomy and the physical sciences i methodology and goodness of fit statistic of poisson data |
| topic | Astrostatistics Regression Maximum likelihood estimation Poisson distribution Parametric hypothesis tests Measurement error model |
| url | https://doi.org/10.3847/1538-4357/ad9b1e |
| work_keys_str_mv | AT massimilianobonamente maximumlikelihoodregressionwithsystematicerrorsforastronomyandthephysicalsciencesimethodologyandgoodnessoffitstatisticofpoissondata AT yangchen maximumlikelihoodregressionwithsystematicerrorsforastronomyandthephysicalsciencesimethodologyandgoodnessoffitstatisticofpoissondata AT dalezimmerman maximumlikelihoodregressionwithsystematicerrorsforastronomyandthephysicalsciencesimethodologyandgoodnessoffitstatisticofpoissondata |