Maximum-likelihood regression with systematic errors for astronomy and the physical sciences: I. Methodology and goodness-of-fit statistic of Poisson data

Max Bonamente; Yang Chen; Dale Zimmerman

doi:10.48550/arxiv.2407.12132

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Maximum-likelihood regression with systematic errors for astronomy and the physical sciences: I. Methodology and goodness-of-fit statistic of Poisson data

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Maximum-likelihood regression with systematic errors for astronomy and the physical sciences: I. Methodology and goodness-of-fit statistic of Poisson data

Max Bonamente, Yang Chen and Dale Zimmerman

arXiv.org

Cornell University

07/16/2024

DOI: 10.48550/arxiv.2407.12132

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

The 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.

Physics - Instrumentation and Methods for Astrophysics

Statistics - Methodology

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: Max Bonamente - University of Alabama in Huntsville
Yang Chen - University of Michigan
Dale Zimmerman - University of Iowa
Resource Type: Preprint
Publication Details: arXiv.org
DOI: 10.48550/arxiv.2407.12132
eISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 07/16/2024
Academic Unit: Statistics and Actuarial Science; Biostatistics
Record Identifier: 9984658253402771

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