Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data

Massimiliano Bonamente; Yang Chen; Dale Zimmerman

doi:10.3847/1538-4357/ad9b1e

Back

Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data

Journal article

Open access

Peer reviewed

Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data

Massimiliano Bonamente, Yang Chen and Dale Zimmerman

The Astrophysical journal, Vol.980(1), 139

02/10/2025

DOI: 10.3847/1538-4357/ad9b1e

Files and links (1)

url

https://doi.org/10.3847/1538-4357/ad9b1eView

Published (Version of record) Open Access

Abstract

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.

Regression

Astrostatistics

Maximum likelihood estimation

Measurement error model

Parametric hypothesis tests

Poisson distribution

Details

Title: Subtitle: Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data
Creators: Massimiliano Bonamente - University of Alabama in Huntsville
Yang Chen - University of Michigan Department of Statistics, Ann Arbor, MI 48109, USA
Dale Zimmerman - University of Iowa Department of Statistics and Actuarial Science, Iowa City, IA 52242, USA
Resource Type: Journal article
Publication Details: The Astrophysical journal, Vol.980(1), 139
Publisher: The American Astronomical Society
DOI: 10.3847/1538-4357/ad9b1e
ISSN: 0004-637X
eISSN: 1538-4357
Number of pages: 15
Language: English
Date published: 02/10/2025
Academic Unit: Biostatistics; Statistics and Actuarial Science
Record Identifier: 9984790973802771

Metrics

1 Record Views