Application of the Iterated Weighted Least-Squares Fit to counting experiments

• Published in: arXiv.org 2019-06
• Main Authors: Dembinski, Hans, Schmelling, Michael, Waldi, Roland
• Format: Article
• Language: English
• Subjects: Data analysis; Least squares method
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1807.07911

Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the well known fact that commonly used variants of the least-squares fit applied to Poisson-distributed data produce biased estimates. The bias can be overcome with an iterated weighted least-squares method, which produces results identical to the maximum-likelihood method. For linear models, the iterated weighted least-squares method converges faster than the equivalent maximum-likelihood method, and does not require problem-specific starting values, which may be a practical advantage. The equivalence of both methods also holds for binomially distributed data. We further show that the unbinned maximum-likelihood method can be derived as a limiting case of the iterated least-squares fit when the bin width goes to zero, which demonstrates a deep connection between the two methods.